Task: Taxicab numbers


C++: #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;

    
    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());

    
    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;
}


C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace TaxicabNumber
{
    class Program
    {
        static void Main(string[] args)
        {
            IDictionary<long, IList<Tuple<int, int>>> taxicabNumbers = GetTaxicabNumbers(2006);
            PrintTaxicabNumbers(taxicabNumbers);
            Console.ReadKey();
        }

        private static IDictionary<long, IList<Tuple<int, int>>> GetTaxicabNumbers(int length)
        {
            SortedList<long, IList<Tuple<int, int>>> sumsOfTwoCubes = new SortedList<long, IList<Tuple<int, int>>>();

            for (int i = 1; i < int.MaxValue; i++)
            {
                for (int j = 1; j < int.MaxValue; j++)
                {
                    long sum = (long)(Math.Pow((double)i, 3) + Math.Pow((double)j, 3));

                    if (!sumsOfTwoCubes.ContainsKey(sum))
                    {
                        sumsOfTwoCubes.Add(sum, new List<Tuple<int, int>>());
                    }

                    sumsOfTwoCubes[sum].Add(new Tuple<int, int>(i, j));

                    if (j >= i)
                    {
                        break;
                    }
                }

                
                if (sumsOfTwoCubes.Count(t => t.Value.Count >= 2) >= length * 1.1)
                {
                    break;
                }
            }

            IDictionary<long, IList<Tuple<int, int>>> values = (from t in sumsOfTwoCubes where t.Value.Count >= 2 select t)
                .Take(2006)
                .ToDictionary(u => u.Key, u => u.Value);

            return values;
        }

        private static void PrintTaxicabNumbers(IDictionary<long, IList<Tuple<int, int>>> values)
        {
            int i = 1;

            foreach (long taxicabNumber in values.Keys)
            {
                StringBuilder output = new StringBuilder().AppendFormat("{0,10}\t{1,4}", i, taxicabNumber);

                foreach (Tuple<int, int> numbers in values[taxicabNumber])
                {
                    output.AppendFormat("\t= {0}^3 + {1}^3", numbers.Item1, numbers.Item2);
                }

                if (i <= 25 || (i >= 2000 && i <= 2006))
                {
                    Console.WriteLine(output.ToString());
                }

                i++;
            }
        }
    }
}