首页 > 代码库 > POj 3253 Fence Repair(修农场栅栏，锯木板)（小根堆 + 哈弗曼建树得最小权值思想 ）

POj 3253 Fence Repair(修农场栅栏，锯木板)（小根堆 + 哈弗曼建树得最小权值思想 ）

2024-11-21 05:29:02   203人阅读

Fence Repair
Time Limit: 2000MS Memory Limit: 65536K
Total Submissions: 28359 Accepted: 9213

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 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.

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

3858

Sample Output

34

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：农夫约翰，想要修复农场栅栏， 它需要n段木板，第二行输入这n段木板的长。
   现在，他用借来的锯子锯木板，每次锯都需要付费，每次锯所要的话费是：当前要锯的这块木板的长度。约翰现在拿着一个长度刚好为所需要各个子木板的长度总和的大木板。
   现在要把它锯成各个子木板，问：最小话费是多少？
  逆向建哈夫曼树的思想，最后得到的一定最小的权值总和，即是最小花费。
  由于数据在累加的过程中比较大，int会溢出，所以需要用long long int。 （2Y）
 
  代码：
 
#include <stdio.h>#include <string.h>#include <stdlib.h>#include <iostream>#include <string>#include <algorithm>#include <queue>using namespace std;int main(){	int n, dd;	int i, j;	priority_queue<int, vector<int>, greater<int> >q;	scanf("%d", &n);	for(i=0; i<n; i++)	{		scanf("%d", &dd);		q.push(dd);	}	long long int x, y;	long long int sum=0;	while(q.size()>1)	{		x=q.top(); q.pop();		y=q.top(); q.pop();		x=x+y; q.push(x);		sum=sum+x;		//printf("%d--", sum );	}	printf("%lld\n", sum);	return 0;}

 

POj 3253 Fence Repair(修农场栅栏，锯木板)（小根堆 + 哈弗曼建树得最小权值思想 ）


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