LightOJ - 1026 Critical Links(桥)

最新推荐文章于 2019-01-25 22:15:06 发布

原创最新推荐文章于 2019-01-25 22:15:06 发布 · 602 阅读

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本文介绍了一种求解无向图中桥的数量的方法。通过深度优先搜索算法(DFS)来确定图中的桥，并详细展示了从初始化图结构到深度遍历、记录关键路径的完整流程。最终输出所有关键链接。

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题目大意：给你一张无向图，问这张图中，桥的数量

解题思路：模版题

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 10010;
const int M = 100010;

struct Edge{
    int u, v, next;
    Edge() {}
    Edge(int u, int v, int next): u(u), v(v), next(next) {}
}E[M * 2];

struct Bridge {
    int u, v;
    Bridge() {}
    Bridge(int u, int v) {
        if (u > v) swap(u, v);
        this->u = u;
        this->v = v;
    }
}B[M * 2];

int head[N], dfn[N], lowlink[N];
int tot, n, dfs_clock, bridgeNum, cas = 1;

void AddEdge(int u, int v) {
    E[tot] = Edge(u, v, head[u]);
    head[u] = tot++;
    E[tot] = Edge(v, u, head[v]);
    head[v] = tot++;
}

void init() {
    memset(head, -1, sizeof(head));
    tot = 0;

    scanf("%d", &n);
    int u, k, v;
    for (int i = 0; i < n; i++) {
        scanf("%d (%d)", &u, &k);
        for (int j = 0; j < k; j++) {
            scanf("%d", &v);
            if (v < u) continue;
            AddEdge(u, v);
        }
    }
}

void dfs(int u, int fa) {
    dfn[u] = lowlink[u] = ++dfs_clock;
    for (int i = head[u]; ~i; i = E[i].next) {
        int v = E[i].v;
        if (!dfn[v]) {
            dfs(v, u);
            lowlink[u] = min(lowlink[u], lowlink[v]);
            if (lowlink[v] > dfn[u]) {
                B[++bridgeNum] = Bridge(u, v);
            }
        }
        else if (v != fa) lowlink[u] = min(dfn[v], lowlink[u]);
    }
}

bool cmp(const Bridge &a, const Bridge &b) {
    if (a.u == b.u)
        return a.v < b.v;
    return a.u < b.u;
}

void solve() {
    memset(dfn, 0, sizeof(dfn));
    dfs_clock = bridgeNum = 0;

    for (int i = 0; i < n; i++)
        if (!dfn[i]) dfs(i, -1);
    printf("Case %d:\n", cas++);
    printf("%d critical links\n", bridgeNum);
    sort(B + 1, B + 1 + bridgeNum, cmp);
    for (int i = 1; i <= bridgeNum; i++) 
        printf("%d - %d\n", B[i].u, B[i].v);
}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) {
        init();
        solve();
    }
    return 0;
}