HDU 4005 The war（tarjan bcc + dp）

题意:

N<=105,M<=105的无向图,现在有可能在任意位置新建一条边,我们要删掉一条边使得图不连通,求最小花费

分析:

bcc肯定不能删边,所以先bcc缩点成树,树边都是桥都可以删除
但是怎么删除呢−−最小那条边一定会被新建的边形成的环(bcc)包括进去,懒得说了,别人写的挺清楚的
别人的题解
虽说画图可以帮助解这个题,我鬼画符了一晚上也没发现这个规律,鬼画符之前要先猜啊

代码:

////  Created by TaoSama on 2015-11-24//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;const int M = 2e5 + 10;int n, m;struct Edge {    int v, nxt, c;} edge[M], raw[M];int head[N], rawHead[N], cnt;void addRawEdge(int u, int v, int c) {    raw[cnt] = (Edge) {v, rawHead[u], c};    rawHead[u] = cnt++;    raw[cnt] = (Edge) {u, rawHead[v], c};    rawHead[v] = cnt++;}void addEdge(int u, int v, int c) {    edge[cnt] = (Edge) {v, head[u], c};    head[u] = cnt++;}int dfn[N], low[N], in[N], id[N], bcc, dfsNum;int stk[N], top;void tarjan(int u, int f) {    dfn[u] = low[u] = ++dfsNum;    stk[++top] = u;    in[u] = true;    for(int i = rawHead[u]; ~i; i = raw[i].nxt) {        int v = raw[i].v;        if(i == (f ^ 1)) continue;        if(!dfn[v]) {            tarjan(v, i);            low[u] = min(low[u], low[v]);        } else if(in[v]) low[u] = min(low[u], dfn[v]);    }    if(low[u] == dfn[u]) {        ++bcc;        while(true) {            int v = stk[top--];            in[v] = false;            id[v] = bcc;            if(v == u) break;        }    }}void init() {    bcc = dfsNum = 0;    memset(dfn, 0, sizeof dfn);}int ans, dp[N][2]; //0->minimum 1->minorvoid dfs(int u, int f) {    dp[u][0] = dp[u][1] = INF;    for(int i = head[u]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(v == f) continue;        dfs(v, u);        dp[u][1] = min(dp[u][1], dp[v][0]);        dp[u][1] = min(dp[u][1], edge[i].c);        if(dp[u][1] < dp[u][0]) swap(dp[u][1], dp[u][0]);    }    ans = min(ans, dp[u][1]);}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif//    ios_base::sync_with_stdio(0);    while(scanf("%d%d", &n, &m) == 2) {        cnt = 0; memset(rawHead, -1, sizeof rawHead);        while(m--) {            int u, v, c; scanf("%d%d%d", &u, &v, &c);            addRawEdge(u, v, c);        }        init();        tarjan(1, -1);        cnt = 0; memset(head, -1, sizeof head);        int a, b, minE = INF;        for(int i = 1; i <= n; ++i) {            int u = id[i];            for(int j = rawHead[i]; ~j; j = raw[j].nxt) {                int v = id[raw[j].v];                if(u == v) continue;                addEdge(u, v, raw[j].c);                if(raw[j].c < minE) {                    minE = raw[j].c;                    a = u, b = v;                }            }        }        ans = INF;        dfs(a, b);        dfs(b, a);        if(ans == INF) ans = -1;        printf("%d\n", ans);    }    return 0;}