poj 3253 Fence Repair

最新推荐文章于 2023-03-04 18:57:46 发布

wdmzsly

最新推荐文章于 2023-03-04 18:57:46 发布

阅读量685

点赞数

分类专栏：优先队列

本文链接：https://blog.youkuaiyun.com/wdmzsly/article/details/51365170

版权

优先队列专栏收录该内容

1 篇文章

订阅专栏

本文介绍了一种解决木板切割问题的算法，目标是最小化切割过程中产生的成本。通过优先选择最短的两块木板进行合并，最终实现整体成本最小化。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 37649		Accepted: 12210

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).

题意：

将一个长度为L的木板分成n个长度的小木板

每次切木板时开销为大木板的长度

比如长度为21的木板切成5，8，8，时

21->13，8 开销为21

13->5，8 开销是13

总开销为：21+13=34

求最小开销

思路：

只需每次取出最短的两块，并把两块长度之和加到集合中

直到集合中剩下一个木板为止

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;

priority_queue<int,vector<int>,greater<int> > q;

int main(){
    long long s;
    int i,n,k,u,v;
    while(~scanf("%d",&n)){
        while(!q.empty())
            q.pop();
        while(n--){
            scanf("%d",&k);
            q.push(k);
        }
        s=0;
        while(q.size()>1){
            u=q.top();
            q.pop();
            v=q.top();
            q.pop();
            s+=u+v;
            q.push(u+v);
        }
        cout<<s<<endl;
    }
    return 0;
}