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
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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
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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：
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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
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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：
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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
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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：
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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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原文链接：https://blog.csdn.net/qq_25879801/article/details/111332992
