Count All Paths from Top left to bottom right in Two Dimensional Array including Diagonal Paths

Objective: Count all the paths from left top corner to the right bottom corner in two-dimensional array.

Input: Two Dimensional array

Output: No of paths.

Approach :

1. Recursive

The recursive solution to this problem is similar to Print All Paths from Top left to bottom right in Two Dimensional Array

But the Time complexity will be exponential because there will be many sub-problems that will be solved again and again to get the final solution. read this: “Dynamic programming vs Recursion

2. Dynamic Programming (Better Solution)

Create two-dimensional resultCount array to store the number of paths from top left corner.

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Merge or Combine Two Sorted Linked Lists

Objective: Given two sorted linked lists, objective is to merge both the lists in sorted order.

Input: Two sorted linked list List a, List b.


List a :




Merged List: ->1->2->3->6->17->18->19



Without Recursion:

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Quick Sort Implementation

Objective: Write an algorithm to sort an array in increasing or decreasing order using Quick Sort.

Input:  An Array arrA[]

Output: A sorted array.


  • Choose any element from the array and call it as pivot element, Example here we have selected middle element as pivot
  • Place all the elements smaller than pivot in the left side of pivot.
  • Place all the elements greater than pivot in the right side of pivot.
  • Sort left side and right side recursively.


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Valid or Well Formed Parentheses | Part – 1

Objective: You have been asked to write an algorithm to find Whether Given the Sequence of parentheses is well-formed. This question was asked in the Amazon Interview.

Input: A String contains a sequence of parentheses

Output: true or false on whether parentheses are well-formed or not


  • Idea is to have two counters, one for open parentheses ‘{‘ and one for close ‘}’
  • Read one character at a time and increment one of the counters
  • If any given point of time count of close parentheses is greater than the open one, return false
  • If at the end both counters are equal, return true

Example: { { } { } } – Well-formed

{ { } { = Not well-formed


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Find an Element in 2 dimensional sorted array

Objective: Write an algorithm to find an element in 2-dimensional array where rows and columns are sorted respectively.

Input: A two dimensional sorted array, arrA[][].

Sorted 2D array

Output: True or false based on whether the element exists and its location


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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 that is greater than or equal to both of its neighbors.

Input:  Array, arrA[] .

Output: A peak element and its index


A simple approach is to do a linear scan of an array and using a 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 a Missing Number From a Sequence of Consecutive Numbers

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

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

Output: missing number


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

Example : suppose array given is  {1,2,3,4,5,6,8,9,10} and range is 10.

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