A*搜尋演算法。目前只保證了H是最小，所以F有可能不是最短的。 F = G + H 。G = 從起點 A 移動到指定方格的移動代價，H = 從指定的方格移動到終點 的估算成本。
體驗地址
原理
1 定義起始點周圍點
2 起始點周圍點距終點距離排序。距離計算方法為 終點座標與改點座標差的絕對值的和
3 選取最近的一個點作為下一點。其它點放進一個陣列中待用（當最近的那個點不能走出的時候，回退使用待用點）
4 不斷重複1,2,3.直到走出終點
程式碼
<?php
$n=20;
$positions=[];
for ($i=0;$i<=$n;$i++){
for ($j=0;$j<=$n;$j++){
$positions[] =[$j,$i] ;
}
}
//開始的點
$startDot=[0,0];
//已經放置的點
$placedDot=[];
//不可放置的點
$notPlacedDot=notPlacedDot($positions,$n);
$placedDot[]=$startDot;
//所有穿過的點
list($lineDot,$finishDot)=line($positions,$startDot,$placedDot,$notPlacedDot,$n);
//平面上的所有迷宮點
$mazePositions=mazePosition($positions,$lineDot);
//查詢最小的點
$line=[];
$canReOpen=[];//庫存
$startDot=[0,0];//開始的點
$line[]=[0,0];
$shortLine=getShortLine($line,$canReOpen,$startDot,$mazePositions,$notPlacedDot,$finishDot,$n);
echo "解迷宮";
echo getHtml($positions,$lineDot,$shortLine,$n);
echo "<br>";
echo "迷宮路線";
echo getAllHtml($positions,$lineDot,$n);
function line($positions,$startDot,$placedDot,$notPlacedDot,$n){
$dotWrapper=GetDotWrappers($startDot);
$key=rand(0,3);
$nextDot = $dotWrapper[$key];
$i=0;
$notPlacedDotAll =array_merge($notPlacedDot,[]);
while (in_array($nextDot,$placedDot)||in_array($nextDot,$notPlacedDotAll)){
$i++;
if(badDot($nextDot,$placedDot,$notPlacedDot,$n)){//是否是壞點
$notPlacedDotAll[]=$nextDot;
$startDot=$placedDot[count($placedDot)-1];
$dotWrapper=GetDotWrappers($startDot);
$key=rand(0,3);
$nextDot = $dotWrapper[$key];
if(badDot($startDot,$placedDot,$notPlacedDotAll,$n)){//本身是否是壞點
$notPlacedDotAll[]= array_pop($placedDot);
$startDot=$placedDot[count($placedDot)-1];
$dotWrapper=GetDotWrappers($startDot);
$key=rand(0,3);
$nextDot = $dotWrapper[$key];
}
}else{
$key=rand(0,3);
$nextDot = $dotWrapper[$key];
}
if($i>4&&count($placedDot)>1){//迴圈大於3次 還沒找到去除該點
$i=0;
$notPlacedDot[]= array_pop($placedDot);
$startDot=$placedDot[count($placedDot)-1];
$dotWrapper=GetDotWrappers($startDot);
$key=rand(0,3);
$nextDot = $dotWrapper[$key];
}
}
$placedDot[]=$nextDot;
if($nextDot[0]>=$n&&$nextDot[1]>0&&$nextDot[1]<=$n){
return [$placedDot,$nextDot];
}
return line($positions,$nextDot,$placedDot,$notPlacedDot,$n);
}
function mazePosition($positions,$lineDot){
$mazePositions=[];
foreach ($positions as $position){
if(in_array($position,$lineDot)){
$mazePositions[]=$position;
}
}
return $mazePositions;
}
function getShortLine($line,$canReOpen,$startDot,$mazePositions,$notPlacedDot,$endDot,$n){
if($startDot==$endDot){
// echo(json_encode($line));
return $line;
}
$dotWrapper=GetDotWrappers($startDot);
$allOpen = array_reduce($canReOpen, 'array_merge', array());
$arr=[];
foreach ($dotWrapper as $dot){
if(in_array($dot,$mazePositions)&&!in_array($dot,$line)&&!in_array($dot,$allOpen)&&!in_array($dot,$notPlacedDot)){
$arr[distance($dot,$endDot)][]=$dot;
}
}
if(empty($arr)){//死點
$notPlacedDot[]=$startDot;//這個點不能放
array_pop($line);//去除這個點
$length=count($line);
$dot=$line[$length-1];//去除上面這個點的最後一個點
$dotWrapper=GetDotWrappers($dot);//這個點周圍的點
if(!empty($canReOpen)){//庫存中是否有點
$reOpen = array_pop($canReOpen);//取出庫存中最後一個庫存
$ifIntersect=false;
foreach ($reOpen as $open){
if(in_array($open,$dotWrapper)){//有交集，說明最後一個庫存可用
$ifIntersect=true;
break;
}
}
if($ifIntersect){//可用的庫存
$nextStartDot=array_shift($reOpen);//庫存中的第一個點預設是最短距離的
array_push($line,$nextStartDot);
if(!empty($reOpen)){//沒用完，再放進去
array_push($canReOpen,$reOpen);
}
}else{//不可用。把庫存再放進去
array_push($canReOpen,$reOpen);
$nextStartDot = $dot;
}
}else{
$nextStartDot = $dot;
}
}else{
ksort($arr);//按距離大小升序排序
$arr = array_reduce($arr, 'array_merge', array());
// echo json_encode($arr);
// echo "<br>";
$nextStartDot=array_shift($arr);//取出最小距離的作為開始點
array_push($line,$nextStartDot);
if(!empty($arr)){//還有可用的點，放進庫存
$canReOpen[] = array_values($arr);
}
}
return getShortLine($line,$canReOpen,$nextStartDot,$mazePositions,$notPlacedDot,$endDot,$n);
}
function getAllHtml($positions,$lineDot,$n){
$str="<table border='1'>";
foreach (array_chunk($positions,$n+1) as $row){
$str.="<tr>";
foreach ($row as $tr){
if(in_array($tr,$lineDot)){
$str.="<td style='color: white;background-color: red'>點{$tr[0]},{$tr[1]}</td>";
}else{
$str.="<td>{$tr[0]},{$tr[1]}</td>";
}
}
$str.="<tr>";
};
$str.="</table>";
return $str;
}
function getHtml($positions,$lineDot,$shortLine,$n){
$str="<table border='1'>";
foreach (array_chunk($positions,$n+1) as $row){
$str.="<tr>";
foreach ($row as $tr){
if(in_array($tr,$lineDot)){
if(in_array($tr,$shortLine)){
$str.="<td style='color: white;background-color: blue'>點{$tr[0]},{$tr[1]}</td>";
}else{
$str.="<td style='color: white;background-color: red'>點{$tr[0]},{$tr[1]}</td>";
}
}else{
$str.="<td>{$tr[0]},{$tr[1]}</td>";
}
}
$str.="<tr>";
};
$str.="</table>";
return $str;
}
function distance($start,$end){
return abs($end[0]-$start[0])+abs($end[1]-$start[1]);
}
function notPlacedDot($positions,$n)
{
$notPlacedDot=[];
foreach ($positions as $position){
$dotWrapper=GetDotWrappers($position);
foreach ($dotWrapper as $dot){
if($dot[0]<0||$dot[1]<0||$dot[0]>$n||$dot[1]>$n){
$notPlacedDot[]=$dot;
}
}
}
return $notPlacedDot;
}
/**
* 是否是壞點
* @param $dotWrapper
* @param $placedDot
* @param $notPlacedDot
* @return bool
*/
function badDot($position,$placedDot,$notPlacedDot,$n){
$dotWrapper=GetDotWrappers($position);
$i=0;
foreach ($dotWrapper as $dot){
if($dot[0]<0||$dot[1]<0||$dot[1]>$n||in_array($dot,$placedDot)||in_array($dot,$notPlacedDot)){
$i++;
}
}
if($i==4){
return true;
}
return false;
}
function GetDotWrappers($placementEd){
$top = calculateXY($placementEd[0],$placementEd[1],'top');
$bottom = calculateXY($placementEd[0],$placementEd[1],'bottom');
$left = calculateXY($placementEd[0],$placementEd[1],'left');
$right = calculateXY($placementEd[0],$placementEd[1],'right');
return [$top,$bottom,$left,$right];
}
function calculateXY($x,$y,$default='top')
{
switch ($default){
case 'top':
$y=$y+1;
break;
case 'bottom':
$y=$y-1;
break;
case 'left':
$x=$x-1;
break;
case 'right':
$x=($x+1);
break;
case 'left_top':
$x=($x-1);
$y=($y+1);
break;
case 'right_top':
$x=($x+1);
$y=($y+1);
break;
case 'right_bottom':
$x=($x+1);
$y=($y-1);
break;
case 'left_bottom':
$x=($x-1);
$y=($y-1);
break;
}
return [$x,$y];
}