[POJ3253]-Fence Repair

最新推荐文章于 2022-09-27 09:16:56 发布

原创最新推荐文章于 2022-09-27 09:16:56 发布 · 307 阅读

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#哈夫曼树

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本文介绍了一种使用哈弗曼树解决木板切割成本最小化的问题。通过C++ STL中的multiset实现自动排序并选取最短两段进行合并，以此递归直至所有木板被切割完成，从而得出最小总花费。

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K

Description

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 L_i (1 ≤ L_i ≤ 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 L_i). 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.

Input

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

Output

Line 1: One integer: the minimum amount of money he must spend to make N-1 cuts

Sample Input

Sample Output

Hint

He wants to cut a board of length 21 into pieces of lengths 8, 5, and 8.
The original board measures 8+5+8=21. The first cut will cost 21, and should be used to cut the board into pieces measuring 13 and 8. The second cut will cost 13, and should be used to cut the 13 into 8 and 5. This would cost 21+13=34. If the 21 was cut into 16 and 5 instead, the second cut would cost 16 for a total of 37 (which is more than 34).

题目描述：

John想修筑Fence需要木材，于是要去割木材，这时他需要工具，但是它不是免费的，每次切n长度的木材时需要n单位的金币，给出John需要的木材数和木材长度，问John最小花费是多少。

解题思路：

此题符合哈弗曼树的特性，所以需利用哈弗曼思想求解。

我这里使用了c++中STL之multiset来进行求解，非常方便，multiset是自动升序的，每次我取第一，二个数据求和插入，并将第一，二数据删除，最后的只剩一个时就是结果了

#include <set>
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
//#define N 100000
typedef long long LL;
//int wood[N];
int main()
{
//	freopen("data.txt","r",stdin);
	int n;
	while(~scanf("%d",&n))
	{

		multiset<int> s;
		LL res=0;
//		multiset<int>::iterator it = s.begin();
		int wood;
		for(int i = 0;i < n;++ i)
		{
			scanf("%d",&wood);
			s.insert(wood);
		}
		multiset<int>::iterator begin;
		int temp=0;
		while(s.size()>1)
		{
			begin = s.begin();
			temp = *begin;
			s.erase(begin);
			begin = s.begin();
			temp+= *begin;
			s.erase(begin);
			res+=temp;
			s.insert(temp);
		}
		printf("%lld\n",res);
	}
	return 0;
}