How to trace a recursion?

问题

I saw this code online but what I am asking is how did the program come up with an answer of 12 ?

I did a tracing of the program, and I only come up with an answer of 6 .

Why is the answer 12 ?

The inputs are a=6 and b=6.

This is the code:

public static int addxy(int a, int b)
{
    if (a==0)
        return b;
    else if (b==0)
        return a;
    else
        return 1 + addxy(a, b-1);
}

回答1:

addxy(6,6)
1+addxy(6,5)
1+1+addxy(6,4)
1+1+1+addxy(6,3)
1+1+1+1addxy(6,2)
1+1+1+1+1+addxy(6,1)
1+1+1+1+1+1+addxy(6,0) = 12

回答2:

Try walking over it step by step:

addxy(6, 6) returns 1 + addxy(6, 5)
addxy(6, 5) returns 1 + addxy(6, 4)
addxy(6, 4) returns 1 + addxy(6, 3)
addxy(6, 3) returns 1 + addxy(6, 2)
addxy(6, 2) returns 1 + addxy(6, 1)
addxy(6, 1) returns 1 + addxy(6, 0)
addxy(6, 0) returns 6
So, addxy(6, 1) returns 1 + 6 = 7
So, addxy(6, 2) returns 1 + 7 = 8
So, addxy(6, 3) returns 1 + 8 = 9
So, addxy(6, 4) returns 1 + 9 = 10
So, addxy(6, 5) returns 1 + 10 = 11
So, addxy(6, 6) returns 1 + 11 = 12

回答3:

This

 return 1 + addxy(a, b-1);

returns 1 plus the result of calling the method recursively while removing 1 from b. This basically means that it adds b.

When b is 0, you return a.

else if (b==0)
    return a;

(You also return b, when a is 0.

Without even tracing anything, you can tell that (with non-negative values for a and b) the method simply adds a and b and returns the result.

回答4:

Look at the return statement

return 1 + addxy(a, b-1);

You have a function call in the return statement to the same function. This is called a recursive function. So as long as b is not 0, it keeps on calling it again n again but by adding 1 and subtracting b by 1. This goes on till b becomes 0. Which is 6 times. And thats why you get 1*6 + a = 6

Equivalent execution would be

return 1 + addxy(6, 5);
return 1 + 1 + addxy(6, 4);
return 1 + 1 + 1 + addxy(6, 3);
return 1 + 1 + 1 + 1 + addxy(6, 2);
return 1 + 1 + 1 + 1 + 1 + addxy(6, 1);
return 1 + 1 + 1 + 1 + 1 + 1 + addxy(6, 0);
return 1 + 1 + 1 + 1 + 1 + 1 + 6; // Value of a = 6
return 12;

回答5:

As @Mureinik answer is perfect but you didn't understand it ,

So Lets start with a very basic example of Calculating Factorial via Recursion:

public int factorial(int num){
   if(num==0) //break condition of Recursion Since 0! is always 1
      return 1;
   return num*fact(num-1);
}

So here is the Tracing

factorial(4) return 4*factorial(3);
factorial(3) return 3*factorial(2);
factorial(2) return 2*factorial(1);
factorial(1) return 1*factorial(0);
factorial(0) returns 1;

, Now backtrace this answers and this below image is formed

May Be now you are able to understand it

来源：https://stackoverflow.com/questions/28524087/how-to-trace-a-recursion

标签

java

recursion