POJ3364 HDU1802 UVA11231 Black and white painting【数学】

Black and white painting
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 2842 Accepted: 1938

Description

You are visiting the Centre Pompidou which contains a lot of modern paintings. In particular you notice one painting which consists solely of black and white squares, arranged in rows and columns like in a chess board (no two adjacent squares have the same colour). By the way, the artist did not use the tool of problem A to create the painting.

Since you are bored, you wonder how many 8 × 8 chess boards are embedded within this painting. The bottom right corner of a chess board must always be white.

Input

The input contains several test cases. Each test case consists of one line with three integers n, m and c. (8 ≤ n, m ≤ 40000), where n is the number of rows of the painting, and m is the number of columns of the painting. c is always 0 or 1, where 0 indicates that the bottom right corner of the painting is black, and 1 indicates that this corner is white.

The last test case is followed by a line containing three zeros.

Output

For each test case, print the number of chess boards embedded within the given painting.

Sample Input

8 8 0
8 8 1
9 9 1
40000 39999 0
0 0 0

Sample Output

0
1
2
799700028

Source

Ulm Local 2007

问题链接：POJ3364 HDU1802 UVA11231 Black and white painting
问题简述：（略）
问题分析：
    给定一个nm大小的黑白相间的棋盘（第三个参数表示右下角是黑色还是白色），问一个88黑白相间的模板（右下角为白色）有多少个匹配位置可以放置。
    模板右下角只有k=(n-7)*(m-7)的位置可能放置，而且如果k为偶数，无论棋盘右下角是黑是白可以放置的位置相同；如果k是奇数，则白比黑多1。
程序说明：（略）
参考链接：（略）
题记：（略）

AC的C++语言程序如下：

/* POJ3364 HDU1802 UVA11231 Black and white painting */

#include <iostream>
#include <cstdio>

using namespace std;

int main()
{
    int n, m, c, ans;
    while(~scanf("%d%d%d", &n, &m, &c) && (n || m || c))  {
        if(n < 8 || m < 8)
            ans = 0;
        else {
            int tmp = (n - 8 + 1) * (m - 8 + 1);
            ans = c ? (tmp  + 1) / 2 : tmp / 2;
        }
        printf("%d\n", ans);
    }

    return 0;
}