Need explanation on recursive functions?

[3UMLy60M]

Hello all,

Can someone please explain to me how calling m3(3, 4) causes 81 to be the output of the following recursive function?

int m3 (int a, int b)
{
    if (b == 0)
        return 1;
    else
        return a * m3(a, b - 1);
}

And also, why is the output here 12 when m2(3, 4) is called?

int m2(int a, int b)
{
    if (a == 0)
        return 0;
    else
        return a * m2(a - 1, b);
}

Thanks!

[Smac89]

m2:

Breakpoint 2, m2 (a=3, b=4) at cap.cc:13
13	   if (a == 0)
(gdb) display a
1: a = 3
(gdb) display b
2: b = 4
(gdb) n
16	      return a * m2(a - 1, b);
2: b = 4
1: a = 3
(gdb) 

Breakpoint 2, m2 (a=2, b=4) at cap.cc:13
13	   if (a == 0)
2: b = 4
1: a = 2
(gdb) 
16	      return a * m2(a - 1, b);
2: b = 4
1: a = 2
(gdb) 

Breakpoint 2, m2 (a=1, b=4) at cap.cc:13
13	   if (a == 0)
2: b = 4
1: a = 1
(gdb) 
16	      return a * m2(a - 1, b);
2: b = 4
1: a = 1
(gdb) 

Breakpoint 2, m2 (a=0, b=4) at cap.cc:13
13	   if (a == 0)
2: b = 4
1: a = 0
(gdb) 
14	      return 0;
2: b = 4
1: a = 0
(gdb) 
17	}
2: b = 4
1: a = 0
(gdb) 
17	}
2: b = 4
1: a = 1
(gdb) 
17	}
2: b = 4
1: a = 2
(gdb) 
17	}
2: b = 4
1: a = 3
(gdb)

m3:

Breakpoint 1, m3 (a=3, b=4) at cap.cc:5
5	   if (b == 0)
8	      return a * m3(a, b - 1);
(gdb) display a
3: a = 3
(gdb) display b
4: b = 4
(gdb) n

Breakpoint 1, m3 (a=3, b=3) at cap.cc:5
5	   if (b == 0)
4: b = 3
3: a = 3
(gdb) 
8	      return a * m3(a, b - 1);
4: b = 3
3: a = 3
(gdb) 

Breakpoint 1, m3 (a=3, b=2) at cap.cc:5
5	   if (b == 0)
4: b = 2
3: a = 3
(gdb) 
8	      return a * m3(a, b - 1);
4: b = 2
3: a = 3
(gdb) 

Breakpoint 1, m3 (a=3, b=1) at cap.cc:5
5	   if (b == 0)
4: b = 1
3: a = 3
(gdb) 
8	      return a * m3(a, b - 1);
4: b = 1
3: a = 3
(gdb) 

Breakpoint 1, m3 (a=3, b=0) at cap.cc:5
5	   if (b == 0)
4: b = 0
3: a = 3
(gdb) 
6	      return 1;
4: b = 0
3: a = 3
(gdb) 
9	}
4: b = 0
3: a = 3
(gdb) 
9	}
4: b = 1
3: a = 3
(gdb) 
9	}
4: b = 2
3: a = 3
(gdb) 
9	}
4: b = 3
3: a = 3
(gdb) 
9	}
4: b = 4
3: a = 3
(gdb) 
81 0

m2 returns 0, not 12 and m3 returns 81

#include <cstdio>

int m3 (int a, int b)
{
   if (b == 0)
      return 1;
   else
      return a * m3(a, b - 1);
}

int m2(int a, int b)
{
   if (a == 0)
      return 0;
   else
      return a * m2(a - 1, b);
}

int main()
{   
   printf("%d %d\n", m3(3,4), m2(3,4));
   
   return 0;
}

[3UMLy60M]

I don't understand this code.

[vlad from moscow]

It is obvious that function m2 has a typo

int m2(int a, int b)
{
    if (a == 0)
        return 0;
    else
        return a * m2(a - 1, b);
}

It always will return 0.

I think you meant plus instead of multiplier

int m2(int a, int b)
{
    if (a == 0)
        return 0;
    else
        return a + m2(a - 1, b);
}