求二叉树中节点的最大距离

《编程之美》 3.8 求二叉树节点中的最大距离

问题：如果把二叉树看成一个图，并且父子结点之间的连线看成是双向的，姑且定义“距离”为两个结点之间边的个数，求一棵二叉树中相距最远的两个结点之间的距离。

解法一：详见《编程之美》3.8以及代码。

代码一：

typedef struct BinTreeNode
{
	char data;
	int nMaxLeft;
	int nMaxRight;
	BinTreeNode *lchild,*rchild;
};
/*------------------------------------------------------------------------*/ 
void FindMaxDist(BinTreeNode *pRoot)
{
	if (pRoot == NULL) {
		return;
	}
	
	if (pRoot->lchild == NULL) {
		pRoot->nMaxLeft = 0;
	}
	if (pRoot->rchild == NULL) {
		pRoot->nMaxRight = 0;
	}
	
	if (pRoot->lchild != NULL) {
		FindMaxDist(pRoot->lchild);
	}
	if (pRoot->rchild != NULL) {
		FindMaxDist(pRoot->rchild);
	}
	
	if (pRoot->lchild != NULL) {
		int nTempMax = 0;
		if (pRoot->lchild->nMaxLeft > pRoot->lchild->nMaxRight) {
			nTempMax = pRoot->lchild->nMaxLeft;
		}
		else {
			nTempMax = pRoot->lchild->nMaxRight;
		}
		pRoot->nMaxLeft = nTempMax + 1;
	}
	if (pRoot->rchild != NULL) {
		int nTempMax = 0;
		if (pRoot->rchild->nMaxLeft > pRoot->rchild->nMaxRight) {
			nTempMax = pRoot->rchild->nMaxLeft;
		}
		else {
			nTempMax = pRoot->rchild->nMaxRight; 
		}
		pRoot->nMaxRight = nTempMax + 1;
	}
	
	if (pRoot->nMaxLeft + pRoot->nMaxRight > nMaxLen) {
		nMaxLen = pRoot->nMaxLeft + pRoot->nMaxRight; 
	}
}

/*-------------------------------------------------------------------------*/

解法二：使用最基本的二叉树结点的定义，详见《 [编程之美]求二叉树中节点的最大距离》。

代码二：

#include <stdio.h>
#include <stdlib.h>
#include <stack>
using namespace std;

typedef struct BinTreeNode * BinTree;
typedef struct BinTreeNode 
{
	char data;
	BinTreeNode *lchild,*rchild;	
};


int MaxDistanceBetweenNodes(BinTreeNode *pRoot,int *pmax)
{
	// return 0 if leaf node
	if (pRoot->lchild == NULL && pRoot->rchild == NULL) {
		return 0;
	}
	
	// depth of two sub-trees
	int ldepth = 0;
	int rdepth = 0;
	
	if (pRoot->lchild != NULL) {
		ldepth = 1 + MaxDistanceBetweenNodes(pRoot->lchild,pmax);
	}
	if (pRoot->rchild != NULL) {
		rdepth = 1 + MaxDistanceBetweenNodes(pRoot->rchild,pmax);
	} 
	
	if (ldepth + rdepth > *pmax) {
		*pmax = ldepth + rdepth;
	}
	
	return ldepth > rdepth ? ldepth : rdepth;
}

int MaxDistanceInBinTree(BinTreeNode *pRoot,int *pmax)
{
	if (pRoot == NULL || pmax == NULL) {
		return -1;
	}
	*pmax = 0;
	return MaxDistanceBetweenNodes(pRoot,pmax);
}

void buildBinTree(BinTree *T,char *str)
{
	stack<BinTree> s;
	*T = NULL;
	BinTree p,t;
	p = t = NULL;
	int i,k;
	i = 0;
	while(str[i])
	{
		switch(str[i]){
			case '(': s.push(p); k = 1; break;
			case ')': t = s.top(); s.pop(); break;
			case ',': k = 2; break;
			default:
				p = new BinTreeNode;
				p->data = str[i];
				p->lchild = p->rchild = NULL;
				if (*T == NULL){
					*T = p;
				}
				else if (k == 1){
					t = s.top();
					t->lchild = p;					
				}
				else {
					t = s.top();
					t->rchild = p;
				}
		}
		i++;
	}
}

int main()
{
	BinTree T;
	char *t = "A(B(C,D),E(F,))";
	buildBinTree(&T,t);
	int *pmax = (int *)malloc(sizeof(int));
	printf("Max Distance : %d %d.\n",*pmax,MaxDistanceInBinTree(T,pmax));
	free(pmax);
}

测试输出：

Max Distance : 4 2.

REF：

1，《编程之美》 3.8 求二叉树中结点的最大距离

2，http://blog.youkuaiyun.com/lalor/article/details/7626678