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Detailed explanation of several recursive total permutation algorithms in JavaScript
Detailed explanation of several recursive total permutation algorithms in JavaScript
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>
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