This assignment focuses on creating and manipulating selection control structure
ID: 3914918 • Letter: T
Question
This assignment focuses on creating and manipulating selection control structures.
The term combination in elementary algebra refers to one of the different ways a certain number of items can be selected from a list of items. For example, the combinations of four items a,b,c,d taken three at a time are abc, abd, acd, and bcd.
In other words, there are a total of four different combinations of four things "taken three at a time". In general, the number of combinations of n things taken k at a time is combinations = n! / ((n-k)!*k!), where the "!" is the symbol for factorial. The value of n! is n*(n-1)*(n-2)*...*1. For example, 4! = 4*3*2*1 = 24.
• Factorial explained
• Combinations explained
• Calculate factorial using C programming 1 and 2
• do while and while loop
• check that the user enters an integer between 0 and 10 only
The assignment is to create a program to display the number of combinations where n and k are entered by the user.
STEPS:
1) Input 1.
Ask for n. Check for bounds (1 <= n && n <= 10). i) If the user entered an integer within (1 and 10), move on to getting the value for k ii) Else keep asking the user till they give a correct value which is an integer within 1 and 10. iii) Reject any input greater than 10 or less than 1 by displaying an error message and then asking the user to re-enter the input. Do this as many times that they enter incorrect input.
2) Input 2.
Ask for k. Check for bounds (1 <= k && k <= n). i. If the user entered an integer within (1 and k), move on to next step. ii. Else keep asking the user till they give a correct value which is an integer within 1 and n. iii. Reject any input greater than n or less than 1 by displaying an error message and then asking the user to re-enter the input. Do this as many times that they enter incorrect input.
3) Calculate n – k.
4) Calculate factorial of n, k and n – k.
5) Calculate the Combination by plugging in factorial of n / (factorial of k * factorial of n - k)
6) Output
Print 5, the number of combinations of n things taken k at a time. This is the output of your program.
Explanation / Answer
Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts. Thanks
//Code
#include<stdio.h>
//method to find factorial of a positive number recursively
int factorial(int num){
if(num<=0){
//base case 1, returning 0 for any number less than or equal to 0
return 0;
}
if(num==1){
//base case 2
return 1;
}
return num*factorial(num-1);
}
int main(){
int n=0, k=0;
//looping until user enters a valid value for n
do{
printf("Enter the value for n (1 - 10): ");
scanf("%d",&n);
if(n<1 || n>10){
printf("Invalid value,try again ");
}
}while(n<1 || n>10);
//looping until user enters a valid value for k
do{
printf("Enter the value for k (1 - %d): ",n);
scanf("%d",&k);
if(k<1 || k>n){
printf("Invalid value,try again ");
}
}while(k<1 || k>n);
int n_k=n-k; //value of n-k
//finding factorials of n, k and n-k
int n_fact=factorial(n);
int k_fact=factorial(k);
int n_k_fact=factorial(n_k);
//finding number of combinations and displaying it
int combinations=n_fact/(n_k_fact*k_fact);
printf("Number of combinations of %d things taken %d at a time: %d",
n,k,combinations);
}
/*OUTPUT*/
Enter the value for n (1 - 10): 11
Invalid value,try again
Enter the value for n (1 - 10): -5
Invalid value,try again
Enter the value for n (1 - 10): 5
Enter the value for k (1 - 5): 6
Invalid value,try again
Enter the value for k (1 - 5): 4
Number of combinations of 5 things taken 4 at a time: 5
/*ANOTHER OUTPUT*/
Enter the value for n (1 - 10): 7
Enter the value for k (1 - 7): 2
Number of combinations of 7 things taken 2 at a time: 21