POJ 2155 Matrix(二维树状数组)

题意:对于一个N行N列的矩阵,有两种操作:

1、C x1 y1 x2 y2,将左上角(x1, y1),右下角(x2, y2)的矩阵反转(0变1,1变0)。

2、Q x y询问A[x, y]的值。

分析:

1、将A[x1][y1]加1(翻转一次),可使左上角(x1, y1),右下角(N,N)的矩阵中每个元素的sum(x, y)都加1,但是显然,只需要将左上角(x1, y1),右下角(x2, y2)的矩阵中每个元素的sum(x, y)都加1即可,所以要使其他无关元素再反转回来,即

(1)将左上角(x1 + 1, y1),右下角(N,N)的矩阵中每个元素的sum(x, y)再加1,这部分元素反转两次等于没反转,同理,

(2)将左上角(x1, y2 + 1),右下角(N,N)的矩阵中每个元素的sum(x, y)再加1

(3)将左上角(x2 + 1, y2 + 1),右下角(N,N)的矩阵中每个元素的sum(x, y)再加1

实质上,只将4个元素加1便达到了目的。

2、询问的时候,直接询问sum(x,y)%2,即左上角(1, 1),右下角(x, y)的矩阵中的加1元素的个数%2。

3、解题过程中充分利用sum函数的性质,即当元素(x, y)加1时,所有左上角(1,1),右下角(xx,yy)的矩阵sum(xx,yy)都加了1,即若要将左上角(x1, y1),右下角(x2, y2)的矩阵反转,无需将矩阵内每个元素都一一反转,而是用左上角(x1, y1)加1后的情况,代替了这一区域矩阵内元素都加1的情况。

#pragma comment(linker, "/STACK:102400000, 102400000")
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<cmath>
#include<iostream>
#include<sstream>
#include<iterator>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<stack>
#include<deque>
#include<queue>
#include<list>
#define Min(a, b) ((a < b) ? a : b)
#define Max(a, b) ((a < b) ? b : a)
#define lowbit(x) (x & (-x))
const double eps = 1e-8;
inline int dcmp(double a, double b){
    if(fabs(a - b) < eps) return 0;
    return a > b ? 1 : -1;
}
typedef long long LL;
typedef unsigned long long ULL;
const int INT_INF = 0x3f3f3f3f;
const int INT_M_INF = 0x7f7f7f7f;
const LL LL_INF = 0x3f3f3f3f3f3f3f3f;
const LL LL_M_INF = 0x7f7f7f7f7f7f7f7f;
const int dr[] = {0, 0, -1, 1, -1, -1, 1, 1};
const int dc[] = {-1, 1, 0, 0, -1, 1, -1, 1};
const int MOD = 1e9 + 7;
const double pi = acos(-1.0);
const int MAXN = 1000 + 10;
const int MAXT = 10000 + 10;
using namespace std;
int N;
int matrix[MAXN][MAXN];
int sum(int x, int y){
    int ans = 0;
    for(int i = x; i >= 1; i -= lowbit(i)){
        for(int j = y; j >= 1; j -= lowbit(j)){
            ans += matrix[i][j];
        }
    }
    return ans;
}
void add(int x, int y, int value){
    for(int i = x; i <= N; i += lowbit(i)){
        for(int j = y; j <= N; j += lowbit(j)){
            matrix[i][j] += value;
        }
    }
}
int main(){
    int T;
    scanf("%d", &T);
    while(T--){
        memset(matrix, 0, sizeof matrix);
        int k;
        scanf("%d%d", &N, &k);
        while(k--){
            getchar();
            char c;
            scanf("%c", &c);
            if(c == 'C'){
                int x1, y1, x2, y2;
                scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
                add(x1, y1, 1);
                add(x1, y2 + 1, 1);
                add(x2 + 1, y1, 1);
                add(x2 + 1, y2 + 1, 1);
            }
            else{
                int x, y;
                scanf("%d%d", &x, &y);
                printf("%d\n", sum(x, y) % 2);
            }
        }
        if(T) printf("\n");
    }
    return 0;
}

  

原文地址:https://www.cnblogs.com/tyty-Somnuspoppy/p/6557452.html