在JavaScript中分解数字的三种方法

本文基于免费代码营基本算法脚本“分解数字”

在数学中，非负整数n的阶乘可能是一个棘手的算法。在本文中，我将解释这种方法，首先使用递归函数，第二种使用而循环，第三种使用以循环。

算法挑战

返回提供的整体的阶乘。

如果整体用字母n表示，则阶乘是所有小于或等于n的正整数的乘积。

阶乘经常用简写符号n！表示！

例如：5！= 1 * 2 * 3 * 4 * 5 = 120

function factorialize(num) {
     
  return num;
}
factorialize(5);

提供的测试用例

• factorialize（0）应该返回1
• factorialize（5）应该返回120
• factorialize（10）应该返回3628800
• factorialize（20）应该返回2432902008176640000

什么是因数分解？

当将一个因数分解时，就是称为数字乘以每个连续的数字减一个。

如果您的电话号码是5，则您将：

5! = 5 * 4 * 3 * 2 * 1

该模式为：

0! = 1
1! = 1
2! = 2 * 1
3! = 3 * 2 * 1
4! = 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1

1.递归分解一个数字

function factorialize(num) {
     
  // If the number is less than 0, reject it.
  if (num < 0) 
        return -1;
    
  // If the number is 0, its factorial is 1.
  else if (num == 0) 
      return 1;
    
  // Otherwise, call the recursive procedure again
    else {
     
        return (num * factorialize(num - 1));
        /* 
        First Part of the recursion method
        You need to remember that you won’t have just one call, you’ll have several nested calls
        
        Each call: num === "?"                   num * factorialize(num - 1)
        1st call – factorialize(5) will return    5  * factorialize(5 - 1) // factorialize(4)
        2nd call – factorialize(4) will return    4  * factorialize(4 - 1) // factorialize(3)
        3rd call – factorialize(3) will return    3  * factorialize(3 - 1) // factorialize(2)
        4th call – factorialize(2) will return    2  * factorialize(2 - 1) // factorialize(1)
        5th call – factorialize(1) will return    1  * factorialize(1 - 1) // factorialize(0)
        
        Second part of the recursion method
        The method hits the if condition, it returns 1 which num will multiply itself with
        The function will exit with the total value
        
        5th call will return (5 * (5 - 1))     // num = 5 * 4
        4th call will return (20 * (4 - 1))    // num = 20 * 3
        3rd call will return (60 * (3 - 1))    // num = 60 * 2
        2nd call will return (120 * (2 - 1))   // num = 120 * 1
        1st call will return (120)             // num = 120
        
        If we sum up all the calls in one line, we have
        (5 * (5 - 1) * (4 - 1) * (3 - 1) * (2 - 1)) = 5 * 4 * 3 * 2 * 1 = 120
        */
    }
}
factorialize(5);

没有注释：

function factorialize(num) {
     
  if (num < 0) 
        return -1;
  else if (num == 0) 
      return 1;
  else {
     
      return (num * factorialize(num - 1));
  }
}
factorialize(5);

2.用WHILE循环分解一个数字

function factorialize(num) {
     
  // Step 1. Create a variable result to store num
  var result = num;
   
  // If num = 0 OR num = 1, the factorial will return 1
  if (num === 0 || num === 1) 
    return 1; 
 
  // Step 2. Create the WHILE loop 
  while (num > 1) {
      
    num--; // decrementation by 1 at each iteration
    result = result * num; // or result *= num; 
    /* 
                    num           num--      var result      result *= num         
    1st iteration:   5             4            5             20 = 5 * 4      
    2nd iteration:   4             3           20             60 = 20 * 3
    3rd iteration:   3             2           60            120 = 60 * 2
    4th iteration:   2             1          120            120 = 120 * 1
    5th iteration:   1             0          120
    End of the WHILE loop 
    */
  }
     
  // Step 3. Return the factorial of the provided integer
  return result; // 120
}
factorialize(5);

没有注释：

function factorialize(num) {
     
  var result = num;
  if (num === 0 || num === 1) 
    return 1; 
  while (num > 1) {
      
    num--;
    result *= num;
  }
  return result;
}
factorialize(5);

3.使用FOR循环分解数字

function factorialize(num) {
     
  // If num = 0 OR num = 1, the factorial will return 1
  if (num === 0 || num === 1)
    return 1;
  
  // We start the FOR loop with i = 4
  // We decrement i after each iteration 
  for (var i = num - 1; i >= 1; i--) {
     
    // We store the value of num at each iteration
    num = num * i; // or num *= i;
    /* 
                    num      var i = num - 1       num *= i         i--       i >= 1?
    1st iteration:   5           4 = 5 - 1         20 = 5 * 4        3          yes   
    2nd iteration:  20           3 = 4 - 1         60 = 20 * 3       2          yes
    3rd iteration:  60           2 = 3 - 1        120 = 60 * 2       1          yes  
    4th iteration: 120           1 = 2 - 1        120 = 120 * 1      0          no             
    5th iteration: 120               0                120
    End of the FOR loop 
    */
  }
  return num; //120
}
factorialize(5);

没有注释：

function factorialize(num) {
     
  if (num === 0 || num === 1)
    return 1;
  for (var i = num - 1; i >= 1; i--) {
     
    num *= i;
  }
  return num;
}
factorialize(5);

关注：Hunter网络安全 获取更多资讯
网站：bbs.kylzrv.com
CTF团队：Hunter网络安全
文章：Sonya Moisset
排版：Hunter-匿名者