luogu P1401 城市

题目链接

luogu P1401 城市

题解

二分最小边权,dinic检验

代码

// luogu-judger-enable-o2
/*
二分最小边权,dinic检验
*/
#include<queue>
#include<cctype>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
inline int read() {
    int x = 0,f = 1;
    char c = getchar();
    while(c < '0' || c > '9'){if(c == '-')f =- 1 , c = getchar(); }
    while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = getchar();
    return x * f;
}
#define INF 1e9 + 7
const int maxn = 40007;
struct node {
    int u,v,w,next;
    bool operator < (const node & a) const {
        return w < a.w;
    }
} e[maxn];
int head[maxn],num = 1;
struct Node {
    int v,flow,next;
} edge[maxn << 2];
inline void add_edge(int u,int v,int flow ) {
    edge[++ num].v = v;edge[num].next = head[u];head[u] = num; edge[num].flow = flow;
    edge[++ num].v = u;edge[num].next = head[v];head[v] = num; edge[num].flow = flow;
}
int cur[maxn];
int S = 1,T ;
int n,m,t;
std::queue<int>q;
int lev[maxn];
bool bfs() {
    for(int i = 0;i <= n;++ i) cur[i] = head[i];
    for(int i = 0;i <= n;++ i) lev[i] = -1;
    q.push(S),lev[S] = 0;
    while(!q.empty()) {
        int u = q.front(); q.pop();
        for(int i = head[u];i;i = edge[i].next)
            if(edge[i].flow > 0 && lev[edge[i].v] == -1) lev[edge[i].v] = lev[u] + 1,q.push(edge[i].v);
    }
    return lev[T] != -1;
}
int dfs(int now,int flow) {
    if(now == T) return flow;
    int rest = 0 , delta;
    for(int &i = cur[now];i;i = edge[i].next) {
        int v = edge[i].v;
        if(lev[v] != lev[now] + 1 || edge[i].flow <= 0) continue;
        delta = dfs(v,std::min(flow - rest,edge[i].flow));
        if(delta) {
            edge[i].flow -= delta;
            edge[i ^ 1].flow += delta;
            rest += delta; if(rest == flow) break;
        }
    }
    if(rest == flow) lev[now] = -1;
    return rest;
}
int dinic() {
    int ret = 0;
    while(bfs()) ret += dfs(S,INF);
    return ret;
}
bool check(int x) {
    num = 1;
    memset(head,0,sizeof head);
    for(int i = 1;i <= m;++ i)
        if(e[i].w <= x) add_edge(e[i].u,e[i].v,1);
        else break;
    return dinic() >= t;
}
int main() {
    n = read(),m = read(),t = read(); T = n;
    for(int i = 1;i <= m;++ i) e[i].u = read(), e[i].v = read(),e[i].w = read();
    std::sort(e + 1, e + m + 1);
    int l = 0,r = 100000007;
    int ans = -1;
    while(l <= r) {
        int mid = l + r >> 1;
        if(check(mid)) ans = mid , r = mid - 1;
        else l = mid + 1;
    }
    printf("%d\n",ans);
    return 0;
}