algorithm - Find maximum value in an array by recursion

Question

// Find a maximum element in the array.
findMax(A)
   findMaxHelper(A, 0, A.length)

findMaxHelper(A, left, right)
   if (left == right - 1) 
      return A[left]
   else
      max1 = findMaxHelper(A, left, (right + left) / 2)
      max2 = findMaxHelper(A, (right + left) / 2, right)

      if (max1 > max2) 
         return max1 
      else 
         return max2

I am having a hard time understanding what is happening in this pseudo-code.

Can someone help explain what is happening at each line. I need to understand this code before I can answer the questions.

I know that the function findMax calls the helper function findMaxHelper, then findMaxHelper uses recursion. Other than that, I really don't understand it.

Answer 1

You are using Divide and Conquer algorithm for finding the maximum element from the array. First, you are dividing the array into individual elements (divide), then you are comparing the elements (conquer). You are dividing the array using calling findMaxHelper recursively.

The general idea of Divide and conquer is shown in the figure:

Example:

Here max is same as your findMaxHelper function with two arguments i.e. left and right.

Check this example for more in depth understanding of the concept.