Write a program to count the number of possible triangles that can be formed with three elements from a given unsorted array of positive integers. The three elements, representing the lengths of the sides of a triangle, must satisfy the triangle inequality: the sum of any two sides must be greater than the third side.

Write a program to implement queue using stack. We should use stack operations like push, pop, top, size, and isEmpty for implementing queue operations like enqueue, dequeue, and front. In this blog, we have discussed two approaches for implementing queue using two stacks: 1) Dequeue O(1) and Enqueue O(n) 2) Enqueue O(1) and Dequeue O(1).

A sorted array is given, write a program to remove duplicates from sorted array. We need to remove repeated elements such that there is a single occurrence of each element and return the length of array containing unique elements. Note: This is an excellent problem to learn fast and slow pointers approach. We have discussed two O(n) time in place solutions.

Given an array A[] of n integers, find out the maximum difference between any two elements such that the larger element appears after the smaller element. In other words, we need to find max(A[j] - A[i]), where A[j] > A[i] and j > i. Note: This is an excellent problem to learn problem-solving using divide and conquer and a single loop.

Given an array X[] of n distinct elements, write a program to find all the unique triplets in the array whose sum is equal to zero. For example, if triplets with zero sum in the array are (X[i], X[j], X[k]), then X[i] + X[j] + X[k] = 0. Hint: This is an excellent problem to learn problem-solving and optimization using hashing and two pointers approach.

Given an array of n integers and a target number, write a program to find whether a pair sum exists in the array or not. In other words, we need to check for a pair of elements in the array that sum exactly to the target value. Assume that all elements are distinct. Note: This is an excellent problem to learn problem solving using two pointers and hash table.

Given an array of n non-negative integers height[n], where each represents a point at coordinate (i, height[i]). n vertical lines are drawn such that endpoints of line i is at (i, height[i]) and (i, 0). Find two lines, which together with x-axis form a container, such that container contains the most water. This is an excellent problem to learn two pointers approach.

Given an array consisting of 0s, 1s, and 2s, write a program to sort this array of 0, 1, and 2 in ascending order. We need to sort the array in O(n) time complexity without using sorting algorithms or extra space. Note: This is a variation of the Dutch national flag problem and an excellent problem to learn problem solving using three pointers.

Given an array X[] of size n, write a program to find the maximum and minimum element in an array. Our algorithm should make the minimum number of comparisons. Note: This is an excellent question to learn problem-solving using a single loop and divide and conquer approach. In the efficient single loop solution, we increment the loop by two.

Given an array X[] of n integers, write a program to find product[] array such that product[i] is equal to product of all array elements except X[i]. We need to solve this problem without using division operations. Note: This is an excellent product array puzzle to learn time complexity optimization using prefix array and a single loop.

Given an n x n 2D matrix, write a program to rotate the matrix by 90 degrees in anticlockwise direction. We should rotate matrix 90 degrees without using extra space. In other words, we have to perform rotation by modifying 2D matrix directly. Note: This is an excellent problem to learn problem-solving using nested loops and transpose of a matrix.

Given an array X[] of n elements filled with several integers, some of them being zeroes, write a program to move all the zeros to the end. We need to preserve the relative order of non-zero elements and solve this problem in place using O(n) time complexity. Note: This is an excellent problem to learn problem solving using two pointers approach.

A sorted and rotated array of size n is given, write a program to find minimum element in rotated sorted array. Rotation by k times means that the first k sorted elements of the array will move to the last k positions, and the last n - k sorted elements will move to the first n - k positions. Note: We don’t know how many times array is rotated in the given problem.

Given a Roman number, write a program to convert Roman number to a corresponding integer value. What are Roman numbers? Roman numbers are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which represent integer values respectively for 1, 5, 10, 50, 100, 500, and 1,000.

Given an array X[] of size n, write a program to find the most frequent element in the array, i.e. the element which occurs the most number of times. If multiple elements have maximum frequency, return the smallest (assume that at least one element is repeated). Note: This is an excellent problem to learn problem-solving using sorting and hash table.

Given two integer arrays, X[] and Y[] of size m and n, write a program to find intersection of these two arrays. The intersection is a list of common elements present in both arrays. Suppose m > n, all array elements are distinct and intersection elements can be in any order. Note: This is an excellent problem to learn problem solving using various approaches.

Given a binary tree, find its minimum depth. The min depth of a binary tree is the number of nodes along the shortest path from root node down to the nearest leaf node. The path has to end on a leaf node. Note: An excellent problem to understand efficient problem solving using breadth-first search (BFS) when the solution node is nearest to the root node.