recursive algorithm to find smallest element in array

Question

I have some pseudo code for a recursive algorithm that finds the smallest number in an array.

Here is the algorithm.

Min(A[0..n - 1])
If n = 1 return A[0]
else
{ 
  temp <-- Min(A[0..n - 2])
  if temp <= A[n - 1]
     return temp
  else return A[n - 1]
}

One part I don't understand about this pseudo code is the line "temp <-- Min(A[0..n - 2])". Specifically why is it "n - 2" in the recursive call instead of "n - 1"?

My other question is how I would implement that line in code. I am using Java.

Thanks in advance for any help.

Each time you recurse to need to be one closer to the end of recursion. (which is when you have only one element) — Peter Lawrey
– Peter Lawrey, Commented Feb 26, 2012 at 21:08
Thanks for the responses. How would I implement this pseudo code? Not clear on how I would handle that line in code. — user695752
– user695752, Commented Feb 27, 2012 at 2:38

Oliver Charlesworth · Accepted Answer · 2012-02-26 21:05:06Z

5

Because you array is indexed from 0 to n-1, inclusive. You need to recurse on a sub-array that's one element smaller, hence n-2.

answered Feb 26, 2012 at 21:05

Oliver Charlesworth

274k34 gold badges591 silver badges687 bronze badges

Sign up to request clarification or add additional context in comments.

Comments

Peggy · Accepted Answer · 2013-05-30 08:54:26Z

1

for your 1st question:

since you are using a recursive algorithm, in order to solve the problem, you first have to solve the same problem with a smaller size. In this pseudocode, for finding the minimum of an array with the length of n, first the minimum of the same array with the size of n-1 is found and then the minimum is compared with nth element. Your array is indexed from 0 to n-1 (which will make it's length = n) so for recursive call, you have to call the array from index 0 to n-2 (n-1 elements).

for your 2nd question: This is how I would implement the code in Java:

public class Minimum {
   public Minimum(int[] A) {
    findMin(A, 0, A.length-1);
}

public int findMin(int [] A, int start, int end){
    if (start== end-1)
        return A[0];
    else{
        int temp=findMin(A, start, end-1 );
        if (temp<=A[end]) 
            return  temp;
        else 
            return A[end];
    }
}

}

answered May 30, 2013 at 8:54

Peggy

3957 silver badges23 bronze badges

1 Comment

Peggy Over a year ago

This is the line you asked about -> int temp=findMin(A, start, end-1 );

Peter Lawrey · Accepted Answer · 2012-02-27 08:15:36Z

0

My other question is how I would implement that line in code.

If you are using an array.

// create an array with one less element.
A a2 = new A[a.length-1];
// copy the elements
System.arrayCopy(a,0,a2,0,a2.length);

If you are using a List

List<A> a2 = a.subList(0, a.length-1);

answered Feb 27, 2012 at 8:15

Peter Lawrey

535k83 gold badges770 silver badges1.2k bronze badges

Collectives™ on Stack Overflow

recursive algorithm to find smallest element in array

3 Answers 3

Comments

1 Comment

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

3 Answers 3

Comments

1 Comment

Comments

Your Answer

Sign up or log in

Post as a guest

Related