Poj 1191 DP + DFS board Segmentation

Question:

Description

Split an 8*8 checker as follows: Cut the original checker down a rectangle checker and make the remaining part as a rectangle. Then, split the remaining part so that (n-1) is cut) after that, there are n rectangular checks in total with the remaining rectangular checkerboard. (Each cut can only be performed along the edges of the checker lattice) Each grid on the original Board has a score. The total score of a rectangle board is the sum of the scores of each grid. Now we need to divide the checkerboard into N rectangular checkerboards according to the above rules, and minimize the mean variance of the total score of Each rectangular checkerboard. Mean Variance. The average value and XI are the total score of the I-th rectangle board. Program the given chessboard and N to find the minimum value of O.

 

ApplicationDynamic Planning,StatusInt D (int K, int X1, int Y1, int X2, int Y2), indicating that the upper left corner is (x1, Y1), and the lower right corner is (X2, Y2) the Minimum Sum of squares that can be achieved when the matrix is cut into N blocks.
State transition equationIs

Nowstate = min (nowstate, DFS (K-1, X1, Y1, A, Y2) + s [A + 1, Y1, X2, y2])

Nowstate = min (nowstate, DFS (K-1, A + 1, Y1, X2, Y2) + s [X1, Y1, A, y2])

Nowstate = min (nowstate, DFS (K-1, X1, B + 1, X2, Y2) + s [X1, Y1, X2, B])

Nowstate = min (nowstate, DFS (K-1, X1, Y1, X2, B) + s [X1, B + 1, X2, y2])

 1 #include <cstdio> 2 #include <cstring> 3 #include <cmath> 4 #include <algorithm> 5 using namespace std; 6 #define INF 0x3f3f3f3f 7 int dp[15][9][9][9][9],val[9][9],n; 8  9 int sum(int x1,int y1,int x2,int y2)10 {11     int ans=val[x2][y2]-val[x1-1][y2]-val[x2][y1-1]+val[x1-1][y1-1];12     return ans*ans;13 }14 15 int dfs(int k,int x1,int y1,int x2,int y2)16 {17     if(dp[k][x1][y1][x2][y2]) return dp[k][x1][y1][x2][y2];18     if(k==1||x1==x2||y1==y2){19         dp[k][x1][y1][x2][y2]= sum(x1,y1,x2,y2);20         return dp[k][x1][y1][x2][y2];21     }22     int nowstate=INF;23     for(int i=x1;i<x2;i++){24         nowstate=min(nowstate,dfs(k-1,i+1,y1,x2,y2)+sum(x1,y1,i,y2));25         nowstate=min(nowstate,dfs(k-1,x1,y1,i,y2)+sum(i+1,y1,x2,y2));26     }27     for(int i=y1;i<y2;i++){28         nowstate=min(nowstate,dfs(k-1,x1,i+1,x2,y2)+sum(x1,y1,x2,i));29         nowstate=min(nowstate,dfs(k-1,x1,y1,x2,i)+sum(x1,i+1,x2,y2));30     }31     dp[k][x1][y1][x2][y2]=nowstate;32     return nowstate;33 }34 35 void change()36 {37     for(int i=0;i<=8;i++)38         val[i][0]=0,val[0][i]=0;39 40     for(int i=1;i<=8;i++)41         for(int j=1;j<=8;j++)42             val[i][j]+=val[i-1][j]+val[i][j-1]-val[i-1][j-1];43 }44 45 int main()46 {47     while(~scanf("%d",&n)){48 49         memset(dp,0,sizeof(dp));50 51         for(int i=1;i<=8;i++)52             for(int j=1;j<=8;j++)53                 scanf("%d",&val[i][j]);54 55         change();56 57         double res;58         double ave=1.0*val[8][8]/n;59         res=sqrt((double)dfs(n,1,1,8,8)/n-ave*ave);60         printf("%.3f\n", res);61     }62     return 0;63 }

 

 

Poj 1191 DP + DFS board Segmentation