Implement a function for each of following problems and count the number of steps executed/Time taken by each function on various inputs and write complexity of each function. Also draw a comparative chart. In each of the following function N will be passed by user.
1. To calculate sum of 1 to N number using loop
CODE:
#include<stdio.h>
#include<conio.h>
void loop(int n);
void main()
{
int n;
clrscr();
printf(“enter the value of n”);
scanf(“%d”,&n);
loop(n);
getch();
}
void loop(int n)
{
int count=0;
int i, sum=0;
count++;
for(i=1;i<=n;i++)
{
count++;
sum=sum+i;
count++;
}
count++;
count++;
printf(“loop of sum=%d”,sum);
printf(“\n count for loop=%d”,count);
}
2. To calculate sum of 1 to N number using equation.
CODE:-
#include<stdio.h>
#include<conio.h>
void equation(int n);
void main()
{
int n;
clrscr();
printf(“enter the value of n”);
scanf(“%d”,&n);
equation(n);
getch();
}
void equation(int n)
{
int sum,count=0;
count++;
sum=n*(n+1)/2;
count++;
printf(“—–equation—–\n”);
printf(“sum=%d”,sum);
printf(“\n count for loop=%d”,count);
}
OUTPUT:
Time Complexity For Find sum using Equation:-2
3. To calculate sum of 1 to N numbers using recursion.
CODE:
#include<stdio.h>
#include<conio.h>
int recursion(int n);
int count=0;
void main()
{
int n;
clrscr();
printf(“enter the value of n”);
scanf(“%d”,&n);
printf(“recursion sum=%d\n”,recursion(n));
printf(“count=%d”,count);
getch();
}
int recursion(int n)
{
count++;
if(n==0)
{
count++;
return 0;
}
else
{
count++;
return (n+recursion(n-1));
}
}
OUTPUT:
Time Complexity For Find sum using Recursion:-2n+2
| Number | Loop | Equation | Recursion |
| 50 | 103 | 2 | 102 |
| 100 | 203 | 2 | 202 |
| 150 | 303 | 2 | 302 |
| 300 | 603 | 2 | 602 |
| 600 | 1203 | 2 | 1202 |
| 1000 | 2003 | 2 | 2002 |
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