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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转载：https://blog.csdn.net/qq_25879801/article/details/111332992
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