[ACM] POJ 3253 Fence Repair （Huffman樹思想，優先隊列）

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 25274		Accepted: 8131

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

解題思路：

對所輸入的數據構造Huffman樹，其中非葉子節點的值加起來的和爲所求。

Huffman樹的構造過程： 每次取所有數中的兩個最小數，相加起來得到一個非葉子節點的值，下次取的時候以前取過的兩個最小數數不能再取，再相加得到非葉子節點的值可以取。

比如 3 ， 4 ， 5  ，先取  3 ，4 相加爲 7 ， 然後取 5 ，7（3,4取過不能再取了),相加爲12，    7+12 =19，即爲所求。

優先隊列可以很好的實現這個操作。

定義int類型優先級從小到大的代碼爲：

priority_queue<int ,vector<int>,greater<int> > q

代碼：

#include <iostream>
#include <queue>
using namespace std;
int main()
{
    priority_queue<int ,vector<int>,greater<int> > q;
    int n;
    int num;
    cin>>n;
    while(n--)
    {
        cin>>num;
        q.push(num);
    }
    long long sum=0;

    while(!q.empty())
    {
        int n1=q.top();
        q.pop();
        int n2=q.top();
        q.pop();
        sum+=n1+n2;
        if(q.empty())
            break;
        q.push(n1+n2);
    }

    cout<<sum<<endl;
    return 0;
}

Fence Repair

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 25274		Accepted: 8131

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

解題思路：

對所輸入的數據構造Huffman樹，其中非葉子節點的值加起來的和爲所求。

Huffman樹的構造過程： 每次取所有數中的兩個最小數，相加起來得到一個非葉子節點的值，下次取的時候以前取過的兩個最小數數不能再取，再相加得到非葉子節點的值可以取。

比如 3 ， 4 ， 5  ，先取  3 ，4 相加爲 7 ， 然後取 5 ，7（3,4取過不能再取了),相加爲12，    7+12 =19，即爲所求。

優先隊列可以很好的實現這個操作。

定義int類型優先級從小到大的代碼爲：

priority_queue<int ,vector<int>,greater<int> > q

代碼：

#include <iostream>
#include <queue>
using namespace std;
int main()
{
    priority_queue<int ,vector<int>,greater<int> > q;
    int n;
    int num;
    cin>>n;
    while(n--)
    {
        cin>>num;
        q.push(num);
    }
    long long sum=0;

    while(!q.empty())
    {
        int n1=q.top();
        q.pop();
        int n2=q.top();
        q.pop();
        sum+=n1+n2;
        if(q.empty())
            break;
        q.push(n1+n2);
    }

    cout<<sum<<endl;
    return 0;
}