POJ2155 Matrix <树套树/二维树状数组>

Matrix

Time Limit: 3000MS Memory Limit: 65536K

Description

Given an N*N matrix A, whose elements are either 0 or 1. A[i, j] means the number in the i-th row and j-th column. Initially we have A[i, j] = 0 (1 <= i, j <= N).

We can change the matrix in the following way. Given a rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2), we change all the elements in the rectangle by using “not” operation (if it is a ‘0’ then change it into ‘1’ otherwise change it into ‘0’). To maintain the information of the matrix, you are asked to write a program to receive and execute two kinds of instructions.

1. C x1 y1 x2 y2 (1 <= x1 <= x2 <= n, 1 <= y1 <= y2 <= n) changes the matrix by using the rectangle whose upper-left corner is (x1, y1) and lower-right corner is (x2, y2).

2. Q x y (1 <= x, y <= n) querys A[x, y].

Input

The first line of the input is an integer X (X <= 10) representing the number of test cases. The following X blocks each represents a test case.

The first line of each block contains two numbers N and T (2 <= N <= 1000, 1 <= T <= 50000) representing the size of the matrix and the number of the instructions. The following T lines each represents an instruction having the format “Q x y” or “C x1 y1 x2 y2”, which has been described above.

Output

For each querying output one line, which has an integer representing A[x, y].

There is a blank line between every two continuous test cases.

Sample Input

1

2 10

C 2 1 2 2

Q 2 2

C 2 1 2 1

Q 1 1

C 1 1 2 1

C 1 2 1 2

C 1 1 2 2

Q 1 1

C 1 1 2 1

Q 2 1

Sample Output

1

0

0

1

标签：线段树套线段树/二维树状数组

此题最简单的方法是二维树状数组，但因为二维树状数组没太大用，所以练习线段树的树套树。

此题用作树套树的模板题再合适不过。

AC代码如下：

#include <iostream>
#include <cstdio>
#include <cstring>
#define MAX_N 1000
using namespace std;
int n, m;
int tr[(MAX_N<<2)+5][(MAX_N<<2)+5];
void modify_y(int v1, int v2, int s, int t, int l, int r) {
if (s >= l && t <= r) {
tr[v1][v2] ^= 1;
return;
}
int mid = s+t>>1;
if (l <= mid)   modify_y(v1, v2<<1, s, mid, l, r);
if (r >= mid+1) modify_y(v1, v2<<1|1, mid+1, t, l, r);
}
void modify_x(int v, int s, int t, int x1, int y1, int x2, int y2) {
if (s >= x1 && t <= x2) {
modify_y(v, 1, 1, n, y1, y2);
return;
}
int mid = s+t>>1;
if (x1 <= mid)  modify_x(v<<1, s, mid, x1, y1, x2, y2);
if (x2 >= mid+1)    modify_x(v<<1|1, mid+1, t, x1, y1, x2, y2);
}
int query_y(int v1, int v2, int s, int t, int pos) {
if (s == t) return tr[v1][v2];
int mid = s+t>>1;
if (pos <= mid) return tr[v1][v2]^query_y(v1, v2<<1, s, mid, pos);
else    return tr[v1][v2]^query_y(v1, v2<<1|1, mid+1, t, pos);
}
int query_x(int v, int s, int t, int x, int y) {
if (s == t) return query_y(v, 1, 1, n, y);
int mid = s+t>>1;
if (x <= mid)   return query_y(v, 1, 1, n, y)^query_x(v<<1, s, mid, x, y);
else    return query_y(v, 1, 1, n, y)^query_x(v<<1|1, mid+1, t, x, y);
}
int main() {
int T;
scanf("%d", &T);
while (T--) {
memset(tr, 0, sizeof(tr));
scanf("%d%d", &n, &m);
while (m--) {
char ch;
cin >> ch;
if (ch == 'C') {
int x1, y1, x2, y2;
scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
modify_x(1, 1, n, x1, y1, x2, y2);
}
if (ch == 'Q') {
int x, y;
scanf("%d%d", &x, &y);
printf("%d\n", query_x(1, 1, n, x, y));
}
}
printf("\n");
}
return 0;
}