Question 3

Problem : Sheldon Cooper and his beverage paradigm Sheldon Cooper, Leonard Hofstadter and Penny decide to go for drinks at Cheese cake factory. Sheldon proposes to make a game out of this. Sheldon proposes as follows, 

• To decide the amount of beverage they plan to consume, say X.
• Then order for a random number of different drinks, say {A, B, C, D, E, F} of quantities {a, b, c, d, e, f} respectively.
• If quantity of any three drinks add up to X then we'll have it else we'll return the order. E.g. If a + d + f = X then True else False

You are given 

1. Number of bottles N corresponding to different beverages and hence their sizes
2. Next N lines, contain a positive integer corresponding to the size of the beverage
3. Last line consists of an integer value, denoted by X above

Your task is to help find out if there can be any combination of three beverage sizes that can sum up to the quantity they intend to consume. If such a combination is possible print True else False
  Input Format: 

1. First line contains number of bottles ordered denoted by N
2. Next N lines, contains a positive integer Ai, the size of the ith bottle
3. Last line contains the quantity they intend to consume denoted by X in text above

  Output Format: True, if combination is possible False, if combination is not possible

  Constraints: N >= 3 Ai > 0 1 <= i <= N X > 0   Sample Input and Output 

SNo.	Input	Output
1	6 1 4 45 6 10 8 22	True
2	4 1 3 12 4 14	False

  Explanation for sample input and output 1: The sum of 2nd, 5th and 6th beverage size is equal to 22. So the output will be True.
  Explanation for sample input and output 2: Since no combination of given beverage sizes sum up to X i.e. 14, the output will be False

program code:(hint:set of all possible combinations with some condition)

#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
void main()
{
 int i,n,q,l,k,j,*a=NULL;
 clrscr();
 printf("enter the no of entries: ");
 scanf("%d",&n);
 a=(int*)calloc(n,sizeof(int));
 for(i=0;i<n;i++)
 {
  scanf("%d",&a[i]);
 }
 printf("enter the quantity to be consumed\n");
 scanf("%d",&q);
 for(i=0;i<n;i++)
 {
  if(a[i]>q)
  {
   a[i]=a[n-1];
   n--;
   i--;
  }
 }
 for(i=0;i<n;i++)
 {
        k=a[i];  //selecting 1st element
        for(j=i+1;k+a[j]<q&&j<n;j++)
        {
   k=k+a[j];      //2nd element decided
   for(l=j+1;l<n;l++)
   {
    if(k+a[l]==q)         //checking for 3rd element
    {
     printf("\tyes\n");
     goto end;
    }
   }
  k=k-a[j];
        }
 k=k-a[i];
  }
  printf("\tno");
      end:getch();
      exit(0);
}