1003. Width of Binary Trees

最新推荐文章于 2021-06-23 14:01:31 发布

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本文介绍了一种计算二叉树最大宽度的方法，利用层次遍历并在每层末尾加入标志结点，以此来准确计算每一层的节点数，从而找出二叉树的最大宽度。

Description

The maximum number of nodes in all levels in a binary tree is called the width of the tree. For example, the binary tree on the right in the following figure has width 4 because the maximum number of nodes is 4 on the third level. Implement the following function that computes the width of a binary tree.

typedef int T;

struct treeNode {
T data;
struct treeNode *left, *right;

treeNode(T d, treeNode *l=NULL, treeNode *r=NULL):data(d),left(l),right(r){};
};

int width(const treeNode * root);

// return the width of the binary tree root.

求二叉树的最大宽度，可用层次遍历二叉树，在遍历完一层后加上一个标志结点，通过标志结点来计算该层的宽度。

#include <iostream>
#include <queue>
using namespace std;

typedef int T;

struct treeNode {
    T data;
    struct treeNode *left, *right;
    
    treeNode(T d, treeNode *l=NULL, treeNode *r=NULL):data(d),left(l),right(r){};
};


int width(const treeNode* root) {
    if (root == NULL) {
        return 0;
    }
    else {
        int max = 1;
        queue<const treeNode* > q;
        q.push(root);
        const treeNode* a = new treeNode(1, NULL, NULL); //标志结点
        q.push(a);
        while (!q.empty()) {  //可以是while (1)
            root = q.front();
            q.pop();
            if (q.size() == 0) break; //用于跳出循环
            if (root == a) {
                q.push(a); //继续将标志结点push进队列，则此时队列中除标志结点均为同层的结点，该层的宽度为size-1
                if (q.size() - 1 > max) {
                    max = q.size() - 1;
                }
            }
            else {
                if (root->left != NULL) {
                    q.push(root->left);
                }
                if (root->right != NULL) {
                    q.push(root->right);
                }
            }
        }
        return max;
    }
}