‘N’ Story Building, with 1,2,3 steps how many ways can a person reach top of building.

A building has n steps. A person can take 1,2 or 3 steps. In how many ways can a person reach top of building.

In order to build logic, lets think from first step
If N=1 and Steps=1. There is only 1 way to reach with 1 step.
F(1)=1

If N=2 and Steps=1. There 1  way to reach with 1+1 step.
F(2)=1

if N=2 and Steps=1,2 . There are 2 ways to reach, with 1+1 & 0+2 steps.
F(2)=2
if N=3 and Steps=1,2 . There are 3 ways to reach, with 1+1+1 , 1+2 & 2+1 steps.
F(3)=3.

if N=4 and Steps=1,2 . There are 5 ways to reach, with 1+1+1+1 , 1+2+1 , 1+1+2 , 2+1+1  & 2+2 steps.
F(4)=5

So what is that function , does it look similar to fibonacchi series ?

F(n) = F(n-1) + F(n-2)

So Extend the same function for 3 steps

F(n) = F(n-1) + F(n-2) + F(n-3)

So code it



int main()
{
  int n, first = 0, second = 1, third=1, next, c;
  printf("Enter the number of terms\n");
  scanf("%d",&n);
  for ( c = 3; c < n ; c++ )
      {
       next = first + second + third;
       first = second;
       second = third;
       third = next ;
      }

  printf("Total Steps required =%d\n",next);
  return 0;
}