hdoj 5113 Black And White(dfs, 剪枝)

题意：给定一个N*M的棋盘，要求用K种颜色对每个格染色，相邻的格的颜色不能相同。并且第i种颜色必须恰好出现c[i]次。求是否存在方案，如果存在，输出任意一种。

搜索好写，但是剪枝不容易想到。

此题的剪枝是设剩下需要need个要填，此时各个颜色还有ci个，若某个ci大于need的一半(即ci > (need+1)/2)肯定会有相邻的同色，所以可以剪去这种情况。

代码：

#include<bits/stdc++.h>
using namespace std;
const int maxn = 10;
int row, col, k, pic[maxn][maxn], c[maxn*maxn];
bool ok;

void dfs(int x, int y)
{
    if(ok) return ;
    if(x == row && y == col+1) { ok = 1; return ; }
    if(y == col+1) { x = x+1, y = 1; }
    int need = row*col-(x-1)*col-y+1;
    for(int i = 1; i <= k; i++)
        if(c[i] > (need+1)/2) return ;
    for(int i = 1; i <= k; i++)
    {
        if(c[i] && pic[x-1][y] != i && pic[x][y-1] != i)
        {
            pic[x][y] = i;
            c[i]--;
            dfs(x, y+1);
            if(ok) return ;
            c[i]++;
        }
    }
}

int main(void)
{
    //freopen("in.txt", "r", stdin);
    int ca = 1, t;
    cin >> t;
    while(t--)
    {
        ok = 0;
        scanf("%d%d%d", &row, &col, &k);
        for(int i = 1; i <= k; i++)
            scanf("%d", &c[i]);
        dfs(1, 1);
        printf("Case #%d:\n", ca++);
        if(!ok) puts("NO");
        else
        {
            puts("YES");
            for(int i = 1; i <= row; i++)
                for(int j = 1; j <= col; j++)
                    printf("%d%c", pic[i][j], j==col ? '\n' : ' ');
        }
    }

    return 0;
}

Black And White

Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 3545    Accepted Submission(s): 955
Special Judge

Problem Description

In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.
— Wikipedia, the free encyclopedia

In this problem, you have to solve the 4-color problem. Hey, I’m just joking.

You are asked to solve a similar problem:

Color an N × M chessboard with K colors numbered from 1 to K such that no two adjacent cells have the same color (two cells are adjacent if they share an edge). The i-th color should be used in exactly c _i cells.

Matt hopes you can tell him a possible coloring.

 

Input

The first line contains only one integer T (1 ≤ T ≤ 5000), which indicates the number of test cases.

For each test case, the first line contains three integers: N, M, K (0 < N, M ≤ 5, 0 < K ≤ N × M ).

The second line contains K integers c _i (c _i > 0), denoting the number of cells where the i-th color should be used.

It’s guaranteed that c ₁ + c ₂ + · · · + c _K = N × M .

 

Output

For each test case, the first line contains “Case #x:”, where x is the case number (starting from 1). 

In the second line, output “NO” if there is no coloring satisfying the requirements. Otherwise, output “YES” in one line. Each of the following N lines contains M numbers seperated by single whitespace, denoting the color of the cells.

If there are multiple solutions, output any of them.

 

Sample Input

  
  

   
   4
1 5 2
4 1
3 3 4
1 2 2 4
2 3 3
2 2 2
3 2 3
2 2 2
  
  

 

Sample Output

  
  

   
   Case #1:
NO
Case #2:
YES
4 3 4
2 1 2
4 3 4
Case #3:
YES
1 2 3
2 3 1
Case #4:
YES
1 2
2 3
3 1
  
  

 

Source

2014ACM/ICPC亚洲区北京站-重现赛（感谢北师和上交）