what is the working rule of this program, Explanation? - c

Question

i am little confuse in this program i want if anyone could explain to me the functionality of this code and the output, i am getting the output of this program as such
1
1
2
2
3
3
All i want to know the working rule of that two functions how they calculating the values?
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
int M(const int n);
int F(const int n)
{
return(n==0)?1:n-M(F(n-1));
}
int M(const int n)
{
return (n==0)?0:n-F(M(n-1));
}
int main()
{
int i;
for(i=0;i<6;i++)
{
printf("%2d\n",F(i));
}
printf("\n");
return 0;
}

Answer 1

Consider on for
for(i=0;i<6;i++)
{
printf("%2d\n",F(i));
}
Short answer:
F(0) => 1;
F(1)=> 1 - M(F(0))
when F(0):1 then F(1) = 1 - M(1)
go to calculate M(1), but we start from 0, M(0)= 0;
M(1) = 1- F(M(0)) = 1- F(0) = 1-1=0;
last we have M(1) = 0; and as F(1) = 1-M(1) = 1-0=1
last we have: F(1)=1
More complete:
Let see F() way of working.
the last command in F(),
return(n==0)?1:n-M(F(n-1));
expanded to
if (n==0){
return 1;
}else{
return n-M(F(n-1));
}
In first for iteration i:0, we want F(0) as n is zero, (n:0), the if (n==0) is true , return 1; is executed and value ofF(0) have to be 1.
for second iteration we want F(1), for that if (n==0) is false and else block is execute.
as now the n:1, F(1) = 1 - M (F(0)).
In previous iteration we have F(0)=1, OK now we can rewire or equation: F(1) = 1 - M(1), it obvious that if we have value of M(1) simply , put it on to the last formula , F(1) have been solved.
for this we must expand M() function.
Similarly we can write for M().
if (n==0){
return 0;
}else{
return n-F(M(n-1));
}
M(0) = 0;
M(1)= 1- F(M(0))= 1- F(0) = 1 - 1=0;
now we have M(1) = 0; by putting it on the F(1) = 1 - M(1)
we achieve to F(1) = 1.
Now the first two pair of 1 in output of your code is calculated by hand.
for others, do this way over and over.

Answer 2

As suggested in the comments try to trace the code by hand, I will go through the first two iterations with you so you get the idea
When your program starts it calls your main function, and starts executing the for loop as follows:
i=0 => calls F(n=0) => is n==0 true? Yes => return 1 => print 1
i=1 => calls F(n=1) => is n==0 true? No => then 1-M(F(0)) => F(0) calculated from the previous iteration to return a value of 1 => call M(n=1) => is n==0 true? No => then 1-F(M(0)) => M(0) returns 0 since n==0 is true => then 1-F(M(0)) is equal to 1-F(0) => we calculated F(0) to return 1 => so 1-F(0) return 0 from M => take the return back to 1-M(F(0)) => 1-0 = 1 => print 1
Do not be frustrated because what you are asking would be actually much easier to understand with some patient. I extremely recommend that you hold down a pen and paper and start tracing yourself.
Go iteration by iteration as I did.
Call each function according to the correct flow of the if conditions.
When you call a function, mark where you have left in the code to jump to said function, such that once it returns a value, you know exactly where to place the returned value.
Peace of paper, patience, and trace.