poj 3253 Fence Repair（哈夫曼树）

Fence Repair

Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

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
8
5

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).

一道简单的哈夫曼树，可以用优先队列做。

使用贪心策略，每次选取其中最小的两个出对，合并后再插入队列。

一.用priority_queue：

由于默认是由大到小，所以这里自己定义优先级

#include <iostream>#include <stdio.h>#include <queue>using namespace std;struct node{    friend bool operator<(node a,node b)    {        return a.x>b.x;    }    int x;};int main(){    priority_queue<node> Q;    int n,i;    __int64 sum=0;    node a;    scanf("%d",&n);    for(i=0; i<n; i++)    {        scanf("%d",&a.x);        Q.push(a);    }    while(Q.size()>1)    {        a.x=Q.top().x;        Q.pop();        a.x+=Q.top().x;        Q.pop();        sum+=a.x;        Q.push(a);    }    printf("%I64d\n",sum);    return 0;}

二.构造小根堆，实现出队入队函数：

#include <iostream>#include <stdio.h>using namespace std;const int maxn=20005;int len;int heap[maxn];void insert(int k)  //将k插入小根堆，并维护其性质{    int t=++len;    //插入队尾    heap[t]=k;    while(t>1)      //自下而上，将k移到合适位置    {        if(heap[t/2]>heap[t])           {            swap(heap[t/2],heap[t]);            t/=2;        }        else break;    }}void pop()      //取堆首，并维护其性质{    int t=1;         heap[t]=heap[len];  //队尾元素移至堆首，堆长减一    len--;    while(t*2<=len)     //从堆首开始，自上而下调整    {        int k=t*2;        if(k<len && heap[k]>heap[k+1])            k++;        if(heap[t]>heap[k])        {            swap(heap[k],heap[t]);            t=k;        }        else break;    }}int main(){    int n,i,a;    int p[maxn];    scanf("%d",&n);    for(i=1;i<=n;i++)        scanf("%d",&p[i]);    len=0;    for(i=1;i<=n;i++)        insert(p[i]);    __int64 sum=0;    while(len>1)    {        a=heap[1];        pop();        a+=heap[1];        pop();        sum+=a;        insert(a);    }    printf("%I64d\n",sum);    return 0;}