本文實例講述了PHP基于非遞歸算法實現(xiàn)先序、中序及后序遍歷二叉樹操作刊殉。分享給大家供大家參考,具體如下
概述:
二叉樹遍歷原理如下:
image
針對上圖所示二叉樹遍歷:
1. 前序遍歷:先遍歷根結(jié)點州胳,然后遍歷左子樹记焊,最后遍歷右子樹。
ABDHECFG
2.中序遍歷:先遍歷左子樹栓撞,然后遍歷根結(jié)點遍膜,最后遍歷右子樹。
HDBEAFCG
3.后序遍歷:先遍歷左子樹瓤湘,然后遍歷右子樹瓢颅,最后遍歷根節(jié)點。
HDEBFGCA
實現(xiàn)方法:
先序遍歷:利用棧先進后出的特性弛说,先訪問根節(jié)點挽懦,再把右子樹壓入,再壓入左子樹木人。這樣取出的時候是先取出左子樹巾兆,最后取出右子樹。
function preorder($root){
$stack = array();
array_push($stack, $root);
while(!empty($stack)){
$center_node = array_pop($stack);
echo $center_node->value; // 根節(jié)點
if($center_node->right != null)
array_push($stack, $center_node->right); // 壓入右子樹
if($center_node->left != null)
array_push($stack, $center_node->left); // 壓入左子樹
}
}
中序:需要從下向上遍歷虎囚,所以先把左子樹壓入棧,然后逐個訪問根節(jié)點和右子樹蔫磨。
function inorder($root){
$stack = array();
$center_node = $root;
while(!empty($stack) || $center_node != null){
while($center_node != null){
array_push($stack, $center_node);
$center_node = $center_node->left;
}
$center_node = array_pop($stack);
echo $center_node->value;
$center_node = $center_node->right;
}
}
后序:先把根節(jié)點存起來淘讥,然后依次儲存左子樹和右子樹。然后輸出堤如。
function tailorder($root){
$stack = array();
$outstack = array();
array_push($$stack, $root);
while($empty($stack)){
$center_node = array_pop($stack);
array_push($outstack, $center_node);
if($center_node->right != null)
array_push($stack, $center_node->right);
if($center_node->left != null)
array_push($stack, $center_node->left);
}
while($empty($outstack)){
$center_node = array_pop($outstack);
echo $center_node->value;
}
}