HDOJ 2391 Filthy Rich

Filthy Rich

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2108    Accepted Submission(s): 949

Problem Description

They say that in Phrygia, the streets are paved with gold. You’re currently on vacation in Phrygia, and to your astonishment you discover that this is to be taken literally: small heaps of gold are distributed throughout the city. On a certain day, the Phrygians even allow all the tourists to collect as much gold as they can in a limited rectangular area. As it happens, this day is tomorrow, and you decide to become filthy rich on this day. All the other tourists decided the same however, so it’s going to get crowded. Thus, you only have one chance to cross the field. What is the best way to do so?

Given a rectangular map and amounts of gold on every field, determine the maximum amount of gold you can collect when starting in the upper left corner of the map and moving to the adjacent field in the east, south, or south-east in each step, until you end up in the lower right corner.

 

Input

The input starts with a line containing a single integer, the number of test cases.
Each test case starts with a line, containing the two integers r and c, separated by a space (1 <= r, c <= 1000). This line is followed by r rows, each containing c many integers, separated by a space. These integers tell you how much gold is on each field. The amount of gold never negative.
The maximum amount of gold will always fit in an int.

 

Output

For each test case, write a line containing “Scenario #i:”, where i is the number of the test case, followed by a line containing the maximum amount of gold you can collect in this test case. Finish each test case with an empty line.

 

Sample Input

   
   
   
   

    
    
    
    1
3 4
1 10 8 8
0 0 1 8
0 27 0 4
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    Scenario #1:
42
   
   
   
   

 

题目大概的意思是：在一个矩阵里面，不同的位置放置着不同的黄金。要从左上角出发，只能向下，向右或者向右下走。

求到达右下角时能收集到的最大黄金量是多少？用动态规划求解，还是不太懂。

代码如下：

#include<stdio.h>
#include<string.h>
int map[1010][1010];
int main()
{
	int i,j,t,r,c,max,k=0;
	scanf("%d",&t);
	while(t--)
	{
		k++;
		memset(map,0,sizeof(map));
		scanf("%d%d",&r,&c);
		for(i=1;i<=r;i++)
		{
			for(j=1;j<=c;j++)
			{
				scanf("%d",&map[i][j]);
			}
		}
		for(i=1;i<=r;i++)
		{
			for(j=1;j<=c;j++)
			{
				int a=map[i][j]+map[i][j-1];
				int b=map[i][j]+map[i-1][j];
				int c=map[i][j]+map[i-1][j-1];
				max=0;
				if(a>max)
				    max=a;
				if(b>max)
				    max=b;
				if(c>max)
				    max=c;
				map[i][j]=max;
			}
		}
		printf("Scenario #%d:\n",k);
		printf("%d\n",map[r][c]);
		printf("\n");
	}
	return 0;
}