「TJOI2018」智力竞赛
题解好难看啊。。。
就是求可重路径覆盖之后最大化剩余点的最小权值
二分答案后就是一个可重复路径覆盖
处理出可达点做二分图匹配就好了
#include<cstdio> #include<cstring> #include<algorithm> #define gc getchar() #define pc putchar inline int read() { int x = 0,f = 1; char c = getchar(); while(c < '0' || c > '9') c = gc; while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = gc; return x * f; } void print(int x) { if(x < 0) { pc('-'); x = -x; } if(x >= 10) print(x / 10); pc(x % 10 + '0'); } const int maxn = 507; int n,m; bool mp[maxn][maxn]; int val[maxn]; int a[maxn]; void floyd() { for(int k = 1;k <= n;++ k) for(int i = 1;i <= n;++ i) for(int j = 1;j <= n;++ j) mp[i][j] |= mp[i][k] & mp[k][j]; } int vis[maxn]; int tot = 0; int bel[maxn]; bool find(int x,int fa) { for(int i = 1;i <= tot;++ i) { if(vis[i] != fa && mp[a[x]][a[i]]) { vis[i] = fa; if(!bel[i] || find(bel[i],fa)) { bel[i] = x; return true; } } } return false; } int check(int x) { tot = 0; for(int i = 1;i <= m;++ i) if(val[i] < x) //统计有效点有多少个 a[++ tot] = i; int ret = tot; memset(bel,0,sizeof bel); for(int i = 1;i <= tot;++ i) { if(find(i,i)) ret --; } return ret; //返回最小路径覆盖的值 } int main() { //freopen("contest2.in","r",stdin); n = read() + 1, m = read(); int mx = 0; for(int k,i = 1;i <= m;++ i) { val[i] = read(); mx = std::max(mx,val[i]); k = read(); for(int v,j = 1;j <= k;++ j) { v = read(); mp[i][v] = 1; } } floyd(); int ans = -1; int l = 1,r = mx; while(l <= r) { int mid = l + r >> 1; if(check(mid) <= n) //如果覆盖成功的话,则左边界可以再增加 l = mid + 1,ans = mid; else r = mid - 1; } if(l <= mx) print(ans),pc('\n'); else puts("AK"); return 0; }