POJ 1656 二维树状数组简单应用
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一个水题。。。结果因为一个加号写成了减号。。。硬是耗费了一个多小时。。。T^T
Counting Black
Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 10012 Accepted: 6466
Description
There is a board with 100 * 100 grids as shown below. The left-top gird is denoted as (1, 1) and the right-bottom grid is (100, 100).
We may apply three commands to the board:
In the beginning, all the grids on the board are white. We apply a series of commands to the board. Your task is to write a program to give the numbers of black grids within a required region when a TEST command is applied.
We may apply three commands to the board:
1.WHITE x, y, L // Paint a white square on the board, // the square is defined by left-top grid (x, y) // and right-bottom grid (x+L-1, y+L-1)2.BLACK x, y, L // Paint a black square on the board, // the square is defined by left-top grid (x, y) // and right-bottom grid (x+L-1, y+L-1)3.TEST x, y, L // Ask for the number of black grids // in the square (x, y)- (x+L-1, y+L-1)
In the beginning, all the grids on the board are white. We apply a series of commands to the board. Your task is to write a program to give the numbers of black grids within a required region when a TEST command is applied.
Input
The first line of the input is an integer t (1 <= t <= 100), representing the number of commands. In each of the following lines, there is a command. Assume all the commands are legal which means that they won't try to paint/test the grids outside the board.
Output
For each TEST command, print a line with the number of black grids in the required region.
Sample Input
5BLACK 1 1 2BLACK 2 2 2TEST 1 1 3WHITE 2 1 1TEST 1 1 3
Sample Output
76
就是多次统计某一个区域里黑色方块的数量,有人说用直接模拟就能过去。。。我没试。。。为了保险还是用树状数组撸了。。。
用一个atlas数组来记录某一个状态时黑白方块的数量(奇怪的是。。我用bool数组的话 time是16ms。。。如果是int数组的话 time是0ms。。。)atlas[i][j]为1表示black,为0表示white。
然后一次一次查询时修改即可。
至于二维树状数组的写法,只要在一维的基础上加一层循环即可。
下面放出代码
#include <iostream>#include <cstdio>#include <cstdlib>#include <string>#include <cstring>#include <algorithm>#include <numeric>#include <vector>#include <queue>#include <stack>using namespace std;#define MAX_N 101int bintree[MAX_N][MAX_N] = { 0 };int atlas[MAX_N][MAX_N] = { 0 };int lowbit(int pos) { return pos & (-pos);}int getsum(int xpos, int ypos) { int sum = 0; while(xpos > 0) { int yypos = ypos; while(yypos > 0) sum += bintree[xpos][yypos], yypos-=lowbit(yypos); xpos -= lowbit(xpos); } return sum;}void update(int xpos, int ypos, int val) { while(xpos <= 100) { int yypos = ypos; while(yypos <= 100) bintree[xpos][yypos] += val, yypos += lowbit(yypos); xpos += lowbit(xpos); }}int main() { int test_n, x, y, l; string order; cin >> test_n; while(test_n--) { cin >> order >> x >> y >> l; if(order == "BLACK") { for(int i = x; i <= x + l - 1; i++) { for(int j = y; j <= y + l - 1; j++) { if(atlas[i][j] == 0) update(i, j, 1), atlas[i][j] = 1; } } } else if(order == "WHITE") { for(int i = x; i <= x + l - 1; i++) { for(int j = y; j <= y + l - 1; j++) { if(atlas[i][j] == 1) update(i, j, -1), atlas[i][j] = 0; } } } else printf("%d\n", getsum(x + l - 1, y + l - 1) + getsum(x - 1, y - 1) - getsum(x - 1, y + l - 1) - getsum(x + l - 1, y - 1)); } return 0;}
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