N - Fence Repair

蔚落 2022-03-20 08:12 159阅读 0赞

### 题目描述： ###

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  
3  
8  
5  
8  
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).  
题意：农夫要修理牧场的一段栅栏，他测量了栅栏，发现需要N块木头，每块木头长度为整数Li个长度单位，于是他购买了一条很长的、能锯成N块的木头，即该木头的长度是Li的总和。  
但是农夫自己没有锯子，请人锯木的酬金跟这段木头的长度成正比。为简单起见，不妨就设酬金等于所锯木头的长度。例如，要将长度为21的木头锯成长度为8、5和8的三段，第一次锯木头花费21，将木头锯成13和8；第二次锯木头花费13，将长度为13的木头锯成8和5，总花费为34。如果第一次将木头锯成16和5，则第二次锯木头花费16，总花费为37（大于34）。  
请编写程序帮助农夫计算将木头锯成N块的最少花费。

##### 分析： #####

这是可以用树做出来， 但是也可以用贪心，优先队列。

#include"stdio.h"
    #include"string.h"
    #include"queue"
    #include"algorithm"
    using namespace std;
    int main()
    {
        long long N;
        long long a[50001];
        long long Price;
        long long i,j,k;
        long long sum,t;
        while(~scanf("%lld",&N))
        {
            sum=0;
            Price=0;
            priority_queue<long long,vector<long long>, greater<long long> > Q;
            for(i=0; i<N; i++)
            {
                scanf("%lld",&a[i]);
                Q.push(a[i]);
            }
            while(Q.size()>=2)
            {
                long long a=Q.top();
                long long b;
                Q.pop();
                b=Q.top();
                Q.pop();
                sum=a+b;
                Price+=sum;
                Q.push(sum);
    
            }
            long long a=Q.top();
            printf("%lld\n",Price);
    
        }
    }