poj 3253 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 · 355 阅读

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解决一个关于如何将长木板锯成多段以达到最小总花费的问题，通过使用哈夫曼树实现贪心策略。

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 24144		Accepted: 7698

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).

大意是给你一块长木板，每次锯开需要的花费与木板长度相同，给你要锯成的每一小块长度，求最小花费。
一个贪心问题，可以用哈夫曼树做

 #include<algorithm>
#include<stdio.h>
using namespace std;
int main()
{
    __int64 a[20000],n,sum=0,b,i=0,j;//这里要声明__int64，输出用%I64d,c++中的64位扩展
    scanf("%I64d",&n);
    for(i=0;i<n;i++)
    {
        scanf("%I64d",&a[i]);
    }
    sort(a,a+n);
    for(i=0;i<n-1;i++)//这个循环是算法核心，每次取最小的两个结合
    {
        b=a[i]+a[i+1];
        j=i+1;
        while(b>a[j]&&j<n)
        {
            a[j-1]=a[j];
            j++;
        }
        a[j-1]=b;
        sum+=b;
    }
    printf("%I64d",sum);
}