poj3253 堆/优先队列

 

 

如题：http://poj.org/problem?id=3253

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 28608		Accepted: 9295

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).

 

题目大意：把一个切木板切成n个长度的n块木板，比如列子8 5 8，没切前是21，先切21成8和13，cost=21，再切13成5和8，cost=21+13=34.

 

一开始的思路是从大到小排序，每次切除最大的，结果是不对的。

 

正确应该是将木板看成一颗树，带权路径最短。 也就是说越小的离跟越远。也就是一颗哈弗曼树。

用小根堆还维护，每次选最小的2个累加到结果，加起来的值继续放入堆维护，直到堆只剩一个元素。

 

下面是手写堆

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
#define longlong long long
longlong heap[20005];
int len=0;

void down(int x)
{
 int p=x*2;
 longlong t=heap[x];
 while(p<=len)
 {
  if(p<len&&heap[p+1]<heap[p])
   p++;
  if(heap[p]>t)
   break;
  else
  {
   heap[x]=heap[p];
   x=p;
   p*=2;
  }
 }
 heap[x]=t;
}
void up(int x)
{
 int p=x/2;
 longlong t=heap[x];
 while(p>=1)
 {
  if(heap[p]>t)
  {
   heap[x]=heap[p];
   x=p;
   p=x/2;
  }
  else
   break;
 }
 heap[x]=t;
}
void push(longlong a)
{
 heap[++len]=a;
 up(len);
}
longlong pop()
{
 longlong t=heap[1];
 heap[1]=heap[len--];
 down(1);
 return t;
}
int main()
{
 int n;
 scanf("%d",&n);
 longlong x;
 longlong sum=0;
 while(n--)
 {
  scanf("%I64d",&x);
  push(x);
 }
 if(len==1)
  printf("%I64d\n",pop());
 else
 {
 while(len>=2)
 {
  longlong a=pop();
  longlong b=pop();
  sum+=a+b;
  push(a+b);
 }
 printf("%I64d\n",sum);
 }
 return 0;
}

 

 

其实堆不用自己写，下面给出C++标准库中的priorith_queue优先队列的操作。

 

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
#define ll long long

class cmp
{
public:
 bool operator()(const ll a,const ll b)
 {
  return a>b;
 }
};
int main()
{
 int n;
 priority_queue<ll,vector<ll>,cmp>q;
 scanf("%d",&n);
 int x,i;
 for(i=1;i<=n;i++)
 {
  scanf("%d",&x);
 q.push(x);
 }
 ll sum=0;
 while(q.size()>1)
 {
  ll a=q.top();
  q.pop();
  ll b=q.top();
  q.pop();
  sum+=a+b;
  q.push(a+b);

 }
 printf("%I64d\n",sum);
}