ZOJ 3820:Building Fire Stations(樹的直徑 Grade C)

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題意：

n個點的樹，邊長全為1，求找出兩個點，使得樹上離這兩個點距離最遠的那個點，到這兩個點（中某個點就行）的距離最小。

思路：

求樹直徑，找中點，刪除中間那條邊（如果直徑上點數為奇數，則刪任何一側都可），分成兩個子樹，再求中心，即為答案。

代碼：

//14:12#include <cstdio>#include <cstring>#include <algorithm>using namespace std;#define N 200100struct Graph{    struct Edge{        int to;        int next;    }e[N*3];    int head[N];    int p;    void clear() {        p = 0;        memset(head, -1, sizeof(head));    }    void addedge(int u, int v) {        e[p].to = v;        e[p].next = head[u];        head[u] = p++;    }}g;int n;int dis[N];int que[N*10];bool vis[N];int fa[N];void generateDis(const Graph &g, int s) {    memset(dis, 0x3f, sizeof(dis));    memset(vis, 0, sizeof(vis));    memset(fa, -1, sizeof(fa));    dis[s] = 0;    int hd = 0;    int tl = 0;    que[tl++] = s;    vis[s] = 1;    while (hd < tl) {        int now = que[hd++];        vis[now] = 0;        for (int i = g.head[now]; i != -1; i = g.e[i].next) {            int to = g.e[i].to;            if (dis[to] > dis[now]+1) {                dis[to] = dis[now]+1;                if (!vis[to]) {                    vis[to] = 1;                    fa[to] = now;                    que[tl++] = to;                }            }        }    }}pair<int, int> getTreeMidPoint(const Graph &g, int s, int &OUT_dis) {    generateDis(g, s);    for (int i = 1; i <= n; i++) {        if (dis[i] == 0x3f3f3f3f) dis[i] = -1;    }    int u = max_element(&dis[1], &dis[1]+n) - dis;        generateDis(g, u);    for (int i = 1; i <= n; i++) {        if (dis[i] == 0x3f3f3f3f) dis[i] = -1;    }    int v = max_element(&dis[1], &dis[1]+n) - dis;    //printf("u = %d, v = %d, dis[v] = %d\n", u, v, dis[v]);    int now = v;    while (dis[now] > (dis[v]+1)/2) {        now = fa[now];    }    OUT_dis = dis[v]/2 + dis[v]%2;    return {fa[now], now};}int main() {    int t;    scanf("%d", &t);    while (t--) {        scanf("%d", &n);        g.clear();        for (int i = 0; i < n-1; i++) {            int a, b;            scanf("%d%d", &a, &b);            g.addedge(a,b);            g.addedge(b,a);        }        int tmpdis[2];        pair<int ,int> point = getTreeMidPoint(g, 1, tmpdis[0]);                //printf("all tree get (%d %d, dis=%d)\n", point.first, point.second, tmpdis[0]);        for (int i = g.head[point.first]; i != -1; i=g.e[i].next) {            if (g.e[i].to == point.second) g.e[i].to = point.first;        }        for (int i = g.head[point.second]; i != -1; i=g.e[i].next) {            if (g.e[i].to == point.first) g.e[i].to = point.second;        }        pair<int ,int> pa = getTreeMidPoint(g, point.first, tmpdis[0]);        pair<int ,int> pb = getTreeMidPoint(g, point.second, tmpdis[1]);        printf("%d %d %d\n", max(tmpdis[0], tmpdis[1]), pa.second, pb.second);    }    return 0;}

 

ZOJ 3820:Building Fire Stations(樹的直徑 Grade C)