Taxicab numbers: Difference between revisions

=={{header|C++}}==

{{trans|C#}}

<lang cpp>#include <algorithm>

#include <iomanip>

#include <iostream>

#include <map>

#include <sstream>

#include <vector>

template <typename T>

size_t indexOf(const std::vector<T> &v, const T &k) {

auto it = std::find(v.cbegin(), v.cend(), k);

if (it != v.cend()) {

return it - v.cbegin();

}

return -1;

}

int main() {

std::vector<size_t> cubes;

auto dump = [&cubes](const std::string &title, const std::map<int, size_t> &items) {

std::cout << title;

for (auto &item : items) {

std::cout << "\n" << std::setw(4) << item.first << " " << std::setw(10) << item.second;

for (auto x : cubes) {

auto y = item.second - x;

if (y < x) {

break;

}

if (std::count(cubes.begin(), cubes.end(), y)) {

std::cout << " = " << std::setw(4) << indexOf(cubes, y) << "^3 + " << std::setw(3) << indexOf(cubes, x) << "^3";

}

}

}

};

std::vector<size_t> sums;

// create sorted list of cube sums

for (size_t i = 0; i < 1190; i++) {

auto cube = i * i * i;

cubes.push_back(cube);

for (auto j : cubes) {

sums.push_back(cube + j);

}

}

std::sort(sums.begin(), sums.end());

// now seek consecutive sums that match

auto nm1 = sums[0];

auto n = sums[1];

int idx = 0;

std::map<int, size_t> task;

std::map<int, size_t> trips;

auto it = sums.cbegin();

auto end = sums.cend();

it++;

it++;

while (it != end) {

auto np1 = *it;

if (nm1 == np1) {

trips.emplace(idx, n);

}

if (nm1 != n && n == np1) {

if (++idx <= 25 || idx >= 2000 == idx <= 2006) {

task.emplace(idx, n);

}

}

nm1 = n;

n = np1;

it++;

}

dump("First 25 Taxicab Numbers, the 2000th, plus the next half-dozen:", task);

std::stringstream ss;

ss << "\n\nFound " << trips.size() << " triple Taxicabs under 2007:";

dump(ss.str(), trips);

return 0;

}</lang>

{{out}}

<pre>First 25 Taxicab Numbers, the 2000th, plus the next half-dozen:

1 1729 = 12^3 + 1^3 = 10^3 + 9^3

2 4104 = 16^3 + 2^3 = 15^3 + 9^3

3 13832 = 24^3 + 2^3 = 20^3 + 18^3

4 20683 = 27^3 + 10^3 = 24^3 + 19^3

5 32832 = 32^3 + 4^3 = 30^3 + 18^3

6 39312 = 34^3 + 2^3 = 33^3 + 15^3

7 40033 = 34^3 + 9^3 = 33^3 + 16^3

8 46683 = 36^3 + 3^3 = 30^3 + 27^3

9 64232 = 39^3 + 17^3 = 36^3 + 26^3

10 65728 = 40^3 + 12^3 = 33^3 + 31^3

11 110656 = 48^3 + 4^3 = 40^3 + 36^3

12 110808 = 48^3 + 6^3 = 45^3 + 27^3

13 134379 = 51^3 + 12^3 = 43^3 + 38^3

14 149389 = 53^3 + 8^3 = 50^3 + 29^3

15 165464 = 54^3 + 20^3 = 48^3 + 38^3

16 171288 = 55^3 + 17^3 = 54^3 + 24^3

17 195841 = 58^3 + 9^3 = 57^3 + 22^3

18 216027 = 60^3 + 3^3 = 59^3 + 22^3

19 216125 = 60^3 + 5^3 = 50^3 + 45^3

20 262656 = 64^3 + 8^3 = 60^3 + 36^3

21 314496 = 68^3 + 4^3 = 66^3 + 30^3

22 320264 = 68^3 + 18^3 = 66^3 + 32^3

23 327763 = 67^3 + 30^3 = 58^3 + 51^3

24 373464 = 72^3 + 6^3 = 60^3 + 54^3

25 402597 = 69^3 + 42^3 = 61^3 + 56^3

2000 1671816384 = 1168^3 + 428^3 = 944^3 + 940^3

2001 1672470592 = 1187^3 + 29^3 = 1124^3 + 632^3

2002 1673170856 = 1164^3 + 458^3 = 1034^3 + 828^3

2003 1675045225 = 1153^3 + 522^3 = 1081^3 + 744^3

2004 1675958167 = 1159^3 + 492^3 = 1096^3 + 711^3

2005 1676926719 = 1188^3 + 63^3 = 1095^3 + 714^3

2006 1677646971 = 1188^3 + 99^3 = 990^3 + 891^3

Found 10 triple Taxicabs under 2007:

455 87539319 = 436^3 + 167^3 = 423^3 + 228^3 = 414^3 + 255^3

535 119824488 = 493^3 + 11^3 = 492^3 + 90^3 = 428^3 + 346^3

588 143604279 = 522^3 + 111^3 = 460^3 + 359^3 = 423^3 + 408^3

655 175959000 = 560^3 + 70^3 = 552^3 + 198^3 = 525^3 + 315^3

888 327763000 = 670^3 + 300^3 = 661^3 + 339^3 = 580^3 + 510^3

1299 700314552 = 872^3 + 334^3 = 846^3 + 456^3 = 828^3 + 510^3

1398 804360375 = 930^3 + 15^3 = 927^3 + 198^3 = 920^3 + 295^3

1515 958595904 = 986^3 + 22^3 = 984^3 + 180^3 = 856^3 + 692^3

1660 1148834232 = 1044^3 + 222^3 = 920^3 + 718^3 = 846^3 + 816^3

1837 1407672000 = 1120^3 + 140^3 = 1104^3 + 396^3 = 1050^3 + 630^3</pre>