LCA

Posted 2022-08-24 smallhester

A - How far away ？

 HDU - 2586 

 题意：给出一棵树，树上的边有权值，查询两个点之间的最短权值和

 LCA倍增

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<stack>
#include<cstdlib>
#include<queue>
#include<set>
#include<string.h>
#include<vector>
#include<deque>
#include<map>
using namespace std;
#define INF 0x3f3f3f3f3f3f3f3f
#define inf 0x3f3f3f3f
#define eps 1e-4
#define bug printf("*********\n")
#define debug(x) cout<<#x"=["<<x<<"]" <<endl
typedef long long LL;
typedef long long ll;
const int maxn = 4e4 + 5;
const int mod = 998244353;

int cnt,DEG = 30;
int vis[maxn],head[maxn],dep[maxn],fa[maxn][30],dis[maxn];
//dep深度数组  fa[i][j]表示结点 i 的第2 ^ j个祖先
//dis[i] root到任意的一个i结点的距离
struct EDGE 
    int next,to,v;
edge[maxn * 2];

void addedge(int x,int y,int z) 
    edge[++cnt].to = y;
    edge[cnt].v = z;
    edge[cnt].next = head[x];
    head[x] = cnt;

void init() 
    cnt = 0;
    memset(vis,0,sizeof vis);
    memset(head,-1,sizeof head);
    memset(dep,0,sizeof dep);
    memset(dis,0,sizeof dis);
    memset(fa,0,sizeof fa);

void bfs(int root) 
    queue<int>que;
    dep[root] = 0;  //根节点的深度为0
    fa[root][0] = root;
    que.push(root);
    while(!que.empty()) 
        int tmp = que.front(); que.pop();
        for(int i = 1; i < DEG; i++)
            fa[tmp][i] = fa[fa[tmp][i - 1]][i - 1]; //tmp这个点的2 ^ i的祖先就是 tmp的 2 ^ (i - 1)的祖先这个点的 2 ^ (i - 1)的祖先
        for(int i = head[tmp]; i != -1; i = edge[i].next) 
            int v = edge[i].to;
            if(v == fa[tmp][0]) continue;
            dep[v] = dep[tmp] + 1;
            dis[v] = dis[tmp] + edge[i].v; //dis距离数组的更新
            fa[v][0] = tmp;
            que.push(v);
        
    

int LCA(int u,int v) 
    if(dep[u] > dep[v]) swap(u,v); //使得v的深度比较大
    int hu = dep[u],hv = dep[v],tu = u,tv = v;
    for(int det = hv - hu, i = 0; det; det >>= 1, i++)
        if(det & 1)
            tv = fa[tv][i];
    if(tu == tv)
        return tu;
    for(int i = DEG - 1; i >= 0; i--) 
        if(fa[tu][i] == fa[tv][i]) continue;
        tu = fa[tu][i];
        tv = fa[tu][i];
    
    return fa[tu][0];

int main()

    int t;
    scanf("%d",&t);
    while (t -- ) 
        init();
        int n, m;
        scanf("%d %d",&n,&m);
        for(int i = 1; i < n; i++) 
            int u,v,k;
            scanf("%d %d %d",&u,&v,&k);
            vis[v] = 1;
            addedge(u,v,k);
            addedge(v,u,k);
        
        int root;
        for(int i = 1; i <= n; i++ ) 
            if(vis[i] == 0) 
                root = i;
                break;
            
        

        bfs(root);
        for(int i = 1; i <= m; i++) 
            int a,b;
            scanf("%d %d",&a,&b);
            int ans = dis[a] + dis[b] - 2 * dis[LCA(a,b)];
            printf("%d\n",ans);
        
    

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