Task: Taxicab numbers
C: #include <stdio.h>
#include <stdlib.h>

typedef unsigned long long xint;
typedef unsigned uint;
typedef struct {
	uint x, y; 
	xint value;
} sum_t;

xint *cube;
uint n_cubes;

sum_t *pq;
uint pq_len, pq_cap;

void add_cube(void)
{
	uint x = n_cubes++;
	cube = realloc(cube, sizeof(xint) * (n_cubes + 1));
	cube[n_cubes] = (xint) n_cubes*n_cubes*n_cubes;
	if (x < 2) return; 

	if (++pq_len >= pq_cap) {
		if (!(pq_cap *= 2)) pq_cap = 2;
		pq = realloc(pq, sizeof(*pq) * pq_cap);
	}

	sum_t tmp = (sum_t) { x, 1, cube[x] + 1 };
	
	uint i, j;
	for (i = pq_len; i >= 1 && pq[j = i>>1].value > tmp.value; i = j)
		pq[i] = pq[j];

	pq[i] = tmp;
}

void next_sum(void)
{
redo:	while (!pq_len || pq[1].value >= cube[n_cubes]) add_cube();

	sum_t tmp = pq[0] = pq[1];	
	if (++tmp.y >= tmp.x) {		
		tmp = pq[pq_len--];
		if (!pq_len) goto redo;	
	} else
		tmp.value += cube[tmp.y] - cube[tmp.y-1];

	uint i, j;
	
	for (i = 1; (j = i<<1) <= pq_len; pq[i] = pq[j], i = j) {
		if (j < pq_len && pq[j+1].value < pq[j].value) ++j;
		if (pq[j].value >= tmp.value) break;
	}
	pq[i] = tmp;
}

uint next_taxi(sum_t *hist)
{
	do next_sum(); while (pq[0].value != pq[1].value);

	uint len = 1;
	hist[0] = pq[0];
	do {
		hist[len++] = pq[1]; 
		next_sum();
	} while (pq[0].value == pq[1].value);

	return len;
}

int main(void)
{
	uint i, l;
	sum_t x[10];
	for (i = 1; i <= 2006; i++) {
		l = next_taxi(x);
		if (25 < i && i < 2000) continue;
		printf("%4u:%10llu", i, x[0].value);
		while (l--) printf(" = %4u^3 + %4u^3", x[l].x, x[l].y);
		putchar('\n');
	}
	return 0;
}

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)
		}
	}
}