POJ 2155 Matrix 树状数组
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Matrix
Problem 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].
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. <br> <br>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. <br>
Output
For each querying output one line, which has an integer representing A[x, y]. <br> <br>There is a blank line between every two continuous test cases. <br>
Sample Input
12 10C 2 1 2 2Q 2 2C 2 1 2 1Q 1 1C 1 1 2 1C 1 2 1 2C 1 1 2 2Q 1 1C 1 1 2 1Q 2 1
Sample Output
1001
//题意:有个N*N的矩阵,每个点的值要么是0,要么是1,每个点一开始的初始值为0。现在有2种操作:“C”:要输入x1,y1,x2,y2(x2>x1 , y2>y1),把以(x1,y1),(x2,y2)为对角线顶点的那个矩形里的值改变(若原来是1,变为0;原来是0,变为1)。“Q”:输入x,y,要求这点的值是0还是1。
//思路:最先想到的应该是定义一个map二维数组,在根据要求去改变map里的值,但只要稍微想一下就知道这么暴力(N*N)绝逼TLE,于是就考虑怎样高效地改变一个区间里的值,那么显然树状数组(复杂度N*logN)是一个好方法。
然后这里还有一个小技巧,每次1->0,0->1很麻烦,其实只要每个点要改变的时候都+1就行了,最后要计算的时候,如果是奇数就是1,偶数就是0。
还有“C”的时候,x2,y2都要+1(即(x2+1,y2+1)),这是考虑到顶点的情况,自己画个图感受下就很清楚了。
(搞清楚树状数组推荐博客:http://blog.csdn.net/int64ago/article/details/7429868)
#include <iostream>#include <cstdio>#include <cstring>#include <string>#include <cmath>#include <cstdlib>#include <algorithm>using namespace std;const int MAX = 1010;int n, num;int c[MAX][MAX];int lowbit(int x){return x&(-x);}void add(int x,int y, int val){for (int i = x; i <= n; i += lowbit(i)){for (int j = y; j <= n; j += lowbit(j)){c[i][j] += val;}}}int sum(int x, int y){int sum = 0;for (int i = x; i > 0; i -= lowbit(i)){for (int j = y; j > 0; j -= lowbit(j)){sum += c[i][j];}}return sum;}int main(){int i, j, k;int T;cin >> T;while (T--){char a;int x1, y1, x2, y2;scanf("%d%d", &n, &num);getchar();memset(c, 0, sizeof(c));for (i = 1; i <= num; i++){scanf("%c", &a);if (a == 'C'){scanf("%d%d%d%d", &x1, &y1, &x2, &y2);//用树状数组只要传入4个角,遍历的复杂度是NlogN//暴搜的话是N平方,肯定TLE//自己画个图更好理解一点//x2,y2都+1是为了考虑4个顶点的情况//改变的每个坐标的值不用真的从0->1,1->0//每次都+1就好了,如果是偶数,表明这点就是0;奇数的话就是1;add(x2 + 1, y2 + 1, 1);add(x1, y1, 1);add(x1, y2 + 1, 1);add(x2 + 1, y1, 1);}else if (a == 'Q'){scanf("%d%d", &x1, &y1);int temp = sum(x1, y1) % 2;printf("%d\n", temp);}getchar();}if (T != 0)printf("\n");}return 0;}
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