Design Analysis of Algorithm(DAA) Solutions by Deepak Shah

Write a function for each of the following problems and count the number of steps for execution and write the time complexity of each function, 1. To calculate the sum of 1 to N numbers using loop. 2. To calculate the sum of 1 to N numbers using equation. 3. To calculate the sum of 1 to N numbers using recursion. #include <stdio.h> #include <conio.h> int rcount=0; int uloop(int n) {   int sum=0,count=0 , i;   count++; count++;   for(i=1;i<=n;i++)   {     sum=sum+i;     count++;   }   count++;   printf(" \n Count is:% d ",count);   return sum; } int uequation( int n) {    int sum,count=0;    count++;    sum=(n*(n+1))/2;    count ++;    count ++; printf(" \n count is:% d ",count);    return sum; } int urecursion(int n) {  rcount++;   if(n<=0)    { rcount++;      return n;    }    else    { rcount++;      return urecursion(n-1)+n;    } }   void main() { i nt n,choice , sum; clrscr();  

Implement functions to print nth Fibonacci number using iteration and recursive method. Compare the performance of two methods by counting number of steps executed on various inputs. Also draw a comparative chart. (Fibonacci series 1, 1, 2, 3, 5, 8…..  Here 8 is the 6th Fibonacci number) #include<stdio.h> #include<conio.h> int iteration(int); int recursive(int); int count=0; void main() { int n,choice,ans; clrscr(); printf("\nenter nth number : "); scanf("%d",&n); printf(“\n==iteration==”); ans=iteration(n); printf(“\nans=%d\ncount=%d”,ans,count); printf(“\n\n==recursive==”); ans=recursive(n); printf("\nans=%d\ncount=%d",ans,count); getch(); } int iteration(int n) { int f=1,s=1,t,i; count++;   count++; for(i=3;i<=n;i++) { t=f+s; count++; f=s; count++; s=t; count++; } count++; return t; } int recursive(int n) { count++; if(n==0 || n==1) { cou

SELECTION SORT: #include<stdio.h> #include<conio.h> #include<math.h> #include<time.h> #define n 10000 void selection_sort(int[]); unsigned long int count=0; void main() {             int a[n];             int choice,i;             clrscr();             printf("1.Sorted Data  2.Random Data \n");             scanf("%d",&choice);             switch(choice)             {                         case 1:                                     for(i=0;i<n;i++)                                     {                                                 a[i]=i+1;                                     }                                     selection_sort(a);                                     break;                         case 2:                                     for(i=0;i<n;i++)                                     {                                                 a[i]=n-i;