P1396 营救(并查集+二分)

思路：检验函数中，先初始化每个节点的下标，每调用检验函数就从新使用一次并查集（并查集的时间复杂度非常低），然后，就看当一条路的价值val<=假设最大值x时，就把他们连接起来。

#include<iostream>
#include<algorithm>
using namespace std;

const int maxn = 1e4 + 10;
int n, m, s, t, st[maxn << 1], en[maxn << 1], val[maxn << 1];
int l = maxn, r, ans, mid, fa[maxn];
//并查集
int getfa(int x){
    if (fa[x] == x)return x;
    return fa[x] = getfa(fa[x]);
}
//并查集判断
bool find(int x, int y){
    return getfa(x) == getfa(y);
}
//并查集合并
void H_(int x, int y){
    if (!find(x, y))fa[getfa(x)] = fa[getfa(y)];
}
bool check(int x){
    for (int i = 1; i <= n; ++i)fa[i] = i;
    for (int i = 1; i <= m;++i)
    if (val[i] <= x)H_(st[i], en[i]);
    return find(s, t);
}

void half(){
    while (l <= r){
        mid = (l + r) >> 1;
        if (check(mid)){ ans = mid; r = mid - 1; }
        else l = mid + 1;
    }
}

int main(){
    cin >> n >> m >> s >> t;
    for (int i = 1; i <= m; ++i)
    {
        cin >> st[i] >> en[i] >> val[i];
        l = min(l, val[i]);    r = max(r, val[i]);
    }
    half();    //二分
    cout << ans << endl;
}