zoj 3623 Battle Ships dp

Battle Ships is a new game which is similar to Star Craft. In this game, the enemy builds a defense tower, which has L longevity. The player has a military factory, which can produce N kinds of battle ships. The factory takes t_i seconds to produce the i-th battle ship and this battle ship can make the tower loss l_i longevity every second when it has been produced. If the longevity of the tower lower than or equal to 0, the player wins. Notice that at each time, the factory can choose only one kind of battle ships to produce or do nothing. And producing more than one battle ships of the same kind is acceptable.

Your job is to find out the minimum time the player should spend to win the game.

There are multiple test cases. 
The first line of each case contains two integers N(1 ≤ N ≤ 30) and L(1 ≤ L ≤ 330), N is the number of the kinds of Battle Ships, L is the longevity of the Defense Tower. Then the following N lines, each line contains two integers t _i(1 ≤ t _i ≤ 20) and l_i(1 ≤ l_i ≤ 330) indicating the produce time and the lethality of the i-th kind Battle Ships.

Output one line for each test case. An integer indicating the minimum time the player should spend to win the game.

1 1
1 1
2 10
1 1
2 5
3 100
1 10
3 20
10 100

2
4
5

题意及分析：

因为每次可以选择做或不做。所以当然选择建一个战舰。dp[j]表示j的时间内造成的伤害。dp[j+t[i]]前t[i]的时间来建战舰。剩余的j的时间则有可以看做一个小的整体。dp[j+t[i]]=max(dp[j+t[i]],dp[j]+j*a[i]]);这就是需要的递推式。

AC代码：