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1. Consider the following algorithm: Algorithm Sum( m , n ) //Input: A positive

ID: 3668621 • Letter: 1

Question

1. Consider the following algorithm:

Algorithm Sum(m, n)

//Input: A positive integer n and another positive integer m n

//Output: ?

sum = 0

for i=m to n do

for j=1 to i do

sum = sum + 5

end for j

end for i

return sum

What does the algorithm compute? Show and determine the formula for the total number of additions (sum = sum + 5) performed by the algorithm.

2. Consider the following recursive algorithm:

Algorithm Recursive(A[0..n-1])

//Input: A list A[0..n-1] of real numbers

//Output: ?

if n == 1 return A[0]

else do

value = Recursive(A[0..n-2])

if value > A[n-1] return value else return A[n-1]

end if

What does the algorithm compute? Establish and solve the recurrence relation for the total number of element comparisons (value > A[n-1]) performed by the algorithm.

Explanation / Answer

1.The algorithm compute that the sum of values incremented by 5.

#include<iostream>
using namespace std;
int sum(int,int);
int main()
{
   int m1,n1;
   cout<<"Enter the values of m1";
   cin>>m1;
   cout<<"Enter the values of n1";
   cin>>n1;
  
   cout<<"The sum="<<sum(m1,n1);
   system("pause");
}

int sum(int m,int n)
{
   int sum=0;
   for(int i=m;i<=n;i++)
   {
       for(int j=1;j<=i;j++)
       {
           sum=sum+5;
       }
   }
   return sum;
}


Sample output:

Enter the values of m1:4
Enter the values of n1:5
The sum=45Press any key to continue . . .

The number of additions =0+5 +10+15+20+25+30+35+40+45=9 =m+n additions