C program: Solve the stop problem

Problem Statement- A program to find a train stopping at r stations out of n stations in such a way that no two stops are consecutive.

Explanation of the problem

This program will count the number of ways the train can stop, that is, the arrangement. Here, the train will travel from point X to Y. Between these points, there are n sites. The train will stop at r stations among these n stations, provided that when stopping at r stations, the train should not stop at two consecutive stations.

This permutation can be found using the straightforward ⁿp_r formula.

Let us give a few examples, p>

Input : n = 16 , r = 6
Output : 462

Explanation - Use the permutation formula given below to find 6 stations out of 16 stations where the train can serve Number of ways to dock:

ⁿp_r or p(n, r) = n! ∕ (n-r)!

Algorithm

Input  : total numbers of stations n and number of stations train can stop r.
Step 1 : For values of n and r calculate the value of p(n,r) = n! / (n-r)!
Step 2 : print the value of p(n,r) using std print method.

Example

Live demonstration

#include<stdio.h>
int main(){
   int n = 16, s = 6;
   printf("Total number of stations = %d</p><p>Number of stopping station = %d</p><p>", s, n);
   int p = s;
   int num = 1, dem = 1;
   while (p!=1) {
      dem*=p;
      p--;
   }
   int t = n-s+1;
   while (t!=(n-2*s+1)) {
      num *= t;
      t--;
   }
   if ((n-s+1) >= s)
      printf("Possible ways = %d", num / dem);
   else
      printf("no possible ways");
}

Output

Total number of stations = 16
Number of stopping station = 6
Possible ways = 462

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