poj3253 Fence Repair

最新推荐文章于 2023-03-04 18:57:46 发布

原创最新推荐文章于 2023-03-04 18:57:46 发布 · 342 阅读

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#优先队列 #数组模拟

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本文介绍了一种通过优先队列实现的最优木板切割算法，旨在解决如何最小化切割成本的问题。通过将所需木板长度排序并逐步合并，该算法能够有效减少总切割费用。

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Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 32257		Accepted: 10372

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).

嗯，题目大意就是锯木头，木头的长度就是所需的钱，问如何据就是先据哪个长度的所花的花费最少。

优先队列，从小到大排，取出两个值取和，再把和放入队列，一直加到最后就出结果啦

这个是STL里优先队列，

#include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
int main()
{
	__int64 n,m,sum,a,b;
	while(~scanf("%I64d",&n))
	{
		sum=0;
		priority_queue<__int64,vector<__int64>,greater<__int64> >q;
		while(n--)
		{
			scanf("%I64d",&m);
			q.push(m);	
		}
		while(q.size()>1)
		{
			a=q.top();
			q.pop();
			b=q.top();
			q.pop();
			sum=sum+a+b;
			q.push(a+b);
		}
		printf("%I64d\n",sum);
	}
	return 0;
}

这个是数组模拟的优先队列

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int cmp(__int64 a,__int64 b)
{
	return a<b;
}
int main()
{
	__int64 i,n,m,minc,sum;
	while(~scanf("%I64d",&n))
	{
		__int64 *w=(__int64 *)malloc((n+1)*sizeof(__int64));
		for(i=0;i<n;++i)
			scanf("%I64d",&w[i]);
		sort(w,w+n,cmp);
		sum=0;// 例如6 7 8 9此时i==0,j==2,8 13 9此时i==0,j从2增到3，若大于则已是最后一位跳出 
		minc=0;//
		for(int i=0;i<n-1;++i)
		{
			sum=w[i]+w[i+1];//前两位相加 
			minc+=sum;
			for(int j=i+2;j<=n-1;++j)
			{
				if(sum>w[j])//与下一位比较 
				{
					w[j-1]=w[j];
					if(j==n-1)//若此时是最大当j==n-1时 意味着它已经移到最后一位了可以跳出循环了 
					{
						w[j]=sum;
						break;	
					}
				}
				else//如果不大于的话，就把它放在前面一位 
				{
					w[j-1]=sum;
					break;
				}
			}
		}
		printf("%I64d\n",minc);
	}
	return 0;
}