#include <iostream>
#include <iomanip>
using namespace std;
//哈夫曼树的存储表示
typedef struct
{
int weight; // 权值
int parent, lChild, rChild; //父母节点,左孩子,右孩子
}HTNode, *HuffmanTree;
// 选择权值最小的两颗树
void SelectMin(HuffmanTree hT, int n, int &s1, int &s2)
{
s1=s2=0;
int i;
for(i=1;i<n;++i)
{
if(hT[i].parent==0)
{
if(s1==0)
s1=i;
else
{
s2=i;
break;
}
}
}
if(hT[s1].weight>hT[s2].weight)
{
int t=s1;
s1=s2;
s2=t;
}
for(i+=1;i<n;++i)
{
if(0==hT[i].parent)
{
if(hT[i].weight<hT[s1].weight)
{
s2=s1;
s1=i;
}
else if(hT[i].weight<hT[s2].weight)
s2=i;
}
}
}
// 构造有n个权值(叶子节点)的哈夫曼树
void CreateHufmanTree(HuffmanTree &hT)
{
int n,m,i;
cin >>n;
m=2*n-1;
hT=new HTNode[m+1]; // 0号节点不使用
for(i=1;i<=m;++i)
{
hT[i].parent=hT[i].lChild=hT[i].rChild=0;
}
for(i=1;i<=n;++i)
{
cin>>hT[i].weight; // 输入权值
}
hT[0].weight=m; // 用0号节点保存节点数量
/****** 初始化完毕, 创建哈夫曼树 ******/
for(i=n+1;i<=m;++i)
{
int s1,s2;
SelectMin(hT,i,s1,s2);
hT[s1].parent=hT[s2].parent=i;
hT[i].lChild=s1; hT[i].rChild=s2; // 作为新节点的孩子
hT[i].weight=hT[s1].weight+hT[s2].weight; // 新节点为左右孩子节点权值之和
}
}
int HuffmanTreeWPL_(HuffmanTree hT, int i, int deepth)
{
if(hT[i].lChild==0&&hT[i].rChild==0)
return
hT[i].weight*deepth;
else
return
HuffmanTreeWPL_(hT,hT[i].lChild, deepth+1) + HuffmanTreeWPL_(hT,hT[i].rChild,deepth+1);
}
// 计算WPL(带权路径长度)
int HuffmanTreeWPL(HuffmanTree hT)
{
return HuffmanTreeWPL_(hT,hT[0].weight,0);
}
// 销毁哈夫曼树
void DestoryHuffmanTree(HuffmanTree &hT)
{
delete[] hT;
hT=NULL;
}
int main()
{
HuffmanTree hT;
CreateHufmanTree(hT);
cout<<HuffmanTreeWPL(hT)<<endl;
DestoryHuffmanTree(hT);
return 0;
}