Data commit

Task/Taxicab-numbers/C/taxicab-numbers.c

@@ -0,0 +1,84 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+typedef unsigned long long xint;
+typedef unsigned uint;
+typedef struct {
+	uint x, y; // x > y always
+	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; // x = 0 or 1 is useless
+
+	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 };
+	// upheap
+	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];	// pq[0] always stores last seen value
+	if (++tmp.y >= tmp.x) {		// done with this x; throw it away
+		tmp = pq[pq_len--];
+		if (!pq_len) goto redo;	// refill empty heap
+	} else
+		tmp.value += cube[tmp.y] - cube[tmp.y-1];
+
+	uint i, j;
+	// downheap
+	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;
+}