构造哈夫曼树

1.算法说明

就是建造哈夫曼树树，从而使得构造出的树带权路径长度最小

 

2.步骤

 

输入叶子结点个数n；

创建长度为2*n-1的数组并初始化；

while(i<n) 循环输入n个叶子结点的权值；

while(n-1次循环建立树){

在parent==-1的元素中查找权最小的两个结点；

合并两个叶子结点，并加入新结点到数组；

}

 

3.代码

//构造haffman树
#include <iostream>
using namespace std;
const int MAX = 10000;
struct Node{
	int weight;			//权值
	int parent;			//双亲
	int lchild;			
	int rchild;
};

//创建一个haffman树
void createHaffman(Node* &a, int n){
	int m1,m2, x1, x2;//m1,m2是最小的两个值，x1,x2是他们的位置
	//n个结点，只需要n-1次就可以构造好
	for(int i=0; i<n-1; i++){
		m1 = m2 = MAX;
		x1 = x2 = 0;
		//查找最小值，在查找到最小的两个值后，构造新的节点，并加入到a中（数组的n+i个节点之后），长度加1,故而查找过程中长度不断增加n+i
		for(int j=0; j<n+i; j++){
			//首先必须满足，还没有双亲的孤立节点,查找m1,m2都是最小
			if(a[j].parent == -1 && a[j].weight < m1){
				m1 = a[j].weight;
				x1 = j;
			}else if(a[j].parent == -1 && a[j].weight < m2){
				m2 = a[j].weight;
				x2 = j;
			}
		}
		//新的节点存入n+i,并设置x1, x2的双亲
		a[x1].parent = n+i;
		a[x2].parent = n+i;
		a[n+i].weight = a[x1].weight + a[x2].weight;
		a[n+i].parent = -1;
		a[n+i].lchild = x1;
		a[n+i].rchild = x2;
	}
}

//测试得到最小和次小的值
void test(){
	int a[] = {3,4,7,0,79,9,12,1,4};
		int m = MAX,k = MAX;
	for(int i=0; i<9; i++){
		if(a[i]<m){
			 m = a[i];
		}else if(a[i]<k){
			 k = a[i];
		}
		
	}
	cout<<m<<" "<<k<<endl;
}


int main(){
	int n;
	cout<<"输入叶子节点个数：";
	cin>>n;
	Node* a = new Node[2*n - 1];
	for(int i=0; i<2*n-1; i++){//初始化
		a[i].weight = 0;
		a[i].parent = -1;
		a[i].lchild = -1;
		a[i].rchild = -1;
	}
	
	cout<<"输入前n个叶子结点的权值"<<endl;
	for(int i=0; i<n; i++){
		cin>>a[i].weight;
	}
	
	cout<<"输出构造好的haffman树"<<endl;
	createHaffman(a, n);
	for(int i=0; i<2*n-1; i++){
		cout<<"["<<a[i].weight<<","<<a[i].parent<<","<<a[i].lchild<<","<<a[i].rchild<<"]"<<endl;
	}
	
	delete[] a;
	return 0;
}