DFS序的应用

原地址：http://www.cnblogs.com/Quinte/p/4898410.html
１.对节点X到Y的最短路上所有点权都加一个数W, 查询某个点的权值

解 :
这个操作等价于
a. 对X到根节点路径上所有点权加W
b. 对Y到根节点路径上所有点权加W
c. 对LCA(x, y)到根节点路径上所有点权值减W
d. 对LCA(x,y)的父节点 parent(LCA(x, y))到根节点路径上所有权值减W
于是要进行四次这样从一个点到根节点的区间修改
将问题进一步简化, 进行一个点X到根节点的区间修改, 查询其他一点Y时
只有X在Y的子树内, X对Y的值才有贡献且贡献值为W
于是只需要更新四个点, 查询一个点的子树内所有点权的和即可

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

using namespace std;

const int MAXN = 1e5 + 10;

vector<int> edge[MAXN];
int s[2 * MAXN];
int seq[2 * MAXN];
int seq1[2 * MAXN];
int depth[2 * MAXN];
int first[MAXN];
int dp[2 * MAXN][25];
int st[MAXN];
int ed[MAXN];
int parent[MAXN];
int cnt, num;

int Lowbit(int x) {
    return x & (-x);
}

void Add(int x, int val, int n) {
    if (x <= 0) return;
    for (int i = x; i <= n; i += Lowbit(i)) {
        s[i] += val;
    }
}

int Sum(int x) {
    int res = 0;
    for (int i = x; i > 0; i -= Lowbit(i)) {
        res += s[i];
    }
    return res;
}

void Dfs(int u, int fa, int dep) {
    parent[u] = fa;
    seq[++cnt] = u;
    seq1[++num] = u;
    first[u] = num;
    depth[num] = dep;
    st[u] = cnt;
    int len = edge[u].size();
    for (int i = 0; i < len; i++) {
        int v = edge[u][i];
        if (v != fa) {
            Dfs(v, u, dep + 1);
            seq1[++num] = u;
            depth[num] = dep;
        }
    }
    seq[++cnt] = u;
    ed[u] = cnt;
}

void RMQ_Init(int n) {
    for (int i = 1; i <= n; i++) {
        dp[i][0] = i;
    }
    for (int j = 1; (1 << j) <= n; j++) {
        for (int i = 1; i + (1 << j) - 1 <= n; i++) {
            int a = dp[i][j - 1], b = dp[i + (1 << (j - 1))][j - 1];
            dp[i][j] = depth[a] < depth[b] ? a : b;
        }
    }
}

int RMQ_Query(int l, int r) {
    int k = 0;
    while ((1 << (k + 1)) <= r - l + 1) k++;
    int a = dp[l][k], b = dp[r - (1 << k) + 1][k];
    return depth[a] < depth[b] ? a : b;
}

int LCA(int u, int v) {
    int a = first[u], b = first[v];
    if (a > b) a ^= b, b ^= a, a ^= b;
    int res = RMQ_Query(a, b);
    return seq1[res];
}

void Init(int n) {
    for (int i = 0; i <= n; i++) {
        edge[i].clear();
    }
    memset(s, 0, sizeof(s));
}

int main() {
    int n, op;
    int u, v, w;
    int cmd;

    while (scanf("%d %d", &n, &op) != EOF) {
        Init(n);
        for (int i = 0; i < n - 1; i++) {
            scanf("%d %d", &u, &v);
            edge[u].push_back(v);
            edge[v].push_back(u);
        }
        cnt = 0, num = 0;
        Dfs(1, -1, 0);
        RMQ_Init(num);
        while (op--) {
            scanf("%d", &cmd);
            if (cmd == 0) {
                scanf("%d %d %d", &u, &v, &w);
                int lca = LCA(u, v);
                Add(st[u], w, cnt);
                Add(st[v], w, cnt);
                Add(lca, -w, cnt);
                Add(parent[lca], -w, cnt);
            } else if (cmd == 1) {
                scanf("%d", &u);
                printf("%d\n", Sum(ed[u]) - Sum(st[u] - 1));
            }
        }
    }

    return 0;
}