UVALive 4960Sensor network（MST+LCA）

题意:

给定N≤350的一个图,求所有MST中最大边−最小边的最小值

分析:

对边排序后,一条一条的加边,成环了就删去环上的最小边
因为加进来的边一定是最大边,减去新的最小边不断更新答案即可

代码:

////  Created by TaoSama on 2015-11-11//  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 = 350 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;const int M = 1e5 + 10;int n, m;struct Edge {    int u, v, c;    Edge() {}    Edge(int u, int v, int c): u(u), v(v), c(c) {}    bool operator< (const Edge& rhs) const {        return c < rhs.c;    }} edge[M];int dis[N][N], vis[N], fa[N], cnt;int lca(int u, int v) {    memset(vis, false, sizeof vis);    while(!vis[u] && u != fa[u]) vis[u] = true, u = fa[u];    vis[u] = true;    while(!vis[v] && v != fa[v]) v = fa[v];    if(!vis[v]) return -1;    return v;}void findCycle(int i) {    int u = edge[i].u, v = edge[i].v;    int _lca = lca(u, v);//  prln(_lca);    if(_lca == -1) return;    int fu = fa[u], minv = INF, to = -1;    while(u != _lca && u != fu) {        if(dis[u][fu] < minv) minv = dis[u][fu], to = u;        u = fu;        fu = fa[fu];    }    int fv = fa[v];    while(v != _lca && v != fv) {        if(dis[v][fv] < minv) minv = dis[v][fv], to = v;        v = fv;        fv = fa[fv];    }    fa[to] = to; //delete the minimum edge in the cycle;    --cnt;}int tmp[N];void addEdge(int i) {    int u = edge[i].u, v = edge[i].v;    if(u == fa[u]) fa[u] = v;    else if(v == fa[v]) fa[v] = u;    else {        int cc = 0;        while(u != fa[u]) tmp[++cc] = u, u = fa[u];        tmp[++cc] = u;        for(int i = cc; i > 1; --i) fa[tmp[i]] = tmp[i - 1];        fa[edge[i].u] = edge[i].v;    }    ++cnt;}int getMinEdge() {    int ret = INF;    for(int i = 1; i <= n; ++i)        if(i != fa[i]) ret = min(ret, dis[i][fa[i]]);    return ret;}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", &n) == 1 && n) {        scanf("%d", &m);        for(int i = 1; i <= m; ++i) {            int u, v, c; scanf("%d%d%d", &u, &v, &c);            ++u; ++v;            dis[u][v] = dis[v][u] = c;            edge[i] = Edge(u, v, c);        }        sort(edge + 1, edge + 1 + m);        cnt = 0;        int ans = INF;        for(int i = 1; i <= n; ++i) fa[i] = i;        for(int i = 1; i <= m; ++i) {            findCycle(i);            addEdge(i);            int minEdge = getMinEdge();//          pr(cnt); prln(minEdge);            if(cnt == n - 1) ans = min(ans, edge[i].c - minEdge);        }        printf("%d\n", ans);    }    return 0;}