poj3253

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 38394		Accepted: 12481

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

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).

Source

USACO 2006 November Gold

题意：一块木板按照某个顺序切成a[1], a[2]...a[n]的长度，每次切都会加上该两段木板的长度，问选择什么顺序切能使得累加和最小

分析：网上说：这是哈夫曼树。很容易想到先切掉最长的，反过来也就是相当于每次取最短的两块合并成一块，直到最后剩下原来的一块，优先队列实现

            我说：本题就是一 合并果子 的变形，末状态为1，即que.size()>1，水过~~

#include<cstdio>
#include<queue>
using namespace std;
#define N 20010
int n,a[N];
priority_queue<int,vector<int>,greater<int> >que;
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d",a+i);
    for(int i=1;i<=n;i++) que.push(a[i]);
    long long ans=0;
    while(que.size()>1){
        int t1=que.top();que.pop();
        int t2=que.top();que.pop();
        ans+=t1+t2;
        que.push(t1+t2);
    }
    printf("%I64d
",ans);
    return 0;
}