Find a peak element in a Given Array

Objective : In this article we will discuss an algorithm to Find a peak element in a Given Array. We will see the recursion techniques to solve this problem.

Peak Element: peak element is the element which is greater than or equal to both of its neighbors.

Input:  Array, arrA[] .

Output: A peak element and its index

Approach:

A simple approach is to do a linear scan to a array and using few variables we can find a peak element. But the Time Complexity will be O(n) but real question is, Can we do better?

The Answer is yes, by using Binary Search techniques.

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Find two Missing Numbers in a Sequence of Consecutive Numbers

Objective : Write an algorithm to find two Missing Numbers in a Sequence of Consecutive Numbers

Input:  Array, arrA[] with two missing numbers and Range

Output : Two missing numbers

Approach:

    • Approach is very simple, Add all the given numbers say S
    • Calculate sum of N numbers by formula n(n+1)/2 , say N
    • Find sum of two missing numbers a+b = N-S

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Find a Missing Number From a Sequence of Consecutive Numbers

Objective : You have been asked to Write an algorithm Find a Missing Number From a Sequence of Consecutive Numbers

Input:  Array, arrA[] with a missing number and Range

Output : missing number

Approach:

  • Approach is very simple, Add all the given numbers say S
  • Calculate sum of N numbers by formula n(n+1)/2 , say N
  • Find missing number m = N-S

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Merge Sort – Updated – Most Efficient ways to Implement

Objective : Write Merge Sort algorithm to sort elements in an array

Input: A unsorted array, arrA[].

Output : A sorted array.

Approach:

Divide and Conquer: In this approach we divide the main problems into smaller problems, solve them and merge the results to get the final result.

How Divide and conquer works in Merge Sort:

We divide the elements into two half’s by middle of the array. We solve the left half and right half recursively and merge the results.

Merging:

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