POJ3230——Travel

Travel

Description

One traveler travels among cities. He has to pay for this while he can get some incomes.

Now there are n cities, and the traveler has m days for traveling. Everyday he may go to another city or stay there and pay some money. When he come to a city ,he can get some money. Even when he stays in the city, he can also get the next day‘s income.
All the incomes may change everyday. The traveler always starts from city 1.

Now is your turn to find the best way for traveling to maximize the total income.

Input

There are multiple cases.

The first line of one case is two positive integers, n and m .n is the number of cities, and m is the number of traveling days. There follows n lines, one line n integers. The j integer in the i line is the expense of traveling from city i to city j. If
i equals to j it means the expense of staying in the city.

After an empty line there are m lines, one line has n integers. The j integer in the i line means the income from city j in the i day.

The input is finished with two zeros.

n,m<100.

Output

You must print one line for each case. It is the max income.

Sample Input

3 3
3 1 2
2 3 1
1 3 2

2 4 3
4 3 2
3 4 2

0 0

Sample Output

8

Hint

In the Sample, the traveler can first go to city 2, then city 1, and finish his travel in city 1. The total income is:

-1+4-2+4-1+4=8;

Source

简单dp题，我们用dp[i][j] 表示到第i天，在城市j时的最大收益，所以方程就很容易写出来了

dp[i][j] = max(dp[i-1][k] - mat[k][j] + w[i][j])

#include <map>
#include <set>
#include <list>
#include <stack>
#include <queue>
#include <vector>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
#include <algorithm>  

using namespace std;

int dp[105][105];
int mat[105][105];
int w[105][105];

int main()
{
	int n, m;
	while (~scanf("%d%d", &n, &m))
	{
		if (!n && !m)
		{
			break;
		}
		memset ( dp, -0x3f3f3f3f, sizeof(dp) );
		for (int i = 1; i <= n; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				scanf("%d", &mat[i][j]);
			}
		}
		for (int i = 1; i <= m; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				scanf("%d", &w[i][j]);
			}
		}
		dp[0][1] = 0;
		for (int i = 1; i <= n; i++)
		{
			dp[1][i] = dp[0][1] - mat[1][i];
		}
		for (int i = 1; i <= m; i++)
		{
			for (int j = 1; j <= n; j++)
			{
				for (int k = 1; k <= n; k++)
				{
					dp[i][j] = max(dp[i][j], dp[i - 1][k] - mat[k][j] + w[i][j]);
				}
			}
		}
		int ans = 0;
		for (int i = 1; i <= n; i++)
		{
			ans = max(ans, dp[m][i]);
		}
		printf("%d\n", ans);
	}
	return 0;
}