Link to the question: Ultraviolet A 10548-find the right changes
Given a, B, c, X, Y, so that Xa + Yb = C, how many solutions are there.
Solution: Expand Euclidean to ensure that X and Y are both greater than or equal to 0, and determine the value of T in the general solution.
#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;typedef long long ll;const ll INF = 0x3f3f3f3f3f3f3f;ll A, B, C;void gcd (ll a, ll b, ll& d, ll& x, ll& y) { if (b == 0) { d = a; x = 1; y = 0; } else { gcd(b, a%b, d, y, x); y -= (a/b) * x; }}void solve () { ll d, x, y; gcd(A, B, d, x, y); if (C % d) { printf("Impossible\n"); return; } ll up = INF, lower = -INF; if (B / d > 0) lower = max(lower, (ll)ceil( (-1.0*x*C) / B) ); else up = min(up, (ll)floor( (-1.0*x*C) / B) ); if (A / d > 0) up = min(up, (ll)floor( (1.0*y*C) / A)); else lower = max(lower, (ll)ceil( (1.0*y*C) / A)); if (up == INF || lower == -INF) printf("Infinitely many solutions\n"); else if (up < lower) printf("Impossible\n"); else printf("%lld\n", up - lower + 1);}int main () { int cas; scanf("%d", &cas); while (cas--) { scanf("%lld%lld%lld", &A, &B, &C); solve(); } return 0;}