Fence Repair
题目描述
Farmer John wants to repair a small length of the fence around the pasture. He measures the fence and finds that he needs N (1 ≤ N ≤ 20,000) planks of wood, each having some integer length Li (1 ≤ Li ≤ 50,000) units. He then purchases a single long board just long enough to saw into the N planks (i.e., whose length is the sum of the lengths Li). FJ is ignoring the “kerf”, the extra length lost to sawdust when a sawcut is made; you should ignore it, too.FJ sadly realizes that he doesn’t own a saw with which to cut the wood, so he mosies over to Farmer Don’s Farm with this long board and politely asks if he may borrow a saw.Farmer Don, a closet capitalist, doesn’t lend FJ a saw but instead offers to charge Farmer John for each of the N-1 cuts in the plank. The charge to cut a piece of wood is exactly equal to its length. Cutting a plank of length 21 costs 21 cents.Farmer Don then lets Farmer John decide the order and locations to cut the plank. Help Farmer John determine the minimum amount of money he can spend to create the N planks. FJ knows that he can cut the board in various different orders which will result in different charges since the resulting intermediate planks are of different lengths.
输入
Line 1: One integer N, the number of planks
Lines 2..N+1: Each line contains a single integer describing the length of a needed plank
输出
Line 1: One integer: the minimum amount of money he must spend to make N-1 cuts
样例输入
3
8
5
8
样例输出
34
题目大意
将一块很长的木板切成N快,给出处理以后的的木板长度,求切割的成本。其中切割成本计算方法:将一块木板切割成两份的成本为切割前的木板长度。
解题思路
- 逆向推导,使用贪心算法,每次都只取长度最小的两块木板,计算这次切割的成本以后,将其当做新的未被切割的木板进行下一步操作
- 就是哈夫曼编码中构造哈夫曼树的过程
代码
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