[POI2015] Odwiedziny

[题目链接]

          https://www.lydsy.com/JudgeOnline/problem.php?id=4381

[算法]

        考虑分块 ， 先设一个阈值B = 200

        记Su , i表示从u节点开始 ， 每次向上跳i步 ， 所经过点的权值和 ， 可以在O(NBlogN)时间内预处理

        对于每次询问 , 若k <= B ， 可以通过预处理的值求出答案 ， 否则暴力处理

        时间复杂度 : O(NBlogN)(取B = 200)

[代码]

       

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define N 50010
#define M 250
#define MAXLOG 20

struct edge {
        int to , nxt;
} e[N << 1];

int n , tot , MAGIC;
int a[N] , b[N] , c[N] , father[N][MAXLOG] , depth[N] , head[N];
ll cnt[N][M];

template <typename T> inline void chkmax(T &x,T y) { 
        x = max(x,y); 
}
template <typename T> inline void chkmin(T &x,T y) { 
        x = min(x,y); 
}
template <typename T> inline void read(T &x) {
    T f = 1; x = 0;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
    for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
    x *= f;
}
inline void addedge(int u , int v) {
        ++tot;
        e[tot] = (edge){v , head[u]};
        head[u] = tot;
}
inline void work(int u , int par) {
        father[u][0] = par;
        depth[u] = depth[par] + 1;
        for (int i = 1; i < MAXLOG; ++i) {
                father[u][i] = father[father[u][i - 1]][i - 1];
        }        
        for (int i = head[u]; i; i = e[i].nxt) {
                int v = e[i].to;
                if (v == par) continue;
                work(v , u);
        }
}
inline int get(int u , int k) {
        for (int i = 0; i < MAXLOG; ++i) {
                if (k & (1 << i))
                      u = father[u][i];
        }
        return u;
}
inline void dfs(int u , int par) {
        for (int i = 1; i <= MAGIC; ++i) {
                cnt[u][i] = a[u] + cnt[get(u , i)][i];
        }
        for (int i = head[u]; i; i = e[i].nxt) {
                int v = e[i].to;
                if (v == par) continue;
                dfs(v , u);
        }
}
inline int lca(int x , int y) {
        if (depth[x] > depth[y]) swap(x , y);
        for (int i = MAXLOG - 1; i >= 0; --i) {
                if (depth[father[y][i]] >= depth[x])
                        y = father[y][i];
        }        
        if (x == y) return x;
        for (int i = MAXLOG - 1; i >= 0; --i) {
                if (father[x][i] != father[y][i])
                        x = father[x][i] , y = father[y][i];
        }
        return father[x][0];
}

int main()
{
        
        read(n);
        for (int i = 1; i <= n; ++i) read(a[i]);
        for (int i = 1; i < n; ++i) {
                int x , y;
                read(x); read(y);
                addedge(x , y);
                addedge(y , x);
        }
        for (int i = 1; i <= n; ++i) read(b[i]);
        for (int i = 2; i <= n; ++i) read(c[i]);
        MAGIC = (int)sqrt(n);
        work(1 , 0);
        dfs(1 , 0);
        for (int i = 2; i <= n; ++i) {
                int x = b[i - 1] , y = b[i];
                int Lca = lca(x , y);
                ll ans = 0;
                if (Lca == x) {
                        if (c[i] <= MAGIC) {
                                int R = (depth[y] - depth[x]) % c[i];
                                if (R > 0) ans += a[y];
                                y = get(y , R);
                                int val = (depth[y] - depth[x]) / c[i] + 1;
                                ans += cnt[y][c[i]] - cnt[get(y , val * c[i])][c[i]]; 
                        } else {
                                int R = (depth[y] - depth[x]) % c[i];
                                if (R > 0) ans += a[y];
                                y = get(y , R);
                                while (depth[y] >= depth[x]) {
                                        ans += a[y];
                                        y = get(y , c[i]);
                                }
                        }
                } else if (Lca == y) {
                        if (c[i] <= MAGIC) {
                                int val = (depth[x] - depth[y]) / c[i] + 1;
                                ans += cnt[x][c[i]] - cnt[get(x , val * c[i])][c[i]];
                        } else {
                                while (depth[x] >= depth[y]) {
                                        ans += a[x];
                                        x = get(x , c[i]);
                                }
                        }
                } else if (c[i] <= MAGIC) {
                        int val = (depth[x] - depth[Lca]) / c[i] + 1;
                        ans += cnt[x][c[i]] - cnt[get(x , val * c[i])][c[i]];
                        int pre = get(x , (val - 1) * c[i]);
                        int R = (depth[pre] - depth[Lca] + depth[y] - depth[Lca]) % c[i];
                        if (R != 0) {
                                int now = get(y , R);
                                val = (depth[now] - depth[Lca]) / c[i] + 1;
                                ans += a[y] + cnt[y][c[i]] - cnt[get(y , val * c[i])][c[i]]; 
                        } else {
                                val = (depth[y] - depth[Lca]) / c[i] + 1;
                                ans += cnt[y][c[i]] - cnt[get(y , val * c[i])][c[i]];
                                if ((depth[x] - depth[Lca]) % c[i] == 0) ans -= a[Lca];
                        } 
                } else {
                        while (depth[x] >= depth[Lca]) {
                                ans += a[x];
                                if (depth[x] - c[i] < depth[Lca]) break;
                                else x = get(x , c[i]);
                        }
                        int R = (depth[x] - depth[Lca] + depth[y] - depth[Lca]) % c[i];
                        if (R != 0) {
                                ans += a[y];
                                y = get(y , R);
                                while (depth[y] >= depth[Lca]) {
                                        ans += a[y];
                                        y = get(y , c[i]);
                                }
                        } else {
                                while (depth[y] >= depth[Lca]) {
                                        ans += a[y];
                                        y = get(y , c[i]);
                                }
                                if (x == Lca) ans -= a[Lca];
                        }
                }
                printf("%lld
" , ans);
        }
        
        return 0;
    
}