Space Elevator
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 2690 | Accepted: 1101 |
Description
The
cows are going to space! They plan to achieve orbit by building a sort
of space elevator: a giant tower of blocks. They have K (1 <= K
<= 400) different types of blocks with which to build the tower.
Each block of type i has height h_i (1 <= h_i <= 100) and is
available in quantity c_i (1 <= c_i <= 10). Due to possible
damage caused by cosmic rays, no part of a block of type i can exceed a
maximum altitude a_i (1 <= a_i <= 40000).
Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.
Help the cows build the tallest space elevator possible by stacking blocks on top of each other according to the rules.
Input
* Line 1: A single integer, K
* Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.
* Lines 2..K+1: Each line contains three space-separated integers: h_i, a_i, and c_i. Line i+1 describes block type i.
Output
* Line 1: A single integer H, the maximum height of a tower that can be built
Sample Input
3
7 40 3
5 23 8
2 52 6
Sample Output
48
Hint
OUTPUT DETAILS:
From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3. Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.
From the bottom: 3 blocks of type 2, below 3 of type 1, below 6 of type 3. Stacking 4 blocks of type 2 and 3 of type 1 is not legal, since the top of the last type 1 block would exceed height 40.
Source
題目大意：
將k種block(每種不超過c[i]),堆得儘量高，但是對某i種block，高度不能超過a[i].求最大高度
1.如果沒有高度限制，只是簡單的堆積，全部用上最好。
2.有高度限制，就像揹包的容量限制，只不過對每種的限制不一樣而已，既然這樣，我們將限制高度從小到大先排列一下，如果保證限制高度小的在下面，那麼一定可以構造出最優解。
3.轉換成了限制數量的物品加入揹包問題(xiaoz想到了限制數量的錢幣湊錢問題---得到了n^2方法，強大！)。
設exist[i][j]表示前i個是否能湊成高度爲j的block～
如果按照n^3方法（當然存在一些優化），就是枚舉已經排好序的物品，以及物品個數，枚舉可以湊到的高度，將相應能湊到的高度標記即可。
用xiaoz的方法就是：首先對高度進行枚舉，同時記錄對任意高度需要某種block的最小值，在枚舉構造過程中改變這個需要的最小值，最後求出最大的高度即可。初始化0高度需要任一種爲0。
moving：如果時限要求嚴格一點也許我的方法就過不去了，沒有想到已經用過的方法，應該反省一下。
