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Detailed explanation of several recursive total permutation algorithms in JavaScript

伊谢尔伦Original: 2017-07-24 13:15:422321browse

Exchange (recursive)

<html xmlns="http://www.w3.org/1999/xhtml">  
<head>  
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />  
    <title>Full Permutation(Recursive Swap) - Mengliao Software</title>  
</head>  
<body>  
<p>Full Permutation(Recursive Swap)<br />  
Mengliao Software Studio - Bosun Network Co., Ltd.<br />  
2011.05.24</p>  
<script type="text/javascript">  
/*  
全排列（递归交换）算法  
1、将第一个位置分别放置各个不同的元素；  
2、对剩余的位置进行全排列（递归）；  
3、递归出口为只对一个元素进行全排列。  
*/ 
function swap(arr,i,j) {  
    if(i!=j) {  
        var temp=arr[i];  
        arr[i]=arr[j];  
        arr[j]=temp;  
    }  
}  
var count=0;  
function show(arr) {  
    document.write("P<sub>"+ ++count+"</sub>: "+arr+"<br />");  
}  
function perm(arr) {  
    (function fn(n) { //为第n个位置选择元素  
        for(var i=n;i<arr.length;i++) {  
            swap(arr,i,n);  
            if(n+1<arr.length-1) //判断数组中剩余的待全排列的元素是否大于1个  
                fn(n+1); //从第n+1个下标进行全排列  
            else 
                show(arr); //显示一组结果  
            swap(arr,i,n);  
        }  
    })(0);  
}  
perm(["e1","e2","e3","e4"]);  
</script>  
</body>  
</html>

Link (recursive)

<html xmlns="http://www.w3.org/1999/xhtml">  
<head>  
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />  
    <title>Full Permutation(Recursive Link) - Mengliao Software</title>  
</head>  
<body>  
<p>Full Permutation(Recursive Link)<br />  
Mengliao Software Studio - Bosun Network Co., Ltd.<br />  
2012.03.29</p>  
<script type="text/javascript">  
/*  
全排列（递归链接）算法  
1、设定源数组为输入数组，结果数组存放排列结果（初始化为空数组）；  
2、逐一将源数组的每个元素链接到结果数组中（生成新数组对象）；  
3、从原数组中删除被链接的元素（生成新数组对象）；  
4、将新的源数组和结果数组作为参数递归调用步骤2、3，直到源数组为空，则输出一个排列。  
*/ 
var count=0;  
function show(arr) {  
    document.write("P<sub>"+ ++count+"</sub>: "+arr+"<br />");  
}  
function perm(arr) {  
    (function fn(source, result) {  
        if (source.length == 0)  
            show(result);  
        else 
            for (var i = 0; i < source.length; i++)  
                fn(source.slice(0, i).concat(source.slice(i + 1)), result.concat(source[i]));  
    })(arr, []);  
}  
perm(["e1", "e2", "e3", "e4"]);  
</script>  
</body>  
</html>

Backtracking (recursive)

<html xmlns="http://www.w3.org/1999/xhtml">  
<head>  
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />  
    <title>Full Permutation(Recursive Backtrack) - Mengliao Software</title>  
</head>  
<body>  
<p>Full Permutation(Recursive Backtrack)<br />  
Mengliao Software Studio - Bosun Network Co., Ltd.<br />  
2012.03.29</p>  
<script type="text/javascript">  
/*  
全排列（递归回溯）算法  
1、建立位置数组，即对位置进行排列，排列成功后转换为元素的排列；  
2、建立递归函数，用来搜索第n个位置；  
3、第n个位置搜索方式与八皇后问题类似。  
*/ 
var count = 0;  
function show(arr) {  
    document.write("P<sub>" + ++count + "</sub>: " + arr + "<br />");  
}  
function seek(index, n) {  
    if (n >= 0) //判断是否已回溯到了第一个位置之前，即已经找到了所有位置排列  
        if (index[n] < index.length - 1) { //还有下一个位置可选  
            index[n]++; //选择下一个位置  
            if ((function () { //该匿名函数判断该位置是否已经被选择过  
                for (var i = 0; i < n; i++)  
                    if (index[i] == index[n]) return true; //已选择  
                return false; //未选择  
            })())  
                return seek(index, n); //重新找位置  
            else 
                return true; //找到  
        }  
        else { //当前无位置可选，进行递归回溯  
            index[n] = -1; //取消当前位置  
            if (seek(index, n - 1)) //继续找上一个位置  
                return seek(index, n); //重新找当前位置  
            else 
                return false; //已无位置可选  
        }  
    else 
        return false;  
}  
function perm(arr) {  
    var index = new Array(arr.length);  
    for (var i = 0; i < index.length; i++)  
        index[i] = -1; //初始化所有位置为-1，以便++后为0  
    for (i = 0; i < index.length - 1; i++)  
        seek(index, i); //先搜索前n-1个位置  
    while (seek(index, index.length - 1)) { //不断搜索第n个位置，即找到所有位置排列  
        var temp = [];  
        for (i = 0; i < index.length; i++) //将位置之转换为元素  
            temp.push(arr[index[i]]);  
        show(temp);  
    }  
}  
perm(["e1", "e2", "e3", "e4"]);  
</script>  
</body>  
</html>

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