【USACO 2857】 Steady Cow Assignment

【题目链接】

点击打开链接

【算法】

二分答案，check的时候跑最大流，即可

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 2000
#define MAXB 1000

int i,j,low,high,mid,st,ed,N,B,tot,ans,tmp;
int h[MAXN+MAXB],U[MAXN*MAXB],V[MAXN*MAXB],
   W[MAXN*MAXB],Head[MAXN*MAXB],Next[MAXN*MAXB],
     other[MAXN*MAXB],v[MAXB+],a[MAXN+][MAXB+];

template <typename T> void read(T &x) {
        int f=; char c = getchar(); x=;
        for (; !isdigit(c); c = getchar()) { if (c=='-') f = -f; }
        for (; isdigit(c); c = getchar()) x=x*+c-'';
        x*=f;
}
template <typename T> inline void write(T x) {
        if (x < ) { putchar('-'); x = -x; }
        if (x > ) write(x/);
        putchar(x %  + '');
}

template <typename T> inline void writeln(T x) {
        write(x);
        puts("");
}

inline void add(int a,int b,int c) {
        ++tot;
        U[tot] = a; V[tot] = b; W[tot] = c;
        Next[tot] = Head[a]; Head[a] = tot;
        other[tot] = ++tot;
        U[tot] = b; V[tot] = a; W[tot] = ;
        Next[tot] = Head[b]; Head[b] = tot;
        other[tot] = tot - ;
}

inline bool bfs() {
        int i,x,y;
        queue<int> q;
        memset(h,,sizeof(h));
        h[st] = ; q.push(st);
        while (!q.empty()) {
                x = q.front(); q.pop();
                for (i = Head[x]; i; i = Next[i]) {
                        y = V[i];
                        if ((W[i] > ) && (!h[y])) {
                                h[y] = h[x] + ;
                                q.push(y);
                        }
                }
        }
        if (h[ed]) return true;
        else return false;
}

inline int maxflow(int x,int f) {
        int i,t,y,sum=;
        if (x == ed) return f;
        for (i = Head[x]; i; i = Next[i]) {
                y = V[i];
                if ((W[i] > ) && (h[y] == h[x] + ) && (sum < f)) {
                        sum += (t = maxflow(y,min(W[i],f-sum)));
                        W[i] -= t; W[other[i]] += t;
                }
        }
        if (!sum) h[x] = ;
        return sum;
}

inline bool check(int ml) {
        int i,j,l,r,sum;
        for (l = ; l <= N - ml + ; l++) {
                r = l + ml - ;
                for (i = ; i <= tot; i++) Head[i] = ;
                tot = ;
                for (i = ; i <= N; i++) add(st,i,);
                for (i = ; i <= B; i++) add(i+N,ed,v[i]);
                for (i = ; i <= N; i++) {
                        for (j = ; j <= B; j++) {
                                if ((a[i][j] >= l) && (a[i][j] <= r))
                                        add(i,j+N,);
                        }
                }
                sum = ;
                while (bfs()) {
                        sum += maxflow(st,N);
                }
                if (sum == N) return true;
        }
        return false;
}

int main() {

        read(N); read(B);
        st = N + B + ; ed = st + ;

        for (i = ; i <= N; i++) {
                for (j = ; j <= B; j++) {
                        read(tmp);
                        a[i][tmp] = j;
                }
        }
        for (i = ; i <= B; i++) read(v[i]);

        low = ; high = B;
        while (low <= high) {
                mid = (low + high) / ;
                if (check(mid)) {
                        high = mid - ;
                        ans = mid;
                } else
                        low = mid + ;
        }
        writeln(ans);

        return ;

}