HDU 5113 Black And White（搜索+剪枝）

题意：给你一个不超过5X5的矩阵，有k种颜色，每种颜色有c[i]个，问可不可以把格子颜色涂满并且相邻格子的颜色不相同

思路：DFS搜索，不过会超时，留意到一个剪枝就是如果当前没有涂色的格子数目/2比最多还没涂的颜色数量小的话就可以直接返回了，因为肯定会相邻了

#include<bits\stdc++.h>
using namespace std;
int n,m,k;
int mp[6][6];
int color[50];
bool check(int x,int y,int c)
{if (x-1>=1 && mp[x-1][y]==c)return false;if (y-1>=1 && mp[x][y-1]==c)return false;return true;
}
bool dfs(int x,int y)
{for (int i = 1;i<=k;i++)if ((n*m-(m*(x-1)+y-1)+1)/2<color[i])return false;for (int i = 1;i<=k;i++){if (color[i]>0 && check(x,y,i)){color[i]--;mp[x][y]=i;if (x==n && y==m)return true;if (y+1<=m){if (dfs(x,y+1))return true;}else{if (x+1<=n){if (dfs(x+1,1))return true;}}color[i]++;mp[x][y]=-1;}}return false;
}
int main()
{int T,cas=1;scanf("%d",&T);while(T--){memset(mp,-1,sizeof(mp));printf("Case #%d:\n",cas++);scanf("%d%d%d",&n,&m,&k);for (int i = 1;i<=k;i++)scanf("%d",&color[i]);if (dfs(1,1)){puts("YES");for (int i = 1;i<=n;i++){for (int j = 1;j<m;j++)printf("%d ",mp[i][j]);printf("%d\n",mp[i][m]);}}elseputs("NO");}
}

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

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