Task: Taxicab numbers



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++;
            }
        }
    }
}


Go: package main

import (
	"container/heap"
	"fmt"
	"strings"
)

type CubeSum struct {
	x, y  uint16
	value uint64
}

func (c *CubeSum) fixvalue() { c.value = cubes[c.x] + cubes[c.y] }

type CubeSumHeap []*CubeSum

func (h CubeSumHeap) Len() int            { return len(h) }
func (h CubeSumHeap) Less(i, j int) bool  { return h[i].value < h[j].value }
func (h CubeSumHeap) Swap(i, j int)       { h[i], h[j] = h[j], h[i] }
func (h *CubeSumHeap) Push(x interface{}) { (*h) = append(*h, x.(*CubeSum)) }
func (h *CubeSumHeap) Pop() interface{} {
	x := (*h)[len(*h)-1]
	*h = (*h)[:len(*h)-1]
	return x
}

type TaxicabGen struct {
	n int
	h CubeSumHeap
}

var cubes []uint64 
func cubesExtend(i int) {
	for n := uint64(len(cubes)); n <= uint64(i); n++ {
		cubes = append(cubes, n*n*n)
	}
}

func (g *TaxicabGen) min() CubeSum {
	for len(g.h) == 0 || g.h[0].value > cubes[g.n] {
		g.n++
		cubesExtend(g.n)
		heap.Push(&g.h, &CubeSum{uint16(g.n), 1, cubes[g.n] + 1})
	}
	
	c := *(g.h[0])
	if c.y+1 <= c.x {
		
		g.h[0].y++
		g.h[0].fixvalue()
		heap.Fix(&g.h, 0)
	} else {
		heap.Pop(&g.h)
	}
	return c
}



type Taxicab []CubeSum

func (t Taxicab) String() string {
	var b strings.Builder
	fmt.Fprintf(&b, "%12d", t[0].value)
	for _, p := range t {
		fmt.Fprintf(&b, " =%5d³ +%5d³", p.x, p.y)
	}
	return b.String()
}

func (g *TaxicabGen) Next() Taxicab {
	a, b := g.min(), g.min()
	for a.value != b.value {
		a, b = b, g.min()
	}
	

	
	
	
	
	
	
	
	
	t := Taxicab{a, b}
	for g.h[0].value == b.value {
		t = append(t, g.min())
	}
	return t
}

func main() {
	const (
		low  = 25
		mid  = 2e3
		high = 4e4
	)
	var tg TaxicabGen
	firstn := 3 
	for i := 1; i <= high+6; i++ {
		t := tg.Next()
		switch {
		case len(t) >= firstn:
			firstn++
			fallthrough
		case i <= low || (mid <= i && i <= mid+6) || i >= high:
			
			fmt.Printf("%5d: %v\n", i, t)
		}
	}
}