#include <stdio.h>
#include <stdlib.h>
 
/* see http://e...content-available-to-author-only...a.org/wiki/Permutation#Generation_in_lexicographic_order */
int permnext(char *p, int n) {
  int kh, k = -1;
  int lh, l = -1;
  char tmp;
 
  for (kh = 0; kh < n - 1; kh++) {
    if (p[kh] < p[kh + 1]) k = kh;
  }
  if (k == -1) return 1;
  for (lh = k + 1; lh < n; lh++) {
    if (p[k] < p[lh]) l = lh;
  }
  if (l == -1) {
    fprintf(stderr, "This didn't happen.\n");
    exit(EXIT_FAILURE);
  }
  tmp = p[k]; p[k] = p[l]; p[l] = tmp;
  l = k + 1;
  lh = n - 1;
  while (l < lh) {
    tmp = p[l]; p[l] = p[lh]; p[lh] = tmp;
    l++;
    lh--;
  }
  return 0;
}
 
void check(const char *p, int nda, int ndb, int ndc, int ndd) {
  int a = 0, b = 0, c = 0, d = 0;
  if (p[nda] == '0') return;
  if (p[nda + ndb] == '0') return;
  if (p[nda + ndb + ndc] == '0') return;
  while (nda--) { a *= 10; a += *p - '0'; p++; }
  while (ndb--) { b *= 10; b += *p - '0'; p++; }
  if (b < a) return;
  while (ndc--) { c *= 10; c += *p - '0'; p++; }
  if (c < a) return;
  while (ndd--) { d *= 10; d += *p - '0'; p++; }
  if (d < c) return;
  if (a*d + b*c == b*d) {
    printf("%d/%d + %d/%d = 1\n", a, b, c, d);
  }
}
 
int main(void) {
  char perm[] = "1023456789";
  do {
    check(perm, 1, 1, 1, 7);
    check(perm, 1, 1, 2, 6);
    check(perm, 1, 1, 3, 5);
    check(perm, 1, 1, 4, 4);
    check(perm, 1, 2, 1, 6);
    check(perm, 1, 2, 2, 5);
    check(perm, 1, 2, 3, 4);
    check(perm, 1, 3, 1, 5);
    check(perm, 1, 3, 2, 4);
    check(perm, 1, 3, 3, 3);
    check(perm, 1, 4, 1, 4);
    check(perm, 1, 4, 2, 3);
    check(perm, 1, 5, 1, 3);
    check(perm, 1, 5, 2, 2);
    check(perm, 1, 6, 1, 2);
    check(perm, 1, 7, 1, 1);
    check(perm, 2, 2, 2, 4);
    check(perm, 2, 2, 3, 3);
    check(perm, 2, 3, 2, 3);
    check(perm, 2, 4, 2, 2);
  } while (permnext(perm, 10) == 0);
  return 0;
}

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