AT5014 Random Tournament

https://www.luogu.com.cn/problem/AT5014

感觉是经典套路题，不过不知道为啥luogu没什么人做

考虑即$L[l][r]$表示$l$能在$[l,r]$中胜出
$R[l][r]$同理

考虑怎么转移
枚举一个$k\in [l+1,r]$
显然如果$l$能战胜$k$且$k$能在$[l+1,r]$中胜出，那么$l$就能在$[l,r]$中胜出
$R$同理

用bitset优化即可

code:

#include<bits/stdc++.h>
#define N 2050
using namespace std;
int n;
bitset<N> L[N], R[N], a[N]; 
int main() {
    scanf("%d", &n);
    for(int i = 1; i <= n; i ++) {
        for(int j = 1; j < i; j ++) {
            char ch;
            scanf(" %c", &ch);
            if(ch == '1') a[i][j] = 1;
            a[j][i] = a[i][j] ^ 1; 
        }
    }

    for(int i = 1; i <= n; i ++) L[i][i] = R[i][i] = 1;
    for(int len = 2; len <= n; len ++) {
        for(int i = 1; i + len - 1 <= n; i ++) {
            int j = i + len - 1;    
            L[j][i] = (L[j] & a[i] & R[i + 1]).count() > 0;
            R[i][j] = (R[i] & a[j] & L[j - 1]).count() > 0;
        }

    }
    int ans = 0;
    for(int i = 1; i <= n; i ++) ans += (L[n][i] & R[1][i]);
    printf("%d", ans);
    return 0;
}