Primes - allocate descendants to their ancestors
You are encouraged to solve this task according to the task description, using any language you may know.
The concept, is to add the decomposition into prime factors of a number to get its 'ancestors'.
The objective is to demonstrate that the choice of the algorithm can be crucial in term of performance.
This solution could be compared to the solution that would use the decomposition into primes for all the numbers between 1 and 333.
The problem is to list, for a delimited set of ancestors (from 1 to 99) :
- the total of their own ancestors (LEVEL),
- their own ancestors (ANCESTORS),
- the total of the direct descendants (DESCENDANTS),
- all the direct descendants.
You only have to consider the prime factors < 100.
A grand total of the descendants has to be printed at the end of the list.
The task should be accomplished in a reasonable time-frame.
Example :
46 = 2*23 --> 2+23 = 25, is the parent of 46. 25 = 5*5 --> 5+5 = 10, is the parent of 25. 10 = 2*5 --> 2+5 = 7, is the parent of 10. 7 is a prime factor and, as such, has no parent. 46 has 3 ancestors (7, 10 and 25). 46 has 557 descendants.
The list layout and the output for Parent [46] :
[46] Level: 3 Ancestors: 7, 10, 25 Descendants: 557 129, 205, 246, 493, 518, 529, 740, 806, 888, 999, 1364, 1508, 1748, 2552, 2871, 3128, 3255, 3472, 3519, 3875, 3906, 4263, 4650, 4960, 5075, 5415, 5580, 5776, 5952, 6090, 6279, 6496, 6498, 6696, 6783, 7250, 7308, 7475, 7533, 8075, 8151, 8619, 8700, 8855, 8970, 9280, 9568, 9690, 10115, 10336, 10440, 10626, 10764, 11136, 11495, 11628, 11745, 12103, 12138, 12155, 12528, 12650, 13794, 14094, 14399, 14450, 14586, 15180, 15379, 15778, 16192, 17290, 17303, 17340, 18216, 18496, 20482, 20493, 20570, 20748, 20808, 21658, 21970, 22540, 23409, 24684, 24700, 26026, 26364, 27048, 29260, 29282, 29640, 30429, 30940, 31616, 32200, 33345, 35112, 35568, 36225, 36652, 37128, 37180, 38640, 39501, 40014, 41216, 41769, 41800, 43125, 43470, 44044, 44200, 44616, 46000, 46368, 47025, 49725, 50160, 50193, 51750, 52136, 52164, 52360, 53040, 53504, 55200, 56430, 56576, 58653, 58880, 58905, 59670, 60192, 62100, 62832, 62920, 63648, 66240, 66248, 67716, 69825, 70125, 70656, 70686, 70785, 71604, 74480, 74520, 74529, 74536, 74800, 75504, 79488, 83125, 83790, 83835, 83853, 84150, 84942, 87465, 88725, 89376, 89424, 89760, 93296, 94640, 95744, 99750, 99825, 100548, 100602, 100980, 104125, 104958, 105105, 105625, 106400, 106470, 106480, 107712, 112112, 113568, 118750, 119700, 119790, 121176, 124509, 124950, 125125, 126126, 126750, 127680, 127764, 127776, 133280, 135200, 136192, 136323, 142500, 143640, 143748, 148225, 148750, 149940, 150150, 152000, 152100, 153216, 156065, 159936, 160160, 161595, 162240, 171000, 172368, 173056, 177870, 178500, 178750, 179928, 180180, 182400, 182520, 184877, 187278, 189728, 190400, 192192, 192375, 193914, 194560, 194688, 202419, 205200, 205335, 211750, 212500, 213444, 214200, 214500, 216216, 218880, 219024, 222950, 228480, 228800, 230850, 233472, 240975, 243243, 243712, 246240, 246402, 254100, 255000, 257040, 257400, 262656, 264110, 267540, 271040, 272000, 274176, 274560, 277020, 285376, 286875, 289170, 289575, 292864, 295488, 302500, 304920, 306000, 308448, 308880, 316932, 318500, 321048, 325248, 326400, 329472, 332424, 343035, 344250, 347004, 347490, 348160, 361179, 363000, 365904, 367200, 370656, 373977, 377300, 382200, 387200, 391680, 407680, 408375, 411642, 413100, 416988, 417792, 429975, 435600, 440640, 452760, 455000, 458640, 464640, 470016, 470596, 482944, 489216, 490050, 495616, 495720, 509355, 511875, 515970, 522720, 528768, 539000, 543312, 546000, 550368, 557568, 557685, 582400, 588060, 594864, 606375, 609375, 611226, 614250, 619164, 627264, 646800, 650000, 655200, 669222, 672280, 689920, 698880, 705672, 721875, 727650, 731250, 737100, 745472, 756315, 770000, 776160, 780000, 786240, 793881, 806736, 827904, 832000, 838656, 859375, 866250, 873180, 877500, 884520, 900375, 907578, 924000, 931392, 936000, 943488, 960400, 985600, 995085, 998400, 1031250, 1039500, 1047816, 1053000, 1061424, 1064960, 1071875, 1080450, 1100000, 1108800, 1123200, 1152480, 1178793, 1182720, 1184625, 1194102, 1198080, 1229312, 1237500, 1247400, 1261568, 1263600, 1277952, 1286250, 1296540, 1320000, 1330560, 1347840, 1372000, 1382976, 1403325, 1408000, 1419264, 1421550, 1437696, 1485000, 1496880, 1516320, 1531250, 1543500, 1555848, 1584000, 1596672, 1617408, 1646400, 1670625, 1683990, 1689600, 1705860, 1750329, 1756160, 1782000, 1796256, 1802240, 1819584, 1837500, 1852200, 1900800, 1960000, 1975680, 2004750, 2020788, 2027520, 2047032, 2083725, 2107392, 2138400, 2162688, 2187500, 2205000, 2222640, 2280960, 2302911, 2352000, 2370816, 2405700, 2433024, 2480625, 2500470, 2508800, 2566080, 2625000, 2646000, 2667168, 2737152, 2800000, 2822400, 2886840, 2953125, 2976750, 3000564, 3010560, 3079296, 3125000, 3150000, 3175200, 3211264, 3247695, 3360000, 3386880, 3464208, 3515625, 3543750, 3572100, 3584000, 3612672, 3750000, 3780000, 3810240, 3897234, 4000000, 4032000, 4064256, 4218750, 4252500, 4286520, 4300800, 4500000, 4536000, 4572288, 4587520, 4800000, 4822335, 4838400, 5062500, 5103000, 5120000, 5143824, 5160960, 5400000, 5443200, 5505024, 5740875, 5760000, 5786802, 5806080, 6075000, 6123600, 6144000, 6193152, 6480000, 6531840, 6553600, 6834375, 6889050, 6912000, 6967296, 7290000, 7348320, 7372800, 7776000, 7838208, 7864320, 8201250, 8266860, 8294400, 8388608, 8748000, 8817984, 8847360, 9331200, 9437184, 9841500, 9920232, 9953280, 10497600, 10616832, 11160261, 11197440, 11809800, 11943936, 12597120, 13286025, 13436928, 14171760, 15116544, 15943230, 17006112, 19131876
Some figures :
The biggest descendant number : 3^33 = 5.559.060.566.555.523 (parent 99) Total Descendants 546.986
AutoHotkey
It is based on the same logic as the Python script.
I seem that the use of an associative array is a little bit slower than the use of a simple array combined with the 'Sort' command, even if the 'Sort' command pumps 85% of the processing time. <lang AutoHotkey>#Warn
- SingleInstance force
- NoEnv ; Recommended for performance and compatibility with future AutoHotkey releases.
SendMode Input ; Recommended for new scripts due to its superior speed and reliability. SetBatchLines, -1 SetFormat, IntegerFast, D
MaxPrime = 99 ; upper bound for the prime factors MaxAncestor = 99 ; greatest parent number
Descendants := []
Primes := GetPrimes(MaxPrime) Exclusions := Primes.Clone() Exclusions.Insert(4)
if A_Is64bitOS { Loop, % MaxAncestor Descendants.Insert({})
for i, Prime in Primes { Descendants[Prime, Prime] := 0
for Parent, Children in Descendants { if ((Sum := Parent+Prime) > MaxAncestor) break
for pr in Children Descendants[Sum, pr*Prime] := 0 } }
for i, v in Exclusions Descendants[v].Remove(v, "") } else { Loop, % MaxAncestor Descendants.Insert([])
for i, Prime in Primes { Descendants[Prime].Insert(Prime)
for Parent, Children in Descendants { if ((Sum := Parent+Prime) > MaxAncestor) break
for j, pr in Children Descendants[Sum].Insert(pr*Prime) } }
for i, v in Exclusions Descendants[v].Remove() }
if (MaxAncestor > MaxPrime) Primes := GetPrimes(MaxAncestor)
IfExist, %A_ScriptName%.txt FileDelete, %A_ScriptName%.txt
- -------------------------------------------------------
- Arrays
- Integer keys are stored using the native integer type
- 32bit key max = 2.147.483.647
- 64bit key max = 9.223.372.036.854.775.807
- -------------------------------------------------------
Tot_desc = 0 for Parent, Children in Descendants { ls_desc = if A_Is64bitOS { nb_desc = 0 for pr in Children ls_desc .= ", " pr, nb_desc++ ls_desc := LTrim(ls_desc, ", ") } else { nb_desc := Children.MaxIndex() for i, pr in Children ls_desc .= "," pr ls_desc := LTrim(ls_desc, ",")
Sort, ls_desc, N D`, StringReplace, ls_desc, ls_desc, `,,`,%A_Space%, All }
ls_anc = nb_anc := GetAncestors(ls_anc, Parent) ls_anc := LTrim(ls_anc, ", ")
FileAppend, % "[" Parent "] Level: " nb_anc "`r`nAncestors: " (nb_anc ? ls_anc : "None") "`r`n" , %A_ScriptName%.txt
if nb_desc { Tot_desc += nb_desc FileAppend, % "Descendants: " nb_desc "`r`n" ls_desc "`r`n`r`n", %A_ScriptName%.txt } else FileAppend, % "Descendants: None`r`n`r`n", %A_ScriptName%.txt }
FileAppend, % "Total descendants " Tot_desc, %A_ScriptName%.txt return
GetAncestors(ByRef _lsAnc, _child) { global Primes
lChild := _child lIndex := lParent := 0
while lChild > 1 { lPrime := Primes[++lIndex] while !mod(lChild, lPrime) lChild //= lPrime, lParent += lPrime }
if (lParent = _child or _child = 1) return 0
_lsAnc := ", " lParent _lsAnc li := GetAncestors(_lsAnc, lParent) return ++li }
GetPrimes(_maxPrime=0, _nbrPrime=0) { lPrimes := []
if (_maxPrime >= 2 or _nbrPrime >= 1) { lPrimes.Insert(2) lValue = 1
while (lValue += 2) <= _maxPrime or lPrimes.MaxIndex() < _nbrPrime { lMaxPrime := Floor(Sqrt(lValue))
for lKey, lPrime in lPrimes { if (lPrime > lMaxPrime) ; if prime divisor is greater than Floor(Sqrt(lValue)) { lPrimes.Insert(lValue) break }
if !Mod(lValue, lPrime) break } } }
return lPrimes }</lang>
C
Full Approach
You can decompose all the numbers from 1 to 333 (5.559.060.566.555.523).
This solution can take a while.
The InsertChild function is replaced by the AppendChild function which appends directly the child as the new last item in the list. <lang c>#include <math.h>
- include <stdio.h>
- include <stdlib.h>
- include <string.h>
- define MAXPRIME 99 // upper bound for the prime factors
- define MAXPARENT 99 // greatest parent number
- define NBRPRIMES 30 // max number of prime factors
- define NBRANCESTORS 10 // max number of parent's ancestors
FILE *FileOut; char format[] = ", %lld";
int Primes[NBRPRIMES]; // table of the prime factors int iPrimes; // max index of the prime factor table
short Ancestors[NBRANCESTORS]; // table of the parent's ancestors
struct Children { long long Child; struct Children *pNext; }; struct Children *Parents[MAXPARENT+1][2]; // table pointing to the root and to the last descendants (per parent) int CptDescendants[MAXPARENT+1]; // counter table of the descendants (per parent) long long MaxDescendant = (long long) pow(3.0, 33.0); // greatest descendant number
short GetParent(long long child); struct Children *AppendChild(struct Children *node, long long child); short GetAncestors(short child); void PrintDescendants(struct Children *node); int GetPrimes(int primes[], int maxPrime);
int main() { long long Child; short i, Parent, Level; int TotDesc = 0;
if ((iPrimes = GetPrimes(Primes, MAXPRIME)) < 0) return 1;
for (Child = 1; Child <= MaxDescendant; Child++) { if (Parent = GetParent(Child)) { Parents[Parent][1] = AppendChild(Parents[Parent][1], Child); if (Parents[Parent][0] == NULL) Parents[Parent][0] = Parents[Parent][1]; CptDescendants[Parent]++; } }
if (MAXPARENT > MAXPRIME) if (GetPrimes(Primes, MAXPARENT) < 0) return 1;
if (fopen_s(&FileOut, "Ancestors.txt", "w")) return 1;
for (Parent = 1; Parent <= MAXPARENT; Parent++) { Level = GetAncestors(Parent);
fprintf(FileOut, "[%d] Level: %d\n", Parent, Level);
if (Level) { fprintf(FileOut, "Ancestors: %d", Ancestors[0]);
for (i = 1; i < Level; i++) fprintf(FileOut, ", %d", Ancestors[i]); } else fprintf(FileOut, "Ancestors: None");
if (CptDescendants[Parent]) { fprintf(FileOut, "\nDescendants: %d\n", CptDescendants[Parent]); strcpy_s(format, "%lld"); PrintDescendants(Parents[Parent][0]); fprintf(FileOut, "\n"); } else fprintf(FileOut, "\nDescendants: None\n");
fprintf(FileOut, "\n"); TotDesc += CptDescendants[Parent]; }
fprintf(FileOut, "Total descendants %d\n\n", TotDesc); if (fclose(FileOut)) return 1;
return 0; }
short GetParent(long long child) { long long Child = child; short Parent = 0; short Index = 0;
while (Child > 1 && Parent <= MAXPARENT) { if (Index > iPrimes) return 0;
while (Child % Primes[Index] == 0) { Child /= Primes[Index]; Parent += Primes[Index]; }
Index++; }
if (Parent == child || Parent > MAXPARENT || child == 1) return 0;
return Parent; }
struct Children *AppendChild(struct Children *node, long long child) { static struct Children *NodeNew;
if (NodeNew = (struct Children *) malloc(sizeof(struct Children))) { NodeNew->Child = child; NodeNew->pNext = NULL; if (node != NULL) node->pNext = NodeNew; }
return NodeNew; }
short GetAncestors(short child) { short Child = child; short Parent = 0; short Index = 0;
while (Child > 1) { while (Child % Primes[Index] == 0) { Child /= Primes[Index]; Parent += Primes[Index]; }
Index++; }
if (Parent == child || child == 1) return 0;
Index = GetAncestors(Parent);
Ancestors[Index] = Parent; return ++Index; }
void PrintDescendants(struct Children *node) { static struct Children *NodeCurr; static struct Children *NodePrev;
NodeCurr = node; NodePrev = NULL; while (NodeCurr) { fprintf(FileOut, format, NodeCurr->Child); strcpy_s(format, ", %lld"); NodePrev = NodeCurr; NodeCurr = NodeCurr->pNext; free(NodePrev); }
return; }
int GetPrimes(int primes[], int maxPrime) { if (maxPrime < 2) return -1;
int Index = 0, Value = 1; int Max, i;
primes[0] = 2;
while ((Value += 2) <= maxPrime) { Max = (int) floor(sqrt((double) Value));
for (i = 0; i <= Index; i++) { if (primes[i] > Max) { if (++Index >= NBRPRIMES) return -1;
primes[Index] = Value; break; }
if (Value % primes[i] == 0) break; } }
return Index; }</lang>
Optimized Approach
You sum the prime factors from the Prime factor table and you calculate the products.
The sums are the ancestors, the products are the descendants.
It is based on the same logic as the Python script. <lang c>#include <math.h>
- include <stdio.h>
- include <stdlib.h>
- include <string.h>
- define MAXPRIME 99 // upper bound for the prime factors
- define MAXPARENT 99 // greatest parent number
- define NBRPRIMES 30 // max number of prime factors
- define NBRANCESTORS 10 // max number of parent's ancestors
FILE *FileOut; char format[] = ", %lld";
int Primes[NBRPRIMES]; // table of the prime factors int iPrimes; // max index of the prime factor table
short Ancestors[NBRANCESTORS]; // table of the parent's ancestors
struct Children { long long Child; struct Children *pLower; struct Children *pHigher; }; struct Children *Parents[MAXPARENT+1]; // table pointing to the root descendants (per parent) int CptDescendants[MAXPARENT+1]; // counter table of the descendants (per parent)
void InsertPreorder(struct Children *node, short sum, int prime); struct Children *InsertChild(struct Children *node, long long child); void RemoveFalseChildren(); short GetAncestors(short child); void PrintDescendants(struct Children *node); int GetPrimes(int primes[], int maxPrime);
int main() { short i, Parent, Sum, Level; int Prime; int TotDesc = 0; int MidPrime;
if ((iPrimes = GetPrimes(Primes, MAXPRIME)) < 0) return 1;
MidPrime = Primes[iPrimes] / 2;
for (i = iPrimes; i >= 0; i--) { Prime = Primes[i]; Parents[Prime] = InsertChild(Parents[Prime], Prime); CptDescendants[Prime]++;
if (Prime > MidPrime) continue;
for (Parent = 1; Parent <= MAXPARENT; Parent++) { if ((Sum = Parent+Prime) > MAXPARENT) break;
if (Parents[Parent]) { InsertPreorder(Parents[Parent], Sum, Prime); CptDescendants[Sum] += CptDescendants[Parent]; } } }
RemoveFalseChildren();
if (MAXPARENT > MAXPRIME) if (GetPrimes(Primes, MAXPARENT) < 0) return 1;
if (fopen_s(&FileOut, "Ancestors.txt", "w")) return 1;
for (Parent = 1; Parent <= MAXPARENT; Parent++) { Level = GetAncestors(Parent);
fprintf(FileOut, "[%d] Level: %d\n", Parent, Level);
if (Level) { fprintf(FileOut, "Ancestors: %d", Ancestors[0]);
for (i = 1; i < Level; i++) fprintf(FileOut, ", %d", Ancestors[i]); } else fprintf(FileOut, "Ancestors: None");
if (CptDescendants[Parent]) { fprintf(FileOut, "\nDescendants: %d\n", CptDescendants[Parent]); strcpy_s(format, "%lld"); PrintDescendants(Parents[Parent]); fprintf(FileOut, "\n"); } else fprintf(FileOut, "\nDescendants: None\n");
fprintf(FileOut, "\n"); TotDesc += CptDescendants[Parent]; }
fprintf(FileOut, "Total descendants %d\n\n", TotDesc);
if (fclose(FileOut)) return 1;
return 0; }
void InsertPreorder(struct Children *node, short sum, int prime) { Parents[sum] = InsertChild(Parents[sum], node->Child * prime);
if (node->pLower) InsertPreorder(node->pLower, sum, prime);
if (node->pHigher) InsertPreorder(node->pHigher, sum, prime); }
struct Children *InsertChild(struct Children *node, long long child) { if (node) { if (child <= node->Child) node->pLower = InsertChild(node->pLower, child); else node->pHigher = InsertChild(node->pHigher, child); } else { if (node = (struct Children *) malloc(sizeof(struct Children))) { node->Child = child; node->pLower = NULL; node->pHigher = NULL; } }
return node; }
void RemoveFalseChildren() { short i, ex; int Exclusions[NBRPRIMES+1]; // table of the prime factors + {4} int iExclusions; // max index of the exclusion table struct Children *ptr;
for (i = 0; i <= iPrimes; i++) Exclusions[i] = Primes[i];
iExclusions = iPrimes + 1; Exclusions[iExclusions] = 4;
for (i = 0; i <= iExclusions; i++) { ex = Exclusions[i]; ptr = Parents[ex]; Parents[ex] = ptr->pHigher; CptDescendants[ex]--; free(ptr); } }
short GetAncestors(short child) { short Child = child; short Parent = 0; short Index = 0;
while (Child > 1) { while (Child % Primes[Index] == 0) { Child /= Primes[Index]; Parent += Primes[Index]; }
Index++; }
if (Parent == child || child == 1) return 0;
Index = GetAncestors(Parent);
Ancestors[Index] = Parent; return ++Index; }
void PrintDescendants(struct Children *node) { if (node->pLower) PrintDescendants(node->pLower);
fprintf(FileOut, format, node->Child); strcpy_s(format, ", %lld");
if (node->pHigher) PrintDescendants(node->pHigher);
free(node); return; }
int GetPrimes(int primes[], int maxPrime) { if (maxPrime < 2) return -1;
int Index = 0, Value = 1; int Max, i;
primes[0] = 2;
while ((Value += 2) <= maxPrime) { Max = (int) floor(sqrt((double) Value));
for (i = 0; i <= Index; i++) { if (primes[i] > Max) { if (++Index >= NBRPRIMES) return -1;
primes[Index] = Value; break; }
if (Value % primes[i] == 0) break; } }
return Index; }</lang>
Go
<lang go>package main
import (
"fmt" "sort"
)
func getPrimes(max int) []int {
if max < 2 {
return []int{}
}
lprimes := []int{2}
outer:
for x := 3; x <= max; x += 2 {
for _, p := range lprimes {
if x%p == 0 {
continue outer
}
}
lprimes = append(lprimes, x)
}
return lprimes
}
func main() {
const maxSum = 99
descendants := make([][]int64, maxSum+1)
ancestors := make([][]int, maxSum+1)
for i := 0; i <= maxSum; i++ {
descendants[i] = []int64{}
ancestors[i] = []int{}
}
primes := getPrimes(maxSum)
for _, p := range primes {
descendants[p] = append(descendants[p], int64(p))
for s := 1; s < len(descendants)-p; s++ {
temp := make([]int64, len(descendants[s]))
for i := 0; i < len(descendants[s]); i++ {
temp[i] = int64(p) * descendants[s][i]
}
descendants[s+p] = append(descendants[s+p], temp...)
}
}
for _, p := range append(primes, 4) {
le := len(descendants[p])
if le == 0 {
continue
}
descendants[p][le-1] = 0
descendants[p] = descendants[p][:le-1]
}
total := 0
for s := 1; s <= maxSum; s++ {
x := descendants[s]
sort.Slice(x, func(i, j int) bool {
return x[i] < x[j]
})
total += len(descendants[s])
index := 0
for ; index < len(descendants[s]); index++ {
if descendants[s][index] > int64(maxSum) {
break
}
}
for _, d := range descendants[s][:index] {
ancestors[d] = append(ancestors[s], s)
}
if (s >= 21 && s <= 45) || (s >= 47 && s <= 73) || (s >= 75 && s < maxSum) {
continue
}
temp := fmt.Sprintf("%v", ancestors[s])
fmt.Printf("%2d: %d Ancestor(s): %-14s", s, len(ancestors[s]), temp)
le := len(descendants[s])
if le <= 10 {
fmt.Printf("%5d Descendant(s): %v\n", le, descendants[s])
} else {
fmt.Printf("%5d Descendant(s): %v\b ...]\n", le, descendants[s][:10])
}
}
fmt.Println("\nTotal descendants", total)
}</lang>
- Output:
1: 0 Ancestor(s): [] 0 Descendant(s): [] 2: 0 Ancestor(s): [] 0 Descendant(s): [] 3: 0 Ancestor(s): [] 0 Descendant(s): [] 4: 0 Ancestor(s): [] 0 Descendant(s): [] 5: 0 Ancestor(s): [] 1 Descendant(s): [6] 6: 1 Ancestor(s): [5] 2 Descendant(s): [8 9] 7: 0 Ancestor(s): [] 2 Descendant(s): [10 12] 8: 2 Ancestor(s): [5 6] 3 Descendant(s): [15 16 18] 9: 2 Ancestor(s): [5 6] 4 Descendant(s): [14 20 24 27] 10: 1 Ancestor(s): [7] 5 Descendant(s): [21 25 30 32 36] 11: 0 Ancestor(s): [] 5 Descendant(s): [28 40 45 48 54] 12: 1 Ancestor(s): [7] 7 Descendant(s): [35 42 50 60 64 72 81] 13: 0 Ancestor(s): [] 8 Descendant(s): [22 56 63 75 80 90 96 108] 14: 3 Ancestor(s): [5 6 9] 10 Descendant(s): [33 49 70 84 100 120 128 135 144 162] 15: 3 Ancestor(s): [5 6 8] 12 Descendant(s): [26 44 105 112 125 126 150 160 180 192 ...] 16: 3 Ancestor(s): [5 6 8] 14 Descendant(s): [39 55 66 98 140 168 189 200 225 240 ...] 17: 0 Ancestor(s): [] 16 Descendant(s): [52 88 99 147 175 210 224 250 252 300 ...] 18: 3 Ancestor(s): [5 6 8] 19 Descendant(s): [65 77 78 110 132 196 280 315 336 375 ...] 19: 0 Ancestor(s): [] 22 Descendant(s): [34 104 117 165 176 198 245 294 350 420 ...] 20: 3 Ancestor(s): [5 6 9] 26 Descendant(s): [51 91 130 154 156 220 264 297 392 441 ...] 46: 3 Ancestor(s): [7 10 25] 557 Descendant(s): [129 205 246 493 518 529 740 806 888 999 ...] 74: 5 Ancestor(s): [5 6 8 16 39] 6336 Descendant(s): [213 469 670 793 804 1333 1342 1369 1534 2014 ...] 99: 1 Ancestor(s): [17] 38257 Descendant(s): [194 1869 2225 2670 2848 3204 3237 4029 4565 5037 ...] Total descendants 546986
J
Definition of terms
For this task, based on extensive discussion and examination of the early example implementations, these definitions might be sufficient:
An "allocation" P of N is a list of primes whose sum is N which includes prime number P. (For example 5 7, 2 5 5, and 2 2 3 5 are each examples of the 5 of 12 allocation.)
The "family" of N is all distinct products of allocations P of N. (So we can think of our lists as being capable of producing sets: if different sequences of primes produced the same product we still would only count that product once.)
The "descendants" or "direct descendants" of N are all members of its family excluding N itself. (As N could be in its own family if it is prime or if N is 4.)
A "deallocation" of N is the sum of its prime factorization. (For example, the deallocation of 12 is 2+2+3 or 7.)
A "family tree" of N is all the distinct values resulting from applying deallocation inductively (or iteratively or recursively or repeatedly). (For example, the family tree of 15 is 15 8 6 5 and the family tree of 12 is 12 7. Note that this means that the smallest member of a "family tree" is always a prime.)
The "ancestors" of N are all members of its family tree excluding itself.
The "total" of a set of numbers X is the number of members in that set. In other words, the "total" of {5,6} is 2. (So we use the word "sum" instead of "total" when talking about addition in the context of this exercise, because this exercise requires that sort of doublethink.)
"Print" means "calculate and store somewhere".
Implementation I
<lang J>require'strings files'
family=:3 :0 M.
if. 2>y do. i.0 NB. no primes less than 2 else. p=. i.&.(p:inv) y (y#~1 p:y),~.;p (* family)&.>y-p end.
)
familytree=: +/@q:^:a: ::("_)
descendants=: family -. ] ancestors=: 1 }. familytree level=: #@ancestors"0
taskfmt=:'None'"_^:(0=#)@rplc&(' ';', ')@":
task1=:3 :0
text=. '[',(":y),'] Level: ',(":level y),LF
text=. text,'Ancestors: ',(taskfmt /:~ancestors y),LF
if. #descendants y do.
text=. text,'Descendants: ',(":#descendants y),LF
text=. text,(taskfmt /:~descendants y),LF
else.
text=. text,'Descendants: None',LF
end.
text=. text,LF
)
task=:3 :0
tot=. 'Total descendants ',(":#@; descendants&.> 1+i.y),LF
((;task1&.>1+i.y),tot) fwrite jpath '~user/temp/Ancestors.txt'
)
task 99</lang>
If you want to inspect individual results, that's fairly straightforward.
The produced text file comes not from the task description but from Implementation II (except omitting the CR at line end - you can use unix/osx/linux/cygwin's diff -bw to compare the generated files).
Can we assume you use the '9!:11 +20' function in your profile? Otherwise the big values are shown in scientific notation.
Some examples
<lang J> #;descendants&.>1+i.99 546986
level 46
3
ancestors 46
25 10 7
#descendants 46
557
descendants 18
512 576 480 336 400 648 280 132 540 196 78 378 450 110 729 315 375 65 77
level 18
3
ancestors 18
8 6 5
#descendants 18
19</lang>
Implementation II
After reading the "Learning J" documentation up to chapter 9 + some additional verbs, I can post my first J script.
The script is based on the same logic as the Python script and therefore on the original task description.
However, I use the 'FamilyTree' function of implementation I, as the 'getancestors' function.
Furthermore, the script produces the full report in a '.txt' file which can easily be compared with the output of some of the other languages. In Windows : fc /N /L
<lang J>getdescendants=: 3 : 0
dd=: (<(>y{dd),y)y}dd
y getproducts"0 >:i.maxsum-y
)
getproducts=: 4 : 'dd=: (<(>(x+y){dd),x*(>y{dd))(x+y)}dd'
delfalsechildren=: 3 : 'dd=: ((}:&.>)y{dd)y}dd'
report=: 3 : 0
ac=. getancestors y
if. (level=. #ac) = 0 do.
ls=. 'None'
else.
ls=. (' ';', ') stringreplace ":ac
end.
line=. '[',(":y),'] Level: ',(":level),CR,LF,'Ancestors: ',ls,CR,LF
if. (nb=. #>y{dd) = 0 do.
line=. line,'Descendants: ','None',CR,LF,CR,LF
else.
ls=. (' ';', ') stringreplace ":/:~>y{dd
line=. line,'Descendants: ',(":nb),CR,LF,ls,CR,LF,CR,LF
end.
line fappend file
)
getancestors=: |.@:(1}.+/@:q:^:a: ::("_))
main=: 3 : 0
if. (pp1=. 9!:10 ) < 20 do. (9!:11) 20 end.
fwrite file
maxsum=: y
dd=: (maxsum+1)$a:
primes=. i.&.(p:inv)maxsum+1
getdescendants"0 primes
delfalsechildren"0 primes,4
report"0 >:i.maxsum
('Total descendants ',":+/#&>dd) fappend file
if. (pp2=. 9!:10 ) ~: pp1 do. (9!:11) pp1 end.
)
file=: jpath '~user/temp/Ancestors.ijs.txt' main 99</lang>
Julia
<lang julia>using Primes
const MAXSUM = 99
function ancestraldecendants(maxsum)
aprimes = primes(maxsum)
descendants = [Vector{Int}() for _ in 1:maxsum + 1]
ancestors = [Vector{Int}() for _ in 1:maxsum + 1]
for p in aprimes
push!(descendants[p + 1], p)
for s in 2:length(descendants) - p
append!(descendants[s + p], [p * pr for pr in descendants[s]])
end
end
foreach(p -> pop!(descendants[p + 1]), vcat(aprimes, [4]))
total = 0
for s in 1:maxsum
sort!(descendants[s + 1])
dstlen = length(descendants[s + 1])
total += dstlen
idx = findfirst(x -> x > MAXSUM, descendants[s + 1])
idx = (idx == nothing) ? dstlen : idx - 1
for d in descendants[s + 1][1:idx]
ancestors[d] = vcat(ancestors[s + 1], [s])
end
if s in vcat(collect(0:20), 46, 74, 99)
print(lpad(s, 3), ":", lpad("$(length(ancestors[s + 1]))", 2))
print(" Ancestor(s):", rpad("$(ancestors[s + 1])", 18))
print(lpad("$(length(descendants[s + 1]))", 5), " Descendant(s): ")
println(rpad(dstlen <= 10 ? "$(descendants[s + 1])" : "$(descendants[s + 1][1:10])\b, ...]", 40))
end
end
print("Total descendants: ", total)
end
ancestraldecendants(MAXSUM)
</lang>
- Output:
1: 0 Ancestor(s):Int64[] 0 Descendant(s): Int64[] 2: 0 Ancestor(s):Int64[] 0 Descendant(s): Int64[] 3: 0 Ancestor(s):Int64[] 0 Descendant(s): Int64[] 4: 0 Ancestor(s):Int64[] 0 Descendant(s): Int64[] 5: 1 Ancestor(s):[5] 1 Descendant(s): [6] 6: 0 Ancestor(s):Int64[] 2 Descendant(s): [8, 9] 7: 1 Ancestor(s):[6] 2 Descendant(s): [10, 12] 8: 1 Ancestor(s):[6] 3 Descendant(s): [15, 16, 18] 9: 2 Ancestor(s):[6, 7] 4 Descendant(s): [14, 20, 24, 27] 10: 0 Ancestor(s):Int64[] 5 Descendant(s): [21, 25, 30, 32, 36] 11: 2 Ancestor(s):[6, 7] 5 Descendant(s): [28, 40, 45, 48, 54] 12: 0 Ancestor(s):Int64[] 7 Descendant(s): [35, 42, 50, 60, 64, 72, 81] 13: 3 Ancestor(s):[6, 7, 9] 8 Descendant(s): [22, 56, 63, 75, 80, 90, 96, 108] 14: 2 Ancestor(s):[6, 8] 10 Descendant(s): [33, 49, 70, 84, 100, 120, 128, 135, 144, 162] 15: 2 Ancestor(s):[6, 8] 12 Descendant(s): [26, 44, 105, 112, 125, 126, 150, 160, 180, 192, ...] 16: 0 Ancestor(s):Int64[] 14 Descendant(s): [39, 55, 66, 98, 140, 168, 189, 200, 225, 240, ...] 17: 2 Ancestor(s):[6, 8] 16 Descendant(s): [52, 88, 99, 147, 175, 210, 224, 250, 252, 300, ...] 18: 0 Ancestor(s):Int64[] 19 Descendant(s): [65, 77, 78, 110, 132, 196, 280, 315, 336, 375, ...] 19: 3 Ancestor(s):[6, 7, 9] 22 Descendant(s): [34, 104, 117, 165, 176, 198, 245, 294, 350, 420, ...] 20: 1 Ancestor(s):[10] 26 Descendant(s): [51, 91, 130, 154, 156, 220, 264, 297, 392, 441, ...] 46: 0 Ancestor(s):Int64[] 557 Descendant(s): [129, 205, 246, 493, 518, 529, 740, 806, 888, 999, ...] 74: 4 Ancestor(s):[6, 7, 9, 13] 6336 Descendant(s): [213, 469, 670, 793, 804, 1333, 1342, 1369, 1534, 2014, ...] 99: 0 Ancestor(s):Int64[] 38257 Descendant(s): [194, 1869, 2225, 2670, 2848, 3204, 3237, 4029, 4565, 5037, ...]Total descendants: 546986
Kotlin
<lang scala>// version 1.1.2
const val MAXSUM = 99
fun getPrimes(max: Int): List<Int> {
if (max < 2) return emptyList<Int>()
val lprimes = mutableListOf(2)
outer@ for (x in 3..max step 2) {
for (p in lprimes) if (x % p == 0) continue@outer
lprimes.add(x)
}
return lprimes
}
fun main(args: Array<String>) {
val descendants = Array(MAXSUM + 1) { mutableListOf<Long>() }
val ancestors = Array(MAXSUM + 1) { mutableListOf<Int>() }
val primes = getPrimes(MAXSUM)
for (p in primes) {
descendants[p].add(p.toLong())
for (s in 1 until descendants.size - p) {
val temp = descendants[s + p] + descendants[s].map { p * it }
descendants[s + p] = temp.toMutableList()
}
}
for (p in primes + 4) descendants[p].removeAt(descendants[p].lastIndex) var total = 0
for (s in 1..MAXSUM) {
descendants[s].sort()
total += descendants[s].size
for (d in descendants[s].takeWhile { it <= MAXSUM.toLong() }) {
ancestors[d.toInt()] = (ancestors[s] + s).toMutableList()
}
if (s in 21..45 || s in 47..73 || s in 75 until MAXSUM) continue
print("${"%2d".format(s)}: ${ancestors[s].size} Ancestor(s): ")
print(ancestors[s].toString().padEnd(18))
print("${"%5d".format(descendants[s].size)} Descendant(s): ")
println("${descendants[s].joinToString(", ", "[", "]", 10)}")
}
println("\nTotal descendants $total")
}</lang>
- Output:
1: 0 Ancestor(s): [] 0 Descendant(s): [] 2: 0 Ancestor(s): [] 0 Descendant(s): [] 3: 0 Ancestor(s): [] 0 Descendant(s): [] 4: 0 Ancestor(s): [] 0 Descendant(s): [] 5: 0 Ancestor(s): [] 1 Descendant(s): [6] 6: 1 Ancestor(s): [5] 2 Descendant(s): [8, 9] 7: 0 Ancestor(s): [] 2 Descendant(s): [10, 12] 8: 2 Ancestor(s): [5, 6] 3 Descendant(s): [15, 16, 18] 9: 2 Ancestor(s): [5, 6] 4 Descendant(s): [14, 20, 24, 27] 10: 1 Ancestor(s): [7] 5 Descendant(s): [21, 25, 30, 32, 36] 11: 0 Ancestor(s): [] 5 Descendant(s): [28, 40, 45, 48, 54] 12: 1 Ancestor(s): [7] 7 Descendant(s): [35, 42, 50, 60, 64, 72, 81] 13: 0 Ancestor(s): [] 8 Descendant(s): [22, 56, 63, 75, 80, 90, 96, 108] 14: 3 Ancestor(s): [5, 6, 9] 10 Descendant(s): [33, 49, 70, 84, 100, 120, 128, 135, 144, 162] 15: 3 Ancestor(s): [5, 6, 8] 12 Descendant(s): [26, 44, 105, 112, 125, 126, 150, 160, 180, 192, ...] 16: 3 Ancestor(s): [5, 6, 8] 14 Descendant(s): [39, 55, 66, 98, 140, 168, 189, 200, 225, 240, ...] 17: 0 Ancestor(s): [] 16 Descendant(s): [52, 88, 99, 147, 175, 210, 224, 250, 252, 300, ...] 18: 3 Ancestor(s): [5, 6, 8] 19 Descendant(s): [65, 77, 78, 110, 132, 196, 280, 315, 336, 375, ...] 19: 0 Ancestor(s): [] 22 Descendant(s): [34, 104, 117, 165, 176, 198, 245, 294, 350, 420, ...] 20: 3 Ancestor(s): [5, 6, 9] 26 Descendant(s): [51, 91, 130, 154, 156, 220, 264, 297, 392, 441, ...] 46: 3 Ancestor(s): [7, 10, 25] 557 Descendant(s): [129, 205, 246, 493, 518, 529, 740, 806, 888, 999, ...] 74: 5 Ancestor(s): [5, 6, 8, 16, 39] 6336 Descendant(s): [213, 469, 670, 793, 804, 1333, 1342, 1369, 1534, 2014, ...] 99: 1 Ancestor(s): [17] 38257 Descendant(s): [194, 1869, 2225, 2670, 2848, 3204, 3237, 4029, 4565, 5037, ...] Total descendants 546986
Perl
<lang perl>use List::Util qw(sum uniq); use ntheory qw(nth_prime);
my $max = 99; my %tree;
sub allocate {
my($n, $i, $sum,, $prod) = @_; $i //= 0; $sum //= 0; $prod //= 1;
for my $k (0..$max) {
next if $k < $i;
my $p = nth_prime($k+1);
if (($sum + $p) <= $max) {
allocate($n, $k, $sum + $p, $prod * $p);
} else {
last if $sum == $prod;
$tree{$sum}{descendants}{$prod} = 1;
$tree{$prod}{ancestor} = [uniq $sum, @{$tree{$sum}{ancestor}}] unless $prod > $max || $sum == 0;
last;
}
}
}
sub abbrev { # abbreviate long lists to first and last 5 elements
my(@d) = @_; return @d if @d < 11; @d[0 .. 4], '...', @d[-5 .. -1];
}
allocate($_) for 1 .. $max;
for (1 .. 15, 46, $max) {
printf "%2d, %2d Ancestors: %-15s", $_, (scalar uniq @{$tree{$_}{ancestor}}),
'[' . join(' ',uniq @{$tree{$_}{ancestor}}) . ']';
my $dn = 0; my $dl = ;
if ($tree{$_}{descendants}) {
$dn = keys %{$tree{$_}{descendants}};
$dl = join ' ', abbrev(sort { $a <=> $b } keys %{$tree{$_}{descendants}});
}
printf "%5d Descendants: %s", $dn, "[$dl]\n";
}
map { for my $k (keys %{$tree{$_}{descendants}}) { $total += $tree{$_}{descendants}{$k} } } 1..$max; print "\nTotal descendants: $total\n";</lang>
- Output:
1, 0 Ancestors: [], 0 Descendants: [] 2, 0 Ancestors: [], 0 Descendants: [] 3, 0 Ancestors: [], 0 Descendants: [] 4, 0 Ancestors: [], 0 Descendants: [] 5, 0 Ancestors: [], 1 Descendants: [6] 6, 1 Ancestors: [5], 2 Descendants: [8 9] 7, 0 Ancestors: [], 2 Descendants: [10 12] 8, 2 Ancestors: [5 6], 3 Descendants: [15 16 18] 9, 2 Ancestors: [5 6], 4 Descendants: [14 20 24 27] 10, 1 Ancestors: [7], 5 Descendants: [21 25 30 32 36] 11, 0 Ancestors: [], 5 Descendants: [28 40 45 48 54] 12, 1 Ancestors: [7], 7 Descendants: [35 42 50 60 64 72 81] 13, 0 Ancestors: [], 8 Descendants: [22 56 63 75 80 90 96 108] 14, 3 Ancestors: [5 6 9], 10 Descendants: [33 49 70 84 100 120 128 135 144 162] 15, 3 Ancestors: [5 6 8], 12 Descendants: [26 44 105 112 125 ... 160 180 192 216 243] 46, 3 Ancestors: [7 10 25], 557 Descendants: [129 205 246 493 518 ... 14171760 15116544 15943230 17006112 19131876] 99, 1 Ancestors: [17], 38257 Descendants: [194 1869 2225 2670 2848 ... 3904305912313344 4117822641892980 4392344151352512 4941387170271576 5559060566555523] Total descendants: 546986
Perl 6
<lang perl6>my $max = 99; my @primes = (2 .. $max).race(:16batch).grep: *.is-prime; my %tree; (1..$max).race(:16batch).map: {
%tree{$_}<ancestor> = ();
%tree{$_}<descendants> = {};
};
sub allocate ($n, $i = 0, $sum = 0, $prod = 1) {
return if $n < 4;
for @primes.kv -> $k, $p {
next if $k < $i;
if ($sum + $p) <= $n {
allocate($n, $k, $sum + $p, $prod * $p);
} else {
last if $sum == $prod;
%tree{$sum}<descendants>{$prod} = True;
last if $prod > $max;
%tree{$prod}<ancestor> = %tree{$sum}<ancestor> (|) $sum;
last;
}
}
}
- abbreviate long lists to first and last 5 elements
sub abbrev (@d) { @d < 11 ?? @d !! ( @d.head(5), '...', @d.tail(5) ) }
my @print = flat 1 .. 15, 46, 74, $max;
(1 .. $max).map: -> $term {
allocate($term);
if $term == any( @print ) # print some representative lines
{
my $dn = +%tree{$term}<descendants> // 0;
my $dl = abbrev(%tree{$term}<descendants>.keys.sort( +*) // ());
printf "%2d, %2d Ancestors: %-14s %5d Descendants: %s\n",
$term, %tree{$term}<ancestor>,
"[{ %tree{$term}<ancestor>.keys.sort: +* }],", $dn, "[$dl]";
}
}
say "\nTotal descendants: ",
sum (1..$max).race(:16batch).map({ +%tree{$_}<descendants> });</lang>
- Output:
1, 0 Ancestors: [], 0 Descendants: [] 2, 0 Ancestors: [], 0 Descendants: [] 3, 0 Ancestors: [], 0 Descendants: [] 4, 0 Ancestors: [], 0 Descendants: [] 5, 0 Ancestors: [], 1 Descendants: [6] 6, 1 Ancestors: [5], 2 Descendants: [8 9] 7, 0 Ancestors: [], 2 Descendants: [10 12] 8, 2 Ancestors: [5 6], 3 Descendants: [15 16 18] 9, 2 Ancestors: [5 6], 4 Descendants: [14 20 24 27] 10, 1 Ancestors: [7], 5 Descendants: [21 25 30 32 36] 11, 0 Ancestors: [], 5 Descendants: [28 40 45 48 54] 12, 1 Ancestors: [7], 7 Descendants: [35 42 50 60 64 72 81] 13, 0 Ancestors: [], 8 Descendants: [22 56 63 75 80 90 96 108] 14, 3 Ancestors: [5 6 9], 10 Descendants: [33 49 70 84 100 120 128 135 144 162] 15, 3 Ancestors: [5 6 8], 12 Descendants: [26 44 105 112 125 ... 160 180 192 216 243] 46, 3 Ancestors: [7 10 25], 557 Descendants: [129 205 246 493 518 ... 14171760 15116544 15943230 17006112 19131876] 74, 5 Ancestors: [5 6 8 16 39], 6336 Descendants: [213 469 670 793 804 ... 418414128120 446308403328 470715894135 502096953744 564859072962] 99, 1 Ancestors: [17], 38257 Descendants: [194 1869 2225 2670 2848 ... 3904305912313344 4117822641892980 4392344151352512 4941387170271576 5559060566555523] Total descendants: 546986
Phix
<lang Phix>constant maxSum = 99
function getPrimes()
sequence primes = {2}
for x=3 to maxSum by 2 do
bool zero = false
for i=1 to length(primes) do
if mod(x,primes[i]) == 0 then
zero = true
exit
end if
end for
if not zero then
primes = append(primes, x)
end if
end for
return primes
end function
function stringify(sequence s)
for i=1 to length(s) do
s[i] = sprintf("%d",s[i])
end for
return s
end function
procedure main() atom t0 = time() integer p
sequence descendants = repeat({},maxSum+1),
ancestors = repeat({},maxSum+1),
primes = getPrimes()
for i=1 to length(primes) do
p = primes[i]
descendants[p] = append(descendants[p], p)
for s=1 to length(descendants)-p do
descendants[s+p] &= sq_mul(descendants[s], p)
end for
end for
p = 4
for i=0 to length(primes) do
if i>0 then p = primes[i] end if
if length(descendants[p])!=0 then
descendants[p] = descendants[p][1..$-1]
end if
end for
integer total = 0
for s=1 to maxSum do
sequence x = sort(descendants[s])
total += length(x)
for i=1 to length(x) do
atom d = x[i]
if d>maxSum then exit end if
ancestors[d] &= append(ancestors[s], s)
end for
if s<26 or find(s,{46,74,99}) then
sequence d = ancestors[s]
integer l = length(d)
string sp = iff(l=1?" ":"s")
d = stringify(d)
printf(1,"%2d: %d Ancestor%s: [%-14s", {s, l, sp, join(d)&"]"})
d = sort(descendants[s])
l = length(d)
sp = iff(l=1?" ":"s")
if l<10 then
d = stringify(d)
else
d[4..-4] = {0}
d = stringify(d)
d[4] = "..."
end if
printf(1,"%5d Descendant%s: [%s]\n", {l, sp, join(d)})
end if
end for
printf(1,"\nTotal descendants %d\n", total)
?elapsed(time()-t0) -- < 1s
?elapsed(5559060566555523/4_000_000_000) -- > 16 days
end procedure main()</lang>
- Output:
1: 0 Ancestors: [] 0 Descendants: [] 2: 0 Ancestors: [] 0 Descendants: [] 3: 0 Ancestors: [] 0 Descendants: [] 4: 0 Ancestors: [] 0 Descendants: [] 5: 0 Ancestors: [] 1 Descendant : [6] 6: 1 Ancestor : [5] 2 Descendants: [8 9] 7: 0 Ancestors: [] 2 Descendants: [10 12] 8: 2 Ancestors: [5 6] 3 Descendants: [15 16 18] 9: 2 Ancestors: [5 6] 4 Descendants: [14 20 24 27] 10: 1 Ancestor : [7] 5 Descendants: [21 25 30 32 36] 11: 0 Ancestors: [] 5 Descendants: [28 40 45 48 54] 12: 1 Ancestor : [7] 7 Descendants: [35 42 50 60 64 72 81] 13: 0 Ancestors: [] 8 Descendants: [22 56 63 75 80 90 96 108] 14: 3 Ancestors: [5 6 9] 10 Descendants: [33 49 70 ... 135 144 162] 15: 3 Ancestors: [5 6 8] 12 Descendants: [26 44 105 ... 192 216 243] 16: 3 Ancestors: [5 6 8] 14 Descendants: [39 55 66 ... 270 288 324] 17: 0 Ancestors: [] 16 Descendants: [52 88 99 ... 405 432 486] 18: 3 Ancestors: [5 6 8] 19 Descendants: [65 77 78 ... 576 648 729] 19: 0 Ancestors: [] 22 Descendants: [34 104 117 ... 810 864 972] 20: 3 Ancestors: [5 6 9] 26 Descendants: [51 91 130 ... 1215 1296 1458] 21: 2 Ancestors: [7 10] 30 Descendants: [38 68 195 ... 1728 1944 2187] 22: 1 Ancestor : [13] 35 Descendants: [57 85 102 ... 2430 2592 2916] 23: 0 Ancestors: [] 39 Descendants: [76 136 153 ... 3645 3888 4374] 24: 3 Ancestors: [5 6 9] 46 Descendants: [95 114 119 ... 5184 5832 6561] 25: 2 Ancestors: [7 10] 52 Descendants: [46 152 171 ... 7290 7776 8748] 46: 3 Ancestors: [7 10 25] 557 Descendants: [129 205 246 ... 15943230 17006112 19131876] 74: 5 Ancestors: [5 6 8 16 39] 6336 Descendants: [213 469 670 ... 470715894135 502096953744 564859072962] 99: 1 Ancestor : [17] 38257 Descendants: [194 1869 2225 ... 4392344151352512 4941387170271576 5559060566555523] Total descendants 546986 "0.7s" "16 days, 2 hours, 2 minutes and 45s"
The quick test at the end suggests that a 4Ghz chip would take at least 16 days just to count to 5559060566555523, let alone decompose those numbers into prime factors (and throwing away the ones you don't need, probably more like 10 million years), which as requested in the task description obviously demonstrates that the algorithm can be crucial in terms of performance.
Python
Python is very flexible, concise and effective with lists. <lang python>from __future__ import print_function from itertools import takewhile
maxsum = 99
def get_primes(max):
if max < 2:
return []
lprimes = [2]
for x in range(3, max + 1, 2):
for p in lprimes:
if x % p == 0:
break
else:
lprimes.append(x)
return lprimes
descendants = [[] for _ in range(maxsum + 1)] ancestors = [[] for _ in range(maxsum + 1)]
primes = get_primes(maxsum)
for p in primes:
descendants[p].append(p)
for s in range(1, len(descendants) - p):
descendants[s + p] += [p * pr for pr in descendants[s]]
for p in primes + [4]:
descendants[p].pop()
total = 0 for s in range(1, maxsum + 1):
descendants[s].sort()
for d in takewhile(lambda x: x <= maxsum, descendants[s]):
ancestors[d] = ancestors[s] + [s]
print([s], "Level:", len(ancestors[s]))
print("Ancestors:", ancestors[s] if len(ancestors[s]) else "None")
print("Descendants:", len(descendants[s]) if len(descendants[s]) else "None")
if len(descendants[s]):
print(descendants[s])
print()
total += len(descendants[s])
print("Total descendants", total)</lang>
Racket
I think that this is not anymore a translation of Python, since the 'Python script I' is gone.
The program has a few changes from the versions in other languages. The equation p*q=p+q has only one integer solution, so all the ancestor candidates are smaller than the number, except for 4=2+2=2*2. So we can replace the inecuality by a special case for 4.
We only show here a few values to be able to compare the output. We also show the total number of ancestors.
We first define a macro to create memorized functions and a few auxiliary functions. In particular (border list) transforms a long list in a list with ellipsis.
<lang Racket>#lang racket
(define-syntax-rule (define/mem (name args ...) body ...)
(begin
(define cache (make-hash))
(define (name args ...)
(hash-ref! cache (list args ...) (lambda () body ...)))))
(define (take-last x n)
(drop x (- (length x) n)))
(define (borders x)
(if (> (length x) 5) (append (take x 2) '(...) (take-last x 2)) x))
(define (add-tail list x)
(reverse (cons x (reverse list))))</lang>
The main part of the program uses the memorized functions.
<lang Racket (define/mem (prime? x)
(if (= x 1)
#f
(not (for/or ([p (in-range 2 x)]
#:break (> (sqr p) x))
(zero? (remainder x p))))))
(define (map* p list)
(map (lambda (x) (* x p)) list))
(define/mem (part-prod x p)
(cond
[(< x 0) '()]
[(zero? x) (list 1)]
[(zero? p) '()]
[(not (prime? p)) (part-prod x (sub1 p))]
[else (append (map* p (part-prod (- x p) p))
(part-prod x (sub1 p)))]))
(define/mem (descendants x)
(if (= x 4)
'()
(sort (part-prod x (sub1 x)) <)))
(define/mem (ancestors z)
(let ([tmp (for/first ([x (in-range (sub1 z) 0 -1)]
#:when (member z (descendants x)))
(add-tail (ancestors x) x))])
(if tmp tmp '())))
(define (show-info x)
(printf "~a " x) (printf "Ancestors: ~a ~a " (length (ancestors x)) (ancestors x)) (printf "Descendants: ~a ~a " (length (descendants x)) (borders (descendants x))) (newline))
(define (total-ancestors n)
(for/sum ([x (in-range 1 (add1 n))]) (length (ancestors x))))
(define (total-descendants n)
(for/sum ([x (in-range 1 (add1 n))]) (length (descendants x))))</lang>
Now we display some results.
<lang Racket>#;(for ([x (in-range 1 (add1 99))])
(show-info x))
(for ([x (in-range 1 (add1 15))])
(show-info x))
(newline) (show-info 18) (show-info 46) (show-info 99)
(newline) (printf "Total ancestors up to 99: ~a\n" (total-ancestors 99)) (printf "Total descendants up to 99: ~a\n" (total-descendants 99))</lang>
- Output:
1 Ancestors: 0 () Descendants: 0 () 2 Ancestors: 0 () Descendants: 0 () 3 Ancestors: 0 () Descendants: 0 () 4 Ancestors: 0 () Descendants: 0 () 5 Ancestors: 0 () Descendants: 1 (6) 6 Ancestors: 1 (5) Descendants: 2 (8 9) 7 Ancestors: 0 () Descendants: 2 (10 12) 8 Ancestors: 2 (5 6) Descendants: 3 (15 16 18) 9 Ancestors: 2 (5 6) Descendants: 4 (14 20 24 27) 10 Ancestors: 1 (7) Descendants: 5 (21 25 30 32 36) 11 Ancestors: 0 () Descendants: 5 (28 40 45 48 54) 12 Ancestors: 1 (7) Descendants: 7 (35 42 ... 72 81) 13 Ancestors: 0 () Descendants: 8 (22 56 ... 96 108) 14 Ancestors: 3 (5 6 9) Descendants: 10 (33 49 ... 144 162) 15 Ancestors: 3 (5 6 8) Descendants: 12 (26 44 ... 216 243) 18 Ancestors: 3 (5 6 8) Descendants: 19 (65 77 ... 648 729) 46 Ancestors: 3 (7 10 25) Descendants: 557 (129 205 ... 17006112 19131876) 99 Ancestors: 1 (17) Descendants: 38257 (194 1869 ... 4941387170271576 5559060566555523) Total ancestors up to 99: 179 Total descendants up to 99: 546986
Simula
<lang simula>COMMENT cim --memory-pool-size=512 allocate-descendants-to-their-ancestors.sim ; BEGIN
COMMENT ABSTRACT FRAMEWORK CLASSES ;
CLASS ITEM; BEGIN END ITEM;
CLASS ITEMLIST; BEGIN
CLASS ITEMARRAY(N); INTEGER N;
BEGIN REF(ITEM) ARRAY DATA(0:N-1);
END ITEMARRAY;
PROCEDURE EXPAND(N); INTEGER N;
BEGIN
INTEGER I;
REF(ITEMARRAY) TEMP;
TEMP :- NEW ITEMARRAY(N);
FOR I := 0 STEP 1 UNTIL SIZE-1 DO
TEMP.DATA(I) :- ITEMS.DATA(I);
ITEMS :- TEMP;
END EXPAND;
PROCEDURE APPEND(RI); REF(ITEM) RI;
BEGIN
IF SIZE + 1 > CAPACITY THEN
BEGIN
CAPACITY := 2 * CAPACITY;
EXPAND(CAPACITY);
END;
ITEMS.DATA(SIZE) :- RI;
SIZE := SIZE + 1;
END APPEND;
PROCEDURE APPENDALL(IL); REF(ITEMLIST) IL;
BEGIN
INTEGER I;
FOR I := 0 STEP 1 UNTIL IL.SIZE-1 DO
APPEND(IL.ELEMENT(I));
END APPENDALL;
REF(ITEM) PROCEDURE ELEMENT(I); INTEGER I;
BEGIN
IF I < 0 OR I > SIZE-1 THEN ERROR("ELEMENT: INDEX OUT OF BOUNDS");
ELEMENT :- ITEMS.DATA(I);
END ELEMENT;
REF(ITEM) PROCEDURE SETELEMENT(I, IT); INTEGER I; REF(ITEM) IT;
BEGIN
IF I < 0 OR I > SIZE-1 THEN ERROR("SETELEMENT: INDEX OUT OF BOUNDS");
ITEMS.DATA(I) :- IT;
END SETELEMENT;
REF(ITEM) PROCEDURE POP;
BEGIN
REF(ITEM) RESULT;
IF SIZE=0 THEN ERROR("POP: EMPTY ITEMLIST");
RESULT :- ITEMS.DATA(SIZE-1);
ITEMS.DATA(SIZE-1) :- NONE;
SIZE := SIZE-1;
POP :- RESULT;
END POP;
PROCEDURE SORT(COMPARE_PROC);
PROCEDURE COMPARE_PROC IS
INTEGER PROCEDURE COMPARE_PROC(IT1,IT2); REF(ITEM) IT1,IT2;;
BEGIN
PROCEDURE SWAP(I,J); INTEGER I,J;
BEGIN
REF(ITEM) T;
T :- ITEMS.DATA(I);
ITEMS.DATA(I) :- ITEMS.DATA(J);
ITEMS.DATA(J) :- T;
END SWAP;
PROCEDURE QUICKSORT(L,R); INTEGER L,R;
BEGIN
REF(ITEM) PIVOT;
INTEGER I, J;
PIVOT :- ITEMS.DATA((L+R)//2); I := L; J := R;
WHILE I <= J DO
BEGIN
WHILE COMPARE_PROC(ITEMS.DATA(I), PIVOT) < 0 DO I := I+1;
WHILE COMPARE_PROC(PIVOT, ITEMS.DATA(J)) < 0 DO J := J-1;
IF I <= J THEN
BEGIN SWAP(I,J); I := I+1; J := J-1;
END;
END;
IF L < J THEN QUICKSORT(L, J);
IF I < R THEN QUICKSORT(I, R);
END QUICKSORT;
IF SIZE >= 2 THEN
QUICKSORT(0,SIZE-1);
END SORT;
INTEGER CAPACITY;
INTEGER SIZE;
REF(ITEMARRAY) ITEMS;
CAPACITY := 20;
SIZE := 0;
EXPAND(CAPACITY);
END ITEMLIST;
COMMENT PROBLEM SPECIFIC PART ;
ITEM CLASS REALITEM(X); LONG REAL X; BEGIN END REALITEM;
ITEMLIST CLASS LIST_OF_REAL;
BEGIN
LONG REAL PROCEDURE ELEMENT(I); INTEGER I;
ELEMENT := ITEMS.DATA(I) QUA REALITEM.X;
PROCEDURE APPEND(X); LONG REAL X;
THIS ITEMLIST.APPEND(NEW REALITEM(X));
PROCEDURE SORT;
BEGIN
INTEGER PROCEDURE CMP(IT1,IT2); REF(ITEM) IT1,IT2;
CMP := IF IT1 QUA REALITEM.X < IT2 QUA REALITEM.X THEN -1 ELSE
IF IT1 QUA REALITEM.X > IT2 QUA REALITEM.X THEN +1 ELSE 0;
THIS ITEMLIST.SORT(CMP);
END SORT;
PROCEDURE OUTLIST;
BEGIN
INTEGER I;
TEXT FMT;
OUTTEXT("[");
FMT :- BLANKS(20);
FOR I := 0 STEP 1 UNTIL SIZE-1 DO
BEGIN
IF I < 3 OR I > SIZE-1-3 THEN BEGIN
IF I > 0 THEN OUTTEXT(", ");
FMT.PUTFIX(ELEMENT(I), 0);
FMT.SETPOS(1);
WHILE FMT.MORE DO
BEGIN
CHARACTER C;
C := FMT.GETCHAR;
IF C <> ' ' THEN OUTCHAR(C);
END
END ELSE BEGIN OUTTEXT(", ..."); I := SIZE-1-3; END;
END;
OUTTEXT("]");
END OUTLIST;
END LIST_OF_REAL;
ITEM CLASS REALLISTITEM(LRL); REF(LIST_OF_REAL) LRL; BEGIN END REALLISTITEM;
ITEMLIST CLASS LIST_OF_REALLIST;
BEGIN
REF(LIST_OF_REAL) PROCEDURE ELEMENT(I); INTEGER I;
ELEMENT :- ITEMS.DATA(I) QUA REALLISTITEM.LRL;
PROCEDURE APPEND(LRL); REF(LIST_OF_REAL) LRL;
THIS ITEMLIST.APPEND(NEW REALLISTITEM(LRL));
PROCEDURE OUTLIST;
BEGIN
INTEGER I;
OUTTEXT("[");
FOR I := 0 STEP 1 UNTIL SIZE-1 DO
BEGIN
IF I > 0 THEN OUTTEXT(", ");
ELEMENT(I).OUTLIST;
END;
OUTTEXT("]");
END OUTLIST;
END LIST_OF_REALLIST;
REF(LIST_OF_REAL) PROCEDURE GET_PRIMES(MAX);
INTEGER MAX;
BEGIN
REF(LIST_OF_REAL) LPRIMES;
LPRIMES :- NEW LIST_OF_REAL;
IF MAX < 2 THEN
GOTO RETURN
ELSE
BEGIN
INTEGER X;
LPRIMES.APPEND(2);
FOR X := 3 STEP 2 UNTIL MAX DO BEGIN
INTEGER I;
LONG REAL P;
FOR I := 0 STEP 1 UNTIL LPRIMES.SIZE-1 DO BEGIN
P := LPRIMES.ELEMENT(I);
IF (X / P) = ENTIER(X / P) THEN GOTO BREAK;
END;
LPRIMES.APPEND(X);
BREAK:
END;
END;
RETURN:
GET_PRIMES :- LPRIMES;
END GET_PRIMES;
INTEGER MAXSUM, I, S, PRI, TOTAL, DI;
REF(LIST_OF_REALLIST) DESCENDANTS, ANCESTORS;
REF(LIST_OF_REAL) PRIMES, LR, LRS;
LONG REAL P, D, PR;
BOOLEAN TAKEWHILE;
MAXSUM := 99;
DESCENDANTS :- NEW LIST_OF_REALLIST;
ANCESTORS :- NEW LIST_OF_REALLIST;
FOR I := 0 STEP 1 UNTIL MAXSUM DO BEGIN
DESCENDANTS.APPEND(NEW LIST_OF_REAL);
ANCESTORS .APPEND(NEW LIST_OF_REAL);
END;
PRIMES :- GET_PRIMES(MAXSUM);
FOR I := 0 STEP 1 UNTIL PRIMES.SIZE-1 DO
BEGIN
P := PRIMES.ELEMENT(I);
DESCENDANTS.ELEMENT(P).APPEND(P);
FOR S := 1 STEP 1 UNTIL DESCENDANTS.SIZE-P-1 DO
BEGIN
LRS :- DESCENDANTS.ELEMENT(S);
FOR PRI := 0 STEP 1 UNTIL LRS.SIZE-1 DO
BEGIN
PR := LRS.ELEMENT(PRI);
DESCENDANTS.ELEMENT(S + P).APPEND(P * PR);
END;
END;
END;
FOR I := 0 STEP 1 UNTIL PRIMES.SIZE-1 DO
BEGIN
P := PRIMES.ELEMENT(I);
DESCENDANTS.ELEMENT(P).POP;
END;
DESCENDANTS.ELEMENT(4).POP;
TOTAL := 0;
FOR S := 1 STEP 1 UNTIL MAXSUM DO
BEGIN
LRS :- DESCENDANTS.ELEMENT(S);
LRS.SORT;
FOR DI := 0 STEP 1 UNTIL LRS.SIZE-1 DO
BEGIN
D := LRS.ELEMENT(DI);
IF D <= MAXSUM THEN
BEGIN
REF(LIST_OF_REAL) ANCD;
ANCD :- NEW LIST_OF_REAL;
ANCD.APPENDALL(ANCESTORS.ELEMENT(S));
ANCD.APPEND(S);
ANCESTORS.SETELEMENT(D, NEW REALLISTITEM(ANCD));
END
ELSE GOTO BREAK;
END;
BREAK:
OUTTEXT("[");
OUTINT(S, 0);
OUTTEXT("] LEVEL: ");
OUTINT(ANCESTORS.ELEMENT(S).SIZE, 0);
OUTIMAGE;
OUTTEXT("ANCESTORS: ");
ANCESTORS.ELEMENT(S).OUTLIST;
OUTIMAGE;
OUTTEXT("DESCENDANTS: ");
OUTINT(LRS.SIZE,0);
OUTIMAGE;
LRS.OUTLIST;
OUTIMAGE;
OUTIMAGE;
TOTAL := TOTAL + LRS.SIZE;
END;
OUTTEXT("TOTAL DESCENDANTS ");
OUTINT(TOTAL, 0);
OUTIMAGE;
END.</lang>
- Output:
[1] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 0 [] [2] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 0 [] [3] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 0 [] [4] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 0 [] [5] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 1 [6] [6] LEVEL: 1 ANCESTORS: [5] DESCENDANTS: 2 [8, 9] [7] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 2 [10, 12] [8] LEVEL: 2 ANCESTORS: [5, 6] DESCENDANTS: 3 [15, 16, 18] [9] LEVEL: 2 ANCESTORS: [5, 6] DESCENDANTS: 4 [14, 20, 24, 27] [10] LEVEL: 1 ANCESTORS: [7] DESCENDANTS: 5 [21, 25, 30, 32, 36] [11] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 5 [28, 40, 45, 48, 54] [12] LEVEL: 1 ANCESTORS: [7] DESCENDANTS: 7 [35, 42, 50, ..., 64, 72, 81] [13] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 8 [22, 56, 63, ..., 90, 96, 108] [14] LEVEL: 3 ANCESTORS: [5, 6, 9] DESCENDANTS: 10 [33, 49, 70, ..., 135, 144, 162] [15] LEVEL: 3 ANCESTORS: [5, 6, 8] DESCENDANTS: 12 [26, 44, 105, ..., 192, 216, 243] ..... [96] LEVEL: 1 ANCESTORS: [13] DESCENDANTS: 31246 [623, 890, 1068, ..., 1464114717117504, 1647129056757192, 1853020188851841] [97] LEVEL: 0 ANCESTORS: [] DESCENDANTS: 33438 [1335, 1424, 1602, ..., 2058911320946490, 2196172075676256, 2470693585135788] [98] LEVEL: 4 ANCESTORS: [5, 6, 8, 16] DESCENDANTS: 35772 [1246, 1501, 1780, ..., 3088366981419735, 3294258113514384, 3706040377703682] [99] LEVEL: 1 ANCESTORS: [17] DESCENDANTS: 38257 [194, 1869, 2225, ..., 4392344151352512, 4941387170271576, 5559060566555523] TOTAL DESCENDANTS 546986
Visual Basic .NET
It is based on the same logic as the Python script. <lang vbnet>Imports System.Math
Module Module1
Const MAXPRIME = 99 ' upper bound for the prime factors Const MAXPARENT = 99 ' greatest parent number
Const NBRCHILDREN = 547100 ' max number of children (total descendants)
Public Primes As New Collection() ' table of the prime factors Public PrimesR As New Collection() ' table of the prime factors in reversed order Public Ancestors As New Collection() ' table of the parent's ancestors
Public Parents(MAXPARENT + 1) As Integer ' index table of the root descendant (per parent) Public CptDescendants(MAXPARENT + 1) As Integer ' counter table of the descendants (per parent) Public Children(NBRCHILDREN) As ChildStruct ' table of the whole descendants Public iChildren As Integer ' max index of the Children table
Public Delimiter As String = ", "
Public Structure ChildStruct
Public Child As Long
Public pLower As Integer
Public pHigher As Integer
End Structure
Sub Main()
Dim Parent As Short
Dim Sum As Short
Dim i As Short
Dim TotDesc As Integer = 0
Dim MidPrime As Integer
If GetPrimes(Primes, MAXPRIME) = vbFalse Then
Return
End If
For i = Primes.Count To 1 Step -1
PrimesR.Add(Primes.Item(i))
Next
MidPrime = PrimesR.Item(1) / 2
For Each Prime In PrimesR
Parents(Prime) = InsertChild(Parents(Prime), Prime)
CptDescendants(Prime) += 1
If Prime > MidPrime Then
Continue For
End If
For Parent = 1 To MAXPARENT
Sum = Parent + Prime
If Sum > MAXPARENT Then
Exit For
End If
If Parents(Parent) Then
InsertPreorder(Parents(Parent), Sum, Prime)
CptDescendants(Sum) += CptDescendants(Parent)
End If
Next
Next
RemoveFalseChildren()
If MAXPARENT > MAXPRIME Then
If GetPrimes(Primes, MAXPARENT) = vbFalse Then
Return
End If
End If
FileOpen(1, "Ancestors.txt", OpenMode.Output)
For Parent = 1 To MAXPARENT
GetAncestors(Parent)
PrintLine(1, "[" & Parent.ToString & "] Level: " & Ancestors.Count.ToString)
If Ancestors.Count Then
Print(1, "Ancestors: " & Ancestors.Item(1).ToString)
For i = 2 To Ancestors.Count
Print(1, ", " & Ancestors.Item(i).ToString)
Next
PrintLine(1)
Ancestors.Clear()
Else
PrintLine(1, "Ancestors: None")
End If
If CptDescendants(Parent) Then
PrintLine(1, "Descendants: " & CptDescendants(Parent).ToString)
Delimiter = ""
PrintDescendants(Parents(Parent))
PrintLine(1)
TotDesc += CptDescendants(Parent)
Else
PrintLine(1, "Descendants: None")
End If
PrintLine(1)
Next
Primes.Clear()
PrimesR.Clear()
PrintLine(1, "Total descendants " & TotDesc.ToString)
PrintLine(1)
FileClose(1)
End Sub
Function InsertPreorder(_index As Integer, _sum As Short, _prime As Short)
Parents(_sum) = InsertChild(Parents(_sum), Children(_index).Child * _prime)
If Children(_index).pLower Then
InsertPreorder(Children(_index).pLower, _sum, _prime)
End If
If Children(_index).pHigher Then
InsertPreorder(Children(_index).pHigher, _sum, _prime)
End If
Return Nothing
End Function
Function InsertChild(_index As Integer, _child As Long) As Integer
If _index Then
If _child <= Children(_index).Child Then
Children(_index).pLower = InsertChild(Children(_index).pLower, _child)
Else
Children(_index).pHigher = InsertChild(Children(_index).pHigher, _child)
End If
Else
iChildren += 1
_index = iChildren
Children(_index).Child = _child
Children(_index).pLower = 0
Children(_index).pHigher = 0
End If
Return _index
End Function
Function RemoveFalseChildren()
Dim Exclusions As New Collection
Exclusions.Add(4)
For Each Prime In Primes
Exclusions.Add(Prime)
Next
For Each ex In Exclusions
Parents(ex) = Children(Parents(ex)).pHigher
CptDescendants(ex) -= 1
Next
Exclusions.Clear()
Return Nothing
End Function
Function GetAncestors(_child As Short)
Dim Child As Short = _child
Dim Parent As Short = 0
For Each Prime In Primes
If Child = 1 Then
Exit For
End If
While Child Mod Prime = 0
Child /= Prime
Parent += Prime
End While
Next
If Parent = _child Or _child = 1 Then
Return Nothing
End If
GetAncestors(Parent)
Ancestors.Add(Parent)
Return Nothing
End Function
Function PrintDescendants(_index As Integer)
If Children(_index).pLower Then
PrintDescendants(Children(_index).pLower)
End If
Print(1, Delimiter.ToString & Children(_index).Child.ToString)
Delimiter = ", "
If Children(_index).pHigher Then
PrintDescendants(Children(_index).pHigher)
End If
Return Nothing
End Function
Function GetPrimes(ByRef _primes As Object, Optional _maxPrime As Integer = 2) As Boolean
Dim Value As Integer = 3
Dim Max As Integer
Dim Prime As Integer
If _maxPrime < 2 Then
Return vbFalse
End If
_primes.Add(2)
While Value <= _maxPrime
Max = Floor(Sqrt(Value))
For Each Prime In _primes
If Prime > Max Then
_primes.Add(Value)
Exit For
End If
If Value Mod Prime = 0 Then
Exit For
End If
Next
Value += 2
End While
Return vbTrue End Function
End Module</lang>
zkl
Using Extensible prime generator#zkl <lang zkl>const maxsum=99;
primes:=Utils.Generator(Import("sieve.zkl").postponed_sieve)
.pump(List,'wrap(p){ (p<=maxsum) and p or Void.Stop });
descendants,ancestors:=List()*(maxsum + 1), List()*(maxsum + 1);
foreach p in (primes){
descendants[p].insert(0,p);
foreach s in ([1..descendants.len() - p - 1]){
descendants[s + p].merge(descendants[s].apply('*(p)));
}
}
// descendants[prime] is a list that starts with prime, remove prime. 4: ???
foreach p in (primes + 4) { descendants[p].pop(0) }
ta,td:=0,0; foreach s in ([1..maxsum]){
foreach d in (descendants[s].filter('<=(maxsum))){
ancestors[d]=ancestors[s].copy() + s;
}
println("%2d Ancestors: ".fmt(s),ancestors[s].len() and ancestors[s] or "None");
println(" Descendants: ", if(z:=descendants[s])
String(z.len()," : ",z) else "None");
ta+=ancestors[s].len(); td+=descendants[s].len();
} println("Total ancestors: %,d".fmt(ta)); println("Total descendants: %,d".fmt(td));</lang>
- Output:
1 Ancestors: None Descendants: None 2 Ancestors: None Descendants: None 3 Ancestors: None Descendants: None 4 Ancestors: None Descendants: None 5 Ancestors: None Descendants: 1 : L(6) 6 Ancestors: L(5) Descendants: 2 : L(8,9) 7 Ancestors: None Descendants: 2 : L(10,12) 8 Ancestors: L(5,6) Descendants: 3 : L(15,16,18) 9 Ancestors: L(5,6) Descendants: 4 : L(14,20,24,27) 10 Ancestors: L(7) Descendants: 5 : L(21,25,30,32,36) 11 Ancestors: None Descendants: 5 : L(28,40,45,48,54) 12 Ancestors: L(7) Descendants: 7 : L(35,42,50,60,64,72,81) 13 Ancestors: None Descendants: 8 : L(22,56,63,75,80,90,96,108) 14 Ancestors: L(5,6,9) Descendants: 10 : L(33,49,70,84,100,120,128,135,144,162) 15 Ancestors: L(5,6,8) Descendants: 12 : L(26,44,105,112,125,126,150,160,180,192,216,243) 18 Ancestors: L(5,6,8) Descendants: 19 : L(65,77,78,110,132,196,280,315,336,375,378,400,450,480,512,540,576,648,729) 46 Ancestors: L(7,10,25) Descendants: 557 : L(129,205,246,493,518,529,740,806,888,999,1364,1508,1748,2552,2871,3128,3255,3472,3519,3875,...) 99 Ancestors: L(17) Descendants: 38257 : L(194,1869,2225,2670,2848,3204,3237,4029,4565,5037,5478,5829,6549,6837,7189,8134,8165,9709,9798,10270,...) Total ancestors: 179 Total descendants: 546,986