小红叒战小紫

小红叒战小紫_第1张图片

 概率dp

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#define ll long long
#define PII pair
#define TUP tuple
using namespace std;
const int N = 60;
const int mod = 1e9 + 7;

int ta[3], tb[3];
ll dp[60][60];//小红还有i张卡片1,小紫还有j张卡片1

ll inv(ll a) {
    ll ret = 1, b = mod - 2;
    while (b) {
        if (b % 2) ret = ret * a % mod;
        b >>= 1;
        a = a * a % mod;
    }
    return ret;
}

int main() {
    int n, m, x;
    cin >> n >> m;
    for (int i = 0; i < n; i++) cin >> x, ta[x]++;
    for (int i = 0; i < m; i++) cin >> x, tb[x]++;
    //dp[i][j] = p1 * dp[i - 1][j] + p2 * dp[i][j - 1];
    //dp[i][j] /= p1 + p2;
    dp[0][0] = 0;
    if (!ta[2] && !tb[2]) {
        cout << 0;
        return 0;
    }
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= m; j++) {
            ll p1 = i * inv(ta[2] + i) % mod * tb[2] % mod * inv(tb[2] + j) % mod;
            ll p2 = ta[2] * inv(ta[2] + i) % mod * j % mod * inv(tb[2] + j) % mod;
            dp[i][j] = dp[i - 1][j] * p1 % mod + p2 * dp[i][j - 1] % mod + 1;
            dp[i][j] *= inv(p1 + p2);
            dp[i][j] %= mod;
        }
    }
    cout << dp[ta[1]][tb[1]];
    return 0;
}

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