UVA 11721 Instant View of Big Bang（负环）

题意:

n<=1000,m<=2000的有向图,无自环,无重边,求所有能到达负环的点集合,升序输出,不存在输出impossible

分析:

−−不知道为啥正向搜一直RE,把oj测爆了也没找到

考虑逆向思考问题,负环能到达的点,构建逆图,逆图的负环当然也是原图的负环

然后找到负环去搜所有能到达的点,标记保证复杂度,问题解决

复杂度O(nm)

代码:

//
//  Created by TaoSama on 2015-11-22
//  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>
#include <ctime>

using namespace std;
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
const int N = 1e3 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const int M = 2e3 + 10;

int n, m;
struct Edge {
int v, nxt, c;
} edge[M];
int head
, cnt;

void addEdge(int u, int v, int c) {
edge[cnt] = (Edge) {v, head[u], c};
head[u] = cnt++;
}

bool in
, vis
;
int dp
, num
, negative;

void dfs(int u) {
vis[u] = true;
for(int i = head[u]; ~i; i = edge[i].nxt) {
int v = edge[i].v;
if(vis[v]) continue;
dfs(v);
}
}

void spfa(int s) {
queue<int> q; q.push(s);
memset(dp, 0x3f, sizeof dp);
memset(in, false, sizeof in);
memset(num, 0, sizeof num);
in[s] = num[s] = 1; dp[s] = 0;
while(q.size()) {
int u = q.front(); q.pop();
in[u] = false;
for(int i = head[u]; ~i; i = edge[i].nxt) {
int v = edge[i].v;
if(vis[v]) continue;
if(dp[v] > dp[u] + edge[i].c) {
dp[v] = dp[u] + edge[i].c;
if(!in[v]) {
in[v] = true;
if(++num[v] >= n) {
negative = true;
dfs(v);
}
q.push(v);
}
}
}
}
}

int main() {
#ifdef LOCAL
freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);
//  freopen("C:\\Users\\TaoSama\\Desktop\\in.txt","w",stdout);
#endif
ios_base::sync_with_stdio(0);

int t; scanf("%d", &t);
int kase = 0;
while(t--) {
cnt = 0; memset(head, -1, sizeof head);
scanf("%d%d", &n, &m);
while(m--) {
int u, v, c; scanf("%d%d%d", &u, &v, &c);
addEdge(v, u, c);  //reversing graph, cycle to point
}

negative = false;
memset(vis, false, sizeof vis);
for(int i = 0; i < n; ++i) {
if(vis[i]) continue;
spfa(i);
}

if(!negative) {
printf("Case %d: impossible\n", ++kase);
continue;
}
printf("Case %d:", ++kase);
for(int i = 0; i < n; ++i) if(vis[i]) printf(" %d", i);
puts("");
}
return 0;
}