HDU 1081 to the Max

http://acm.hdu.edu.cn/showproblem.php?pid=1081

The main idea of a matrix is to ask for the maximum of a sub-matrix. The and representations of the sub-matrices are the and of all elements within the matrix.

Analysis:

The map[i][j] array is stored on the first row of the J column and

On line k, dp[k][i] = max (Dp[k][i-1]+map[k][i],map[k][i]), but this only knows

The maximum and the number of the first I of the K line, without knowing which is the most from the first column to the first column on page K.

Daiwa The state transfer equation is converted to, at the end of the K-Act, the most Yamato from column I to column J

DP[I][J] = max (map[k][j]-map[k][i-1]+ dp[i][j] , map[k][j]-map[k][i-1]);

Then use a max to find out the biggest dp[i][j]. Because it does not involve the case of a specific sub-matrix, simply

To get the optimal solution, the state transfer equation can also be written

ans = max ( map[k][j]-map[k][i-1]+  ans ,map[k][j]-map[k][i-1]  )

Ans is the first k line, to the end of the K-Act, the largest and the first to the first column J

Code Listing 1:

#include <stdio.h>#include<string.h>#include<math.h>#include<stdlib.h>#include<algorithm>#defineINF 0x3f3f3f3f#defineN 110using namespacestd;intMaps[n][n], dp[n][n];intMain () {intN, I, J, K, A;  while(~SCANF ("%d", &N)) { for(i =1; I <= N; i++)        {             for(j =1; J <= N; J + +) {scanf ("%d", &a); MAPS[I][J]= Maps[i][j-1] +A; }        }//Maps[i][j] The and of the first J column of line I        intMax =-INF;  for(j =1; J <= N; J + +)        {             for(i =1; I <= J; i++) {Dp[i][j]=0;  for(k =1; K <= N; k++) {Dp[i][j]= Max (Maps[k][j]-maps[k][i-1] + dp[i][j], Maps[k][j]-maps[k][i-1]); if(Dp[i][j] >Max) Max=Dp[i][j]; }}} printf ("%d\n", Max); }    return 0;}

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Code Listing 2:

For details, please refer to:

http://blog.csdn.net/u013611908/article/details/41781431

#include <stdio.h>#include<string.h>#include<math.h>#include<stdlib.h>#include<algorithm>#defineINF 0x3f3f3f3f#defineN 110using namespacestd;intMaps[n][n], dp[n][n];intMain () {intN, I, J, K, A;  while(~SCANF ("%d", &N)) { for(i =1; I <= N; i++) {dp[i][0] =0;  for(j =1; J <= N; J + +) {scanf ("%d", &a); MAPS[I][J]= Maps[i][j-1] +A; }        }//Maps[i][j] The and of the first J column of line I        intMax =-INF, sum;  for(i =1; I <= N; i++)        {             for(j = i; J <= N; j + +) {sum=0;  for(k =1; K <= N; k++)                {                    if(Sum <0) Sum=0; Sum+ = Maps[k][j]-maps[k][i-1]; Max=Max (max, sum); }}} printf ("%d\n", Max); }    return 0;}

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HDU 1081 to the Max