详解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);

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