ZOJ 3686 A Simple Tree Problem（线段树）

Description

Given a rooted tree, each node has a boolean (0 or 1) labeled on it. Initially, all the labels are 0.

We define this kind of operation: given a subtree, negate all its labels.

And we want to query the numbers of 1's of a subtree.

Input

Multiple test cases.

First line, two integer N and M, denoting the numbers of nodes and numbers of operations and queries.(1<=N<=100000, 1<=M<=10000)

Then a line with N-1 integers, denoting the parent of node 2..N. Root is node 1.

Then M lines, each line are in the format "o node" or "q node", denoting we want to operate or query on the subtree with root of a certain node.

Output

For each query, output an integer in a line.

Output a blank line after each test case.

题目大意：给一棵多叉树，初始值都为0，o x为翻转以x为根的子树，q x为查询以x为根的子树有多少个1

思路：这数据范围，暴力是不行的，怎么暴力都是不行的>_<。这题的要求是：修改一大片、查询一大片，比较容易想到的就是线段树（树状数组也可以，不过要翻转嘛……好像有难度……反正我不会>_<）。问题是这玩意儿怎么转换成线段树呢？要转化成线段树，就要把每个点的子孙们都放到一片连续的空间里。这时，若使用DFS，遍历的顺序刚刚好符合要求，于是我们就DFSo(∩_∩)o 。DFS途中就可以算出每个点的及其子孙覆盖的区域。然后变成线段树之后呢，随便搞搞就行了o(∩_∩)o

 #include <cstdio>
 #include <cstring>

 const int MAX = ;

 int flip[MAX*], sum[MAX*], cnt[MAX*];//tree
 int head[MAX], next[MAX], to[MAX], ecnt;
 int beg[MAX], size[MAX], dfs_clock;
 int y1, y2;

 void tle() {while() ;}

 void init() {
     ecnt = ;
     dfs_clock = ;
     memset(head, , sizeof(head));
     memset(flip, , sizeof(flip));
     memset(cnt, , sizeof(cnt));
 }

 void add_edge(int u, int v) {
     to[ecnt] = v; next[ecnt] = head[u]; head[u] = ecnt++;
 }

 void dfs(int x) {
     size[x] = ;
     beg[x] = ++dfs_clock;
     for(int p = head[x]; p; p = next[p]) {
         dfs(to[p]);
         size[x] += size[to[p]];
     }
 }

 void maintain(int x, int l, int r) {
     int lc = x * , rc = x *  + ;
     if(l < r) {
         cnt[x] = cnt[rc] + cnt[lc];
     }
 }

 void pushdown(int x) {
     int lc = x * , rc = x *  + ;
     if(flip[x]) {
         flip[x] = ;
         flip[lc] ^= ;
         cnt[lc] = sum[lc] - cnt[lc];
         flip[rc] ^= ;
         cnt[rc] = sum[rc] - cnt[rc];
     }
 }

 void update(int x, int l, int r) {
     int lc = x * , rc = x *  + ;
     if(y1 <= l && r <= y2) {
         flip[x] ^= ;
         cnt[x] = sum[x] - cnt[x];
     }
     else {
         pushdown(x);
         int mid = (l + r) / ;
         if(y1 <= mid) update(lc, l, mid);
         if(mid < y2) update(rc, mid + , r);
         maintain(x, l, r);
     }
 }

 int ans;

 void query(int x, int l, int r) {
     int lc = x * , rc = x *  + ;
     if(y1 <= l && r <= y2) ans += cnt[x];
     else {
         pushdown(x);
         int mid = (l + r) / ;
         if(y1 <= mid) query(lc, l, mid);
         if(mid < y2) query(rc, mid + , r);
     }
 }

 void build(int x, int l, int r) {
     int lc = x * , rc = x *  + ;
     if(l == r) {
         sum[x] = ;
     }
     else {
         int mid = (l + r) / ;
         build(lc, l, mid);
         build(rc, mid + , r);
         sum[x] = sum[lc] + sum[rc];
     }
 }

 int main() {
     int n, m, x;
     char c[];
     while(scanf("%d%d", &n, &m) != EOF) {
         init();
         for(int i = ; i <= n; ++i) {
             scanf("%d", &x);
             add_edge(x, i);
         }
         dfs();
         build(, , n);
         while(m--) {
             scanf("%s%d", c, &x);
             y1 = beg[x]; y2 = beg[x] + size[x] - ;
             if(c[] == 'o') {
                 update(, , n);
             }
             if(c[] == 'q') {
                 ans = ;
                 query(, , n);
                 printf("%d\n", ans);
             }
         }
         puts("");
     }
 }