hdu 2874 Connections between cities（LCA）

最新推荐文章于 2020-04-29 02:02:20 发布

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本文介绍了一种用于解决城市间连接问题的算法实现，通过构建图数据结构并使用深度优先搜索、最近公共祖先（LCA）查找等技术，快速判断任意两城市是否相连及计算最短距离。

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题目链接：hdu 2874 Connections between cities

代码

#include <cstdio>
#include <cstring>
#include <vector>
#include <queue>
#include <algorithm>

using namespace std;
typedef pair<int,int> pii;
const int maxn = 10005;
const int inf = 0x3f3f3f3f;
const int BIT = 20;

int dep[maxn], far[maxn][BIT+5];
vector<pii> G[maxn];
queue<int> que;

void ST (int n) {
    for (int k = 1; k <= BIT; k++) {
        for (int i = 1; i <= n; i++) 
            far[i][k] = far[far[i][k-1]][k-1];
    }

    memset(dep, inf, sizeof(dep));
    for (int i = 1; i <= n; i++) if (far[i][0] == 0) {
        dep[i] = 0; que.push(i);
    }

    while (!que.empty()) {
        int u = que.front();
        que.pop();

        for (int i = 0; i < G[u].size(); i++) {
            int v = G[u][i].first;
            if (dep[v] > dep[u] + 1) {
                dep[v] = dep[u] + 1;
                que.push(v);
            }
        }
    }
}

int LCA(int u, int v) {
    if (dep[u] > dep[v]) swap(u, v);

    int mv = dep[v] - dep[u];
    for (int i = 0; i <= BIT && mv; mv >>= 1, i++)
        if (mv&1) v = far[v][i];

    if (u == v) return u;

    for (int i = BIT; i >= 0; i--) {
        if (far[u][i] == far[v][i]) continue;
        u = far[u][i]; v = far[v][i];
    }
    return far[u][0];
}

int N, M, Q, f[maxn];
long long dis[maxn];

int find (int x) { return x == f[x] ? x : f[x] = find(f[x]); }

void dfs (int u, int fa) {
    far[u][0] = fa;

    for (int i = 0; i < G[u].size(); i++) {
        int v = G[u][i].first, w = G[u][i].second;
        if (v == fa) continue;
        dis[v] = dis[u] + w;
        dfs(v, u);
    }
}

void init () {
    memset(dis, 0, sizeof(dis));
    for (int i = 1; i <= N; i++) {
        f[i] = i; far[i][0] = 0;
        G[i].clear();
    }

    int u, v, w;
    while (M--) {
        scanf("%d%d%d", &u, &v, &w);
        G[u].push_back(make_pair(v, w));
        G[v].push_back(make_pair(u, w));
        int p = find(u), q = find(v);
        if (p != q) f[p] = q;
    }
}

int main () {
    while (scanf("%d%d%d", &N, &M, &Q) == 3) {
        init();
        for (int i = 1; i <= N; i++)
            if (far[i][0] == 0) dfs(i, 0);
        ST(N);

        int u, v;
        while (Q--) {
            scanf("%d%d", &u, &v);
            if (find(u) != find(v)) printf("Not connected\n");
            else {
                int k = LCA(u, v);
                printf("%lld\n", dis[u] + dis[v] - 2 * dis[k]);
            }
        }
    }
    return 0;
}