Ultraviolet A 10692-huge Mod (number theory)

Ultraviolet A 10692-huge mod

Question Link

Question: PleaseA0A1A2...MOD M

Idea: it is certainly not possible to calculate it directly. Use the Euler's theorem.AB=A(B MOD PHI(M) +PHI(M))(B> =PHI(M). Then, we can use the fast power to calculate the exponential value, and the calculation process is recursive.

Code:

#include <stdio.h>#include <string.h>const int N = 1005;int phi[N * 10], vis[N * 10], m, n, a[N];char M[15];int pow_mod(int x, int k, int mod) {int now = 1;for (int i = 0; i < k; i++) {if (x == 1) break;now *= x;if (now >= mod) break; } if (now >= mod) now = mod; else now = 0;if (k == 0) return 1;int ans = pow_mod(x * x % mod, k>>1, mod);if (k&1) ans = ans * x % mod;return ans + now;}int dfs(int i, int mod) {if (i == n - 1) { if (a[i] >= mod)   return a[i] % mod + mod;      return a[i];}int k = dfs(i + 1, phi[mod]);return pow_mod(a[i], k, mod);}int main() {for (int i = 1; i <= 10000; i++)phi[i] = i;for (int i = 2; i <= 10000; i++) {if (vis[i]) continue;for (int j = i; j <= 10000; j += i) {phi[j] = phi[j] / i * (i - 1);vis[j] = 1;  } } int cas = 0;while (~scanf("%s", M) && M[0] != '#') { sscanf(M, "%d", &m); scanf("%d", &n); for (int i = 0; i < n; i++) scanf("%d", &a[i]); printf("Case #%d: %d\n", ++cas, dfs(0, m) % m); }return 0;}