Arithmetic derivative: Difference between revisions
Nim solution
(Added C) |
(Nim solution) |
||
Line 618:
D for 10^19 divided by 7 is 19000000000000000000
D for 10^20 divided by 7 is 200000000000000000000
</pre>
=={{header|Nim}}==
{{libheader|Nim-Integers}}
<syntaxhighlight lang="Nim">import std/[strformat, strutils]
import integers
func aDerivative(n: int | Integer): typeof(n) =
## Recursively compute the arithmetic derivative.
## The function works with normal integers or big integers.
## Using a cache to store the derivatives would improve the
## performance, but this is not needed for these tasks.
if n < 0: return -aDerivative(-n)
if n == 0 or n == 1: return 0
if n == 2: return 1
var d = 2
result = 1
while d * d <= n:
if n mod d == 0:
let q = n div d
result = q * aDerivative(d) + d * aDerivative(q)
break
inc d
### Task ###
echo "Arithmetic derivatives for -99 through 100:"
# We can use an "int" variable here.
var col = 0
for n in -99..100:
inc col
stdout.write &"{aDerivative(n):>4}"
stdout.write if col == 10: '\n' else: ' '
if col == 10: col = 0
### Stretch task ###
echo()
# To avoid overflow, we have to use an "Integer" variable.
var n = Integer(1)
for m in 1..20:
n *= 10
let a = aDerivative(n)
let left = &"D(10^{m}) / 7"
echo &"{left:>12} = {a div 7}"
</syntaxhighlight>
{{out}}
<pre>Arithmetic derivatives for -99 through 100:
-75 -77 -1 -272 -24 -49 -34 -96 -20 -123
-1 -140 -32 -45 -22 -124 -1 -43 -108 -176
-1 -71 -18 -80 -55 -39 -1 -156 -1 -59
-26 -72 -1 -61 -18 -192 -51 -33 -1 -92
-1 -31 -22 -92 -16 -81 -1 -56 -20 -45
-14 -112 -1 -25 -39 -48 -1 -41 -1 -68
-16 -21 -1 -60 -12 -19 -14 -80 -1 -31
-1 -32 -27 -15 -10 -44 -1 -13 -10 -24
-1 -21 -1 -32 -8 -9 -1 -16 -1 -7
-6 -12 -1 -5 -1 -4 -1 -1 0 0
0 1 1 4 1 5 1 12 6 7
1 16 1 9 8 32 1 21 1 24
10 13 1 44 10 15 27 32 1 31
1 80 14 19 12 60 1 21 16 68
1 41 1 48 39 25 1 112 14 45
20 56 1 81 16 92 22 31 1 92
1 33 51 192 18 61 1 72 26 59
1 156 1 39 55 80 18 71 1 176
108 43 1 124 22 45 32 140 1 123
20 96 34 49 24 272 1 77 75 140
D(10^1) / 7 = 1
D(10^2) / 7 = 20
D(10^3) / 7 = 300
D(10^4) / 7 = 4000
D(10^5) / 7 = 50000
D(10^6) / 7 = 600000
D(10^7) / 7 = 7000000
D(10^8) / 7 = 80000000
D(10^9) / 7 = 900000000
D(10^10) / 7 = 10000000000
D(10^11) / 7 = 110000000000
D(10^12) / 7 = 1200000000000
D(10^13) / 7 = 13000000000000
D(10^14) / 7 = 140000000000000
D(10^15) / 7 = 1500000000000000
D(10^16) / 7 = 16000000000000000
D(10^17) / 7 = 170000000000000000
D(10^18) / 7 = 1800000000000000000
D(10^19) / 7 = 19000000000000000000
D(10^20) / 7 = 200000000000000000000
</pre>
| |||