【算法框架】构造无限级树并广度深度遍历查找指定节点
前言
最近接到一个关于树的需求，想起了大学那会儿听过俞敏洪有关树的演讲，老师重复在课上放了很多次，N年过去了印象还是很深。
演讲内容是介样的，让我们一起来喝汤~
人的生活方式有两种，
第一种方式是像草一样活着，
你尽管活着，
每年还在成长，
但是你毕竟是一棵草，
你吸收雨露阳光，
但是却长不大。
人们可以踩过你，
但是人们不会因为你的痛苦，而他产生痛苦；
人们不会因为你被踩了，而来怜悯你，
因为人们本身就没有看到你。
所以我们每一个人，
都应该像树一样的成长，
即使我们现在什么都不是，
但是只要你有树的种子，
即使你被踩到泥土中间，
你依然能够吸收泥土的养分，
自己成长起来。
当你长成参天大树以后，
遥远的地方，人们就能看到你；
走近你，你能给人一片绿色。
活着是美丽的风景，
死了依然是栋梁之才，
活着死了都有用。
需求是这样的：
构造无限级树型结构，界面类似下边这样的结构
然后，还需要把所有的橙色标记的叶子节点从垂直方向筛选出来，最终效果就是得到一个这样顺序的一级数组
KKK
QQQ
JJJ
HHH
GGG
LLL
需要根据AAA这个节点和他所有子节点的数据，构造出一个无限级树型结构，如下
数据
- 顶级AAA数据
{"id":348019,"name":"AAA","is_leaf":2,"parent_id":347234,"type":0,"order":["348020"]}
- AAA所有的孩子节点
[{"id":348020,"name":"BBB","is_leaf":2,"parent_id":348019,"type":0,"order":["348037","348033","348021","348023","348034"]},{"id":348021,"name":"CCC","is_leaf":2,"parent_id":348020,"type":0,"order":["348022","348035"]},{"id":348022,"name":"DDD","is_leaf":2,"parent_id":348021,"type":0,"order":["348024","348032","348030"]},{"id":348024,"name":"EEE","is_leaf":2,"parent_id":348022,"type":0,"order":["348025","348036"]},{"id":348025,"name":"FFF","is_leaf":2,"parent_id":348024,"type":0,"order":["348031"]},{"id":348030,"name":"HHH","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348023,"name":"GGG","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348031,"name":"QQQ","is_leaf":1,"parent_id":348025,"type":11,"order":[]},{"id":348032,"name":"JJJ","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348035,"name":"MMM\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348021,"type":0,"order":[]},{"id":348036,"name":"NNN\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348024,"type":0,"order":[]},{"id":348033,"name":"KKK","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348037,"name":"OOO","is_leaf":2,"parent_id":348020,"type":0,"order":[]},{"id":348034,"name":"LLL","is_leaf":1,"parent_id":348020,"type":11,"order":[]}]
节点数据库结构都一样，核心是有一个parent_id，每个节点会保存直属叶子的排序order
实现
其实这里考察的递归构造树、广度优先遍历、深度优先遍历
其实不管啥语言，思想都是这样，因为这个需求是php写的接口，就用php给出实现代码，气氛搞起来~
构造无限级
private function getTree($list, $node)
{
$tree = [];
foreach ($list as $k => $v) {
if ($v['parent_id'] == $node['id']) {
$v['children'] = $this->getTree($list, $v);
$tree[] = $v;
}
}
if (empty($node['order'])) {
return [];
}
//注意：为了保证所有的叶子节点是根据已有的order排序，这里我们重新摆放一下
$treeMap = [];
foreach ($tree as $v) {
$treeMap[$v['id']] = $v;//建立id和数据的map
}
//根据order重新排序
$orderTree = [];
foreach ($node['order'] as $id) {//根据order的顺序重新摆放
$orderTree[] = $treeMap[$id];
}
return $orderTree;
}
我们来使用一下，使用如下
$topNodeJson = '{"id":348019,"name":"AAA","is_leaf":2,"parent_id":347234,"type":0,"order":["348020"]}';
$childrenJson = '[{"id":348020,"name":"BBB","is_leaf":2,"parent_id":348019,"type":0,"order":["348037","348033","348021","348023","348034"]},{"id":348021,"name":"CCC","is_leaf":2,"parent_id":348020,"type":0,"order":["348022","348035"]},{"id":348022,"name":"DDD","is_leaf":2,"parent_id":348021,"type":0,"order":["348024","348032","348030"]},{"id":348024,"name":"EEE","is_leaf":2,"parent_id":348022,"type":0,"order":["348025","348036"]},{"id":348025,"name":"FFF","is_leaf":2,"parent_id":348024,"type":0,"order":["348031"]},{"id":348030,"name":"HHH","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348023,"name":"GGG","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348031,"name":"QQQ","is_leaf":1,"parent_id":348025,"type":11,"order":[]},{"id":348032,"name":"JJJ","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348035,"name":"MMM\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348021,"type":0,"order":[]},{"id":348036,"name":"NNN\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348024,"type":0,"order":[]},{"id":348033,"name":"KKK","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348037,"name":"OOO","is_leaf":2,"parent_id":348020,"type":0,"order":[]},{"id":348034,"name":"LLL","is_leaf":1,"parent_id":348020,"type":11,"order":[]}]';
$topNode = json_decode($topNodeJson, true);
$childrenList = json_decode($childrenJson, true);
$topNode['children'] = $this->getTree($childrenList, $topNode);
echo json_encode($topNode);
最终输出的json如下
可以看到，已经构造出了一个无限级的树，并且和我们的界面是一模一样的层级和顺序
拉下来现在我们要遍历这棵树，为了获取到所有is_leaft=1的节点，我们先用广度优先遍历来试一下，因为这个对于找节点来说性能比较高
广度优先遍历
代码如下
private function bfsFindLeafs($node)
{
if (empty($node['children'])) {
return [];
}
$result = [];//满足条件的组合
$q = [];
$q[] = $node['children'][0];
while (count($q) > 0) {
$size = count($q);
for ($i = 0; $i < $size; $i++) {
$current = array_shift($q);
//判断节点如果是满足条件，加入路径
if ($current['is_leaf'] == 1) {
$result[] = $current;
}
//把所有的子节点加入队列
foreach ($current['children'] as $v) {
$q[] = $v;
}
}
}
return $result;
}
我们来使用一下
$getAllLeafs = $this->bfsFindLeafs($topNode);
echo json_encode($getAllLeafs);
运行后输出
[
{
"id": 348033,
"name": "KKK",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
},
{
"id": 348023,
"name": "GGG",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
},
{
"id": 348034,
"name": "LLL",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
},
{
"id": 348032,
"name": "JJJ",
"is_leaf": 1,
"parent_id": 348022,
"type": 11,
"order": [],
"children": []
},
{
"id": 348030,
"name": "HHH",
"is_leaf": 1,
"parent_id": 348022,
"type": 11,
"order": [],
"children": []
},
{
"id": 348031,
"name": "QQQ",
"is_leaf": 1,
"parent_id": 348025,
"type": 11,
"order": [],
"children": []
}
]
好，我们已经可以获取到所有is_leaf为1的节点了，但是这里有一个问题，不是从上到下输出的，是最近输出的
KKK->GGG->LLL->JJJ->HHH->QQQ
其实这就是因为广度优先遍历是最近输出的，为了从上到下输出，我们需要深度优先遍历来实现了
深度优先遍历
深度优先遍历其实就是回溯算法的一种，为了从上到下输出，需要先序遍历
/**
* 获取所有的叶子路径（深度度优先遍历）
*/
private function dfsFindLeafs($node)
{
$trackList = [];
foreach ($node['children'] as $v) {
if ($v['is_leaf'] == 1) {
$trackList[] = $v;
}
if (empty($v['children'])) {
continue;
}
$trackList = array_merge($trackList, $this->dfsFindLeafs($v));
}
return $trackList;
}
我们再来运行一下
$getAllLeafs = $this->dfsFindLeafs($topNode);
echo json_encode($getAllLeafs);
输出
[
{
"id": 348033,
"name": "KKK",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
},
{
"id": 348031,
"name": "QQQ",
"is_leaf": 1,
"parent_id": 348025,
"type": 11,
"order": [],
"children": []
},
{
"id": 348032,
"name": "JJJ",
"is_leaf": 1,
"parent_id": 348022,
"type": 11,
"order": [],
"children": []
},
{
"id": 348030,
"name": "HHH",
"is_leaf": 1,
"parent_id": 348022,
"type": 11,
"order": [],
"children": []
},
{
"id": 348023,
"name": "GGG",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
},
{
"id": 348034,
"name": "LLL",
"is_leaf": 1,
"parent_id": 348020,
"type": 11,
"order": [],
"children": []
}
]
顺序为
KKK->QQQ->JJJ->HHH->GGG->LLL
这次顺序终于对了，oh yeah~，和我们之前的界面垂直顺序一致
完整代码
下面给出完整代码
<?php
/**
* Class Test
* @author chenqionghe
*/
class Test
{
public function run()
{
$topNodeJson = '{"id":348019,"name":"AAA","is_leaf":2,"parent_id":347234,"type":0,"order":["348020"]}';
$childrenJson = '[{"id":348020,"name":"BBB","is_leaf":2,"parent_id":348019,"type":0,"order":["348037","348033","348021","348023","348034"]},{"id":348021,"name":"CCC","is_leaf":2,"parent_id":348020,"type":0,"order":["348022","348035"]},{"id":348022,"name":"DDD","is_leaf":2,"parent_id":348021,"type":0,"order":["348024","348032","348030"]},{"id":348024,"name":"EEE","is_leaf":2,"parent_id":348022,"type":0,"order":["348025","348036"]},{"id":348025,"name":"FFF","is_leaf":2,"parent_id":348024,"type":0,"order":["348031"]},{"id":348030,"name":"HHH","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348023,"name":"GGG","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348031,"name":"QQQ","is_leaf":1,"parent_id":348025,"type":11,"order":[]},{"id":348032,"name":"JJJ","is_leaf":1,"parent_id":348022,"type":11,"order":[]},{"id":348035,"name":"MMM\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348021,"type":0,"order":[]},{"id":348036,"name":"NNN\u65e0\u53f6\u5b50","is_leaf":2,"parent_id":348024,"type":0,"order":[]},{"id":348033,"name":"KKK","is_leaf":1,"parent_id":348020,"type":11,"order":[]},{"id":348037,"name":"OOO","is_leaf":2,"parent_id":348020,"type":0,"order":[]},{"id":348034,"name":"LLL","is_leaf":1,"parent_id":348020,"type":11,"order":[]}]';
$topNode = json_decode($topNodeJson, true);
$childrenList = json_decode($childrenJson, true);
$topNode['children'] = $this->getTree($childrenList, $topNode);
$getAllLeafs = $this->dfsFindLeafs($topNode);
echo json_encode($getAllLeafs);
}
/**
* 递归构造无限级树
*
* @param $list
* @param $node
* @return array
*/
private function getTree($list, $node)
{
$tree = [];
foreach ($list as $k => $v) {
if ($v['parent_id'] == $node['id']) {
$v['children'] = $this->getTree($list, $v);
$tree[] = $v;
}
}
if (empty($node['order'])) {
return [];
}
//注意：为了保证所有的叶子节点是根据已有的order排序，这里我们重新摆放一下
$treeMap = [];
foreach ($tree as $v) {
$treeMap[$v['id']] = $v;//建立id和数据的map
}
//根据order重新排序
$orderTree = [];
foreach ($node['order'] as $id) {//根据order的顺序重新摆放
$orderTree[] = $treeMap[$id];
}
return $orderTree;
}
/**
* 广度优先遍历获取所有叶子
* @param $node
* @return array
*/
private function bfsFindLeafs($node)
{
if (empty($node['children'])) {
return [];
}
$result = [];//满足条件的组合
$q = [];
$q[] = $node['children'][0];
while (count($q) > 0) {
$size = count($q);
for ($i = 0; $i < $size; $i++) {
$current = array_shift($q);
//判断节点如果是满足条件，加入路径
if ($current['is_leaf'] == 1) {
$result[] = $current;
}
//把所有的子节点加入队列
foreach ($current['children'] as $v) {
$q[] = $v;
}
}
}
return $result;
}
/**
* 获取所有的叶子路径（深度度优先遍历）
*/
private function dfsFindLeafs($node)
{
$trackList = [];
foreach ($node['children'] as $v) {
if ($v['is_leaf'] == 1) {
$trackList[] = $v;
}
if (empty($v['children'])) {
continue;
}
$trackList = array_merge($trackList, $this->dfsFindLeafs($v));
}
return $trackList;
}
}
(new Test())->run();
ok，到这里我们就已经学会如何构造无限级树型结构，并学会用深度优先遍历垂直输出指定条件节点，还知道了怎么用广度优先遍历，giao~
