New Year and Domino 二維前綴和
They say "years are like dominoes, tumbling one after the other". But would a year fit into a grid? I don‘t think so.
Limak is a little polar bear who loves to play. He has recently got a rectangular grid with h
Also, Limak has a single domino. He wants to put it somewhere in a grid. A domino will occupy exactly two adjacent cells, located either in one row or in one column. Both adjacent cells must be empty and must be inside a grid.
Limak needs more fun and thus he is going to consider some queries. In each query he chooses some rectangle and wonders, how many way are there to put a single domino inside of the chosen rectangle?
InputThe first line of the input contains two integers h and w (1?≤?h,?w?≤?500) – the number of rows and the number of columns, respectively.
The next h lines describe a grid. Each line contains a string of the length w. Each character is either ‘.‘ or ‘#‘ — denoting an empty or forbidden cell, respectively.
The next line contains a single integer q (1?≤?q?≤?100?000) — the number of queries.
Each of the next q lines contains four integers r1i, c1i, r2i, c2i (1?≤?r1i?≤?r2i?≤?h,?1?≤?c1i?≤?c2i?≤?w) — the i-th query. Numbers r1i and c1i denote the row and the column (respectively) of the upper left cell of the rectangle. Numbers r2i and c2i denote the row and the column (respectively) of the bottom right cell of the rectangle.
OutputPrint q integers, i-th should be equal to the number of ways to put a single domino inside the i-th rectangle.
Examples input Copy5 8output Copy
....#..#
.#......
##.#....
##..#.##
........
4
1 1 2 3
4 1 4 1
1 2 4 5
2 5 5 8
4input Copy
0
10
15
7 39output Copy
.......................................
.###..###..#..###.....###..###..#..###.
...#..#.#..#..#.........#..#.#..#..#...
.###..#.#..#..###.....###..#.#..#..###.
.#....#.#..#....#.....#....#.#..#..#.#.
.###..###..#..###.....###..###..#..###.
.......................................
6
1 1 3 20
2 10 6 30
2 10 7 30
2 2 7 7
1 7 7 7
1 8 7 8
53Note
89
120
23
0
2
A red frame below corresponds to the first query of the first sample. A domino can be placed in 4 possible ways.
#include <cstdio> #include <cstring> #include <queue> #include <cmath> #include <algorithm> #include <set> #include <iostream> #include <map> #include <stack> #include <string> #include <vector> #define pi acos(-1.0) #define eps 1e-6 #define fi first #define se second #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define bug printf("******\n") #define mem(a,b) memset(a,b,sizeof(a)) #define fuck(x) cout<<"["<<x<<"]"<<endl #define f(a) a*a #define sf(n) scanf("%d", &n) #define sff(a,b) scanf("%d %d", &a, &b) #define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c) #define sffff(a,b,c,d) scanf("%d %d %d %d", &a, &b, &c, &d) #define pf printf #define FRE(i,a,b) for(i = a; i <= b; i++) #define FREE(i,a,b) for(i = a; i >= b; i--) #define FRL(i,a,b) for(i = a; i < b; i++) #define FRLL(i,a,b) for(i = a; i > b; i--) #define FIN freopen("DATA.txt","r",stdin) #define gcd(a,b) __gcd(a,b) #define lowbit(x) x&-x #pragma comment (linker,"/STACK:102400000,102400000") using namespace std; typedef long long LL; typedef unsigned long long ULL; const int maxn = 2e5 + 10; int n, m, sum[505][505], y[505][505], x[505][505]; char mp[505][505]; int main() { sff(n, m); for (int i = 1 ; i <= n ; i++) scanf("%s", mp[i] + 1); for (int i = 1 ; i <= n ; i++) { for (int j = 1 ; j <= m ; j++) { if (mp[i][j] == ‘.‘ && mp[i + 1][j] == ‘.‘ ) { sum[i][j]++; y[i][j] = 1; } if (mp[i][j] == ‘.‘ && mp[i][j + 1] == ‘.‘ ) { sum[i][j]++; x[i][j] = 1; } sum[i][j] += sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1]; } } int q; sf(q); while(q--) { int x1, y1, x2, y2; sffff(x1, y1, x2, y2); int ans = sum[x2][y2] - sum[x1 - 1][y2] - sum[x2][y1 - 1] + sum[x1 - 1][y1 - 1]; for (int i = x1 ; i <= x2 ; i++) ans -= x[i][y2]; for (int i = y1 ; i <= y2 ; i++) ans -= y[x2][i]; printf("%d\n", ans); } return 0; }
New Year and Domino 二維前綴和