js计算--一递归

递归：在运行的过程中调用自己。

1、阶乘的递归。

<script>

alert(multiply(5));

function multiply(n){

if(index==1){

return 1;

}

else{

return multiply(n-1)*n;

}}

</script>

递归算法关键：1、递归出口；2、逐渐向出口推进。

阶乘递归理解:出口是为1时就跳出来。else，n-1，逐渐减到1退出。

multiply(5):

当n=5；执行5*multiply(4);

   n=4:   执行4*multiply(3)

依次到n=2时：2*multiply(1)

这时候，return 1;往上返回。

2*1向上返回，3*（2*1）向上返回，----5*（4*（3*（2*1）））=120；

2、累加的递归。

function sum(n){

if(n==1){

return n;

}else{

return sum(n-1)+n;

}}

3、斐波那契数或者称谓斐波那契数列。

比如：1、1、2、3、5、8，13,21................第三数开始，等于前两个数相加。

第4个数就是（n-1）+(n-2)=n。

求第n个数是什么？

function Fibonacci(num){

if(num==1||num==2){

return 1;

}else{

return Fibonacci(num-1)+Fibonacci(num-2);

}}

要输出前50个斐波那契数：

var  str = new String();

var total = 50;

for(var i= 1;i<total;i++){

str +=Fibonacci(i);

}

4、求一个数的二进制。

十进制转二进制：不断的以除以2得到余数。

当一个数字为1或者0的时候输出本身。

<script>var res = new String();//当字符输出function judge(){var num2 = pardeInt(num/2);<span style="white-space:pre"></span>//通过num2来控制每一次的输出的余数。if(num==1||num==2){res = String(num);}else{judge(num2);res +=String(num%2);}}function output(){

var num = documentElementById('num').value;

judge(num);

alert(res);

}</script>

5、十六进制的递归。

十进制转十六进制：不断的除以16的余数，得到的余数，大于10-15的位A-F

<script>var res = new String();function judge(num){var num2 = parseInt(num/16);if(num2==0){res = String(change(num%16));<span style="white-space:pre"></span>//将传进来的数字要转换}else{judge(num2);res +=String(change(num%16));}}

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function output(){    var num=document.getElementById('num').value;    judge(num);    alert(res);}

</script>