Luogu P3868 [TJOI2009]猜数字

题目链接 (Click) (Here)

中国剩余定理的板子。小心取模。

#include <bits/stdc++.h>
using namespace std;

const int N = 11;
#define int long long


int n, M = 1, a[N], b[N], t[N], ans;

int fmul (int x, int y, int mod) {
	int res = 0;
	while (y) {
		if (y & 1) {
			res = (res + x) % mod;
		}
		x = (x + x) % mod;
		y >>= 1;
	}
	return res;
}

void exgcd (int a, int b, int &x, int &y) {
	if (b == 0) {x = 1, y = 0; return;}
	exgcd (b, a % b, x, y);
	int xx = y, yy = x - (a / b) * y;
    x = xx, y = yy;
}

signed main () {
	cin >> n;
	for (int i = 1; i <= n; ++i) cin >> a[i];
	for (int i = 1; i <= n; ++i) cin >> b[i];
	for (int i = 1; i <= n; ++i) a[i] = ((a[i] % b[i]) + b[i]) % b[i];
	for (int i = 1; i <= n; ++i) M *= b[i];
	for (int i = 1; i <= n; ++i) {
		exgcd (M / b[i], b[i], t[i], t[0]);
		t[i] = ((t[i] % b[i]) + b[i]) % b[i];
		ans = (ans + fmul (fmul (M / b[i], t[i], M), a[i], M)) % M; 
	}
	cout << ((ans % M) + M) % M << endl;
	
}