POJ2495（棋盘分治，染色）

Incomplete chess boards

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 2483		Accepted: 1519

Description

Background 
Tom gets a riddle from his teacher showing 42 chess boards from each of which two squares are removed. The teacher wants to know which boards can be completely covered by 31 dominoes. He promises ten bars of chocolate for the person who solves the problem correctly. Tom likes chocolate, but he cannot solve this problem on his own. So he asks his older brother John for help. John (who likes chocolate as well) agrees, provided that he will get half the prize. 
John's abilities lie more in programming than in thinking and so decides to write a program. Can you help John? Unfortunately you will not win any bars of chocolate, but it might help you win this programming contest. 
Problem 
You are given are 31 dominoes and a chess board of size 8 * 8, two distinct squares of which are removed from the board. The square in row a and column b is denoted by (a, b) with a, b in {1, . . . , 8}. 
A domino of size 2 × 1 can be placed horizontally or vertically onto the chess board, so it can cover either the two squares {(a, b), (a, b + 1)} or {(b, a), (b + 1, a)} with a in {1, . . . , 8} and b in {1, . . . , 7}. The object is to determine if the so-modified chess board can be completely covered by 31 dominoes. 
For example, it is possible to cover the board with 31 dominoes if the squares (8, 4) and (2, 5) are removed, as you can see in Figure 1. 

Input

The first input line contains the number of scenarios k. Each of the following k lines contains four integers a, b, c, and d, separated by single blanks. These integers in the range {1, . . . , 8} represent the chess board from which the squares (a, b) and (c, d) are removed. You may assume that (a, b) != (c, d).

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print the number 1 if the board in this scenario can be completely covered by 31 dominoes, otherwise write a 0. Terminate the output of each scenario with a blank line.

Sample Input

3
8 4 2 5
8 8 1 1
4 4 7 1

Sample Output

Scenario #1:
1

Scenario #2:
0

Scenario #3:
0

Source

TUD Programming Contest 2005, Darmstadt, Germany

 

题意：8*8的棋盘中去掉两个点，如果能用1*2的长方形铺满输出1，否则输出0

思路：二分图匹配是这一类问题的通解，但这题有特殊做法，对棋盘染色，如果去掉的两个点颜色相同则无法铺满，否则可以铺满

/*
ID: LinKArftc
PROG: 2495.cpp
LANG: C++
*/

#include <map>
#include <set>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <cstdio>
#include <string>
#include <utility>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define eps 1e-8
#define randin srand((unsigned int)time(NULL))
#define input freopen("input.txt","r",stdin)
#define debug(s) cout << "s = " << s << endl;
#define outstars cout << "*************" << endl;
const double PI = acos(-1.0);
const double e = exp(1.0);
const int inf = 0x3f3f3f3f;
const int INF = 0x7fffffff;
typedef long long ll;

int mp[10][10];

int main() {
    bool cur = 0;
    for (int i = 1; i <= 8; i ++) {
        for (int j = 1; j <= 8; j ++) {
            mp[i][j] = cur;
            if (j != 8) cur = !cur;
        }
    }
    int a, b, c, d;
    int T, _t = 1;
    scanf("%d", &T);
    while (T --) {
        printf("Scenario #%d:
", _t ++);
        scanf("%d %d %d %d", &a, &b, &c, &d);
        if (mp[a][b] == mp[c][d]) printf("0

");
        else printf("1

");
    }

    return 0;
}