Matrix
Time Limit: 3000MS | Memory Limit: 65536K | |
Total Submissions: 15090 | Accepted: 5662 |
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.
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.
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.
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 Output1
0 0 1
转载:
思路:
这题和树状数组的操作正好相反,树状数组是对点更新,成段求和,这题要
求成段更新,对点求值。但是还是可以转化,我们不妨先来考虑一维的情况,给
定一排数字,每次在区间进行进行成端加上一个数,然后询问某个点的值,很容
易想到线段树,但是线段树的常系数太大,我们试图用树状数组来解决,方法是
给定区间[a, b],如果要求在[a,b]区间都加上T我们只要在a的位置插入一个T,
然后在b+1的位置插入一个-T,这样下次询问某个值k的时候,只要将[1,k]的和求
出来就是k这个位置的值,为什么呢?分三种情况讨论:
1. k < a 先前的插入操作不影响此次结果
2. a <= k <= b a的位置插入T后,统计时值被加了一次
3. k > b。 a的位置有T,b+1的位置有-T,正好抵消
所以结论成立。
然后就可以扩展到二维的情况,也是一样,如果对于(x1, y1) (x2, y2)这个
矩形,只要在(x1, y1) (x2+1, y2+1)这两个点插入T,而(x2+1, y1) (x1, y2+1)
这两个点插入-T即可。
本题的操作是异或,其实还是一样的,就是在二进制内的无进位加法。
#include<iostream> #include<cstdio> #include<cstring> #include<string> using namespace std; int n; int c[1001][1001]; int lowbit(int x) { return (x)&(-x); } void add(int x,int y) { while(x<=n) { int ty=y; while(ty<=n) { c[x][ty]^=1; // c[x][ty]++; ty+=lowbit(ty); } x+=lowbit(x); } } int sum(int x,int y) { int s=0; if(x>n)x=n; if(y>n)y=n; while(x>0) { int ty=y; while(ty>0) { s^=c[x][ty]; //s += c[x][ty]; ty-=lowbit(ty); } x-=lowbit(x); } return s; } int main() { int t,x1,y1,k,x2,y2; char s[3]; scanf("%d",&t); while(t--) { scanf("%d%d",&n,&k); memset(c,0,sizeof(c)); while(k--) { scanf("%s",s); if(s[0]=='C') { scanf("%d%d%d%d",&x1,&y1,&x2,&y2); add(x1,y1); //这里很关键。。。 add(x2+1,y2+1); add(x1,y2+1); add(x2+1,y1); } else { scanf("%d%d",&x1,&y1); printf("%d ",sum(x1,y1)); //printf("%d ",sum(x1,y1)%2); 这样做也可以的。。 } } if(t) printf(" "); } return 0; }