本文基於免費程式碼營基本演算法指令碼“分解數字”

在數學中，非負整數n的階乘可能是一個棘手的演算法。在本文中，我將解釋這種方法，首先使用遞迴函式，第二種使用而迴圈，第三種使用以迴圈。

演算法挑戰

返回提供的整體的階乘。

如果整體用字母n表示，則階乘是所有小於或等於n的正整數的乘積。

階乘經常用簡寫符號n！表示！

例如：5！= 1 * 2 * 3 * 4 * 5 = 120

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

提供的測試用例

• factorialize（0）應該返回1
• factorialize（5）應該返回120
• factorialize（10）應該返回3628800
• factorialize（20）應該返回2432902008176640000

什麼是因數分解？

當將一個因數分解時，就是稱為數字乘以每個連續的數字減一個。

如果您的電話號碼是5，則您將：

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

該模式為：

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

1.遞迴分解一個數字

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);

沒有註釋：

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迴圈分解一個數字

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);

沒有註釋：

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迴圈分解數字

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);

沒有註釋：

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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