如何打印递归轨迹（阶乘函数）？

Question

为了更好地理解递归，我试图弄清楚如何将递归跟踪记录到控制台。我有“追踪”部分，但我不确定如何“冒泡”解决方案。对完美放置的 console.log 语句有什么建议吗？

这是我目前所得到的：

function factorial (num) {
    if (num === 1) {
        console.log('factorial(' + num + ') = ' + num);
        return 1;
    } else {
        console.log('factorial(' + num + ') = ' + num + ' * ' + 'factorial(' + (num - 1) + ')');
        return num * factorial(num - 1);
    }
}

将以下内容打印到控制台：

factorial(5) = 5 * factorial(4)
factorial(4) = 4 * factorial(3)
factorial(3) = 3 * factorial(2)
factorial(2) = 2 * factorial(1)
factorial(1) = 1
120

但是 1 * 2 * 3 * 4 * 5 部分呢？我知道它发生在某处，我该如何打印它？

我想我希望它看起来像这样：

1
1 * 2
2 * 3
6 * 4
24 * 5
120

感谢您的任何建议！

好的，经过更多搜索，我在CodeRanch 找到了这个，不幸的是没有代码（并且是用 Java 编写的）：

Enter fact(6)  
    Enter fact(5)  
        Enter fact(4)  
            Enter fact(3)  
                Enter fact(2)  
                    Enter fact(1)  
                        Enter fact(0)  
                        0!Ret: 1  
                    Ret: 1 * fact(n-1) = 1 * fact(0) = 1 * 1 = 1  
                Ret: 2 * fact(n-1) = 2 * fact(1) = 2 * 1 = 2  
            Ret: 3 * fact(n-1) = 3 * fact(2) = 3 * 2 = 6  
        Ret: 4 * fact(n-1) = 4 * fact(3) = 4 * 6 = 24  
    Ret: 5 * fact(n-1) = 5 * fact(4) = 5 * 24 = 120  
Ret: 6 * fact(n-1) = 6 * fact(5) = 6 * 120 = 720  
fact(6) = 720  

很酷，对吧？经过更多的实验，我仍然无法做到这一点......

Answer 1

function factorial (num) {
    if (num === 1) {
        console.log(num); //print new line after this
        return 1;
    } else {
        var val = factorial(num - 1);
        console.log(num +'*' + val);  //print new line after this
        return num * val;
    }
}

Answer 2

我认为最好使用带有 cmets 的示例（稍作编辑）来解释。假设您第一次调用此函数时将参数设置为 5。

// num = 5, the first time it's called
function factorial (num) {
    console.log('factorial(' + num + ')');

    if (num === 1) {
        // If num === 1, the function will just return 1 and exit.
        return 1;
    } else {
        // Otherwise, which happens almost every time (since 1 is only
        // reached once and then it stops). For 5, this would return
        // 5 * factorial(4), which in order returns 4 * factorial(3),
        // and so on.
        return num * factorial(num - 1);
    }
}

此输出可能有助于您理解：

factorial(5) == (5) * (factorial(4)) // (5) * (4 * 3 * 2 * 1)
factorial(4) == (4) * (factorial(3)) // (4) * (3 * 2 * 1)
factorial(3) == (3) * (factorial(2)) // (3) * (2 * 1)
factorial(2) == (2) * (factorial(1)) // (2) * (1)
factorial(1) == (1)                  // (1)

Answer 3

function factorial (num) {
        for (var i=1; i<6-num; i++)
            console.log('    ');
        }
        console.log('Enter fact('+num+')'); //add code to move new line
        if(num==0) {
            for (var i=1; i<6-num; i++)
                console.log('    ');
            }
            console.log('0!Ret: 1 '); // add code to move new line
            return 1;
        } else {
            int val = factorial(num-1);
            for (var i=1; i<6-num; i++)
                console.log('    ');
            }
            console.log('Ret:'+num+ ' * fact(n-1) = ' + num+ ' * fact('+(num-1)+') = '+num+' * ' + val + ' = ' + (num*val) ); // add code to move new line
            return num*val;
        }
    }