Counting sort is a stable sorting algorithm that works in O(n) time and space complexity when input are integers in the range 0 to k and k = O(n). Instead of comparison, counting sort uses array indexing to determine position of elements. For each element x, it counts values less than x and places x directly into its correct position in the sorted array.

In an array of size 2N, there are N + 1 unique elements, and exactly one of these elements is repeated n times. Write a program to return the N-repeated element in the given 2N size array. Note: This is an excellent problem to learn optimization using the mathematical approach. Sometimes mathematical insights into the problem can help us to get efficient solutions.

You are given an array X[] of n elements, write a program to find majority element in an array. A majority element is an element that appears more than n/2 times, so there is at most one such element. Assume that array is non-empty and majority element always exists in the array. Note: This is an excellent problem to learn various approaches.

Given two unsorted arrays of size m and n, find whether one array is a subset of another array or not. An array Y[] will be a subset of another array X[] if each element of Y[] is present in X[]. Assume that there are no repeated elements in both arrays and n <= m. Note: This is an excellent problem to learn problem solving using various approaches.

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 that includes both positive and negative numbers, write a program to find the first missing positive integer. This is one of the best problems for learning step-by-step time complexity optimization using various approaches. An in-place hashing solution uses the same input array to process values and generate output.

Given array X[] of n integers, write a program to return the count of distinct elements in every window of size k. Here k sized window is a continuous subarray of k elements, and output is an array with the count of unique elements in each window. Note: This is an excellent problem to learn problem-solving using the sliding window approach.

Given a string S, write a program to find the length of longest substring without repeating characters. The substring is a continuous subpart of the string and we need to return the largest substring which has all unique characters. Note: This is an excellent problem to learn problem solving and time complexity optimization using sliding window approach.

Given an integer n, write a program to return string representation of numbers from 1 to n. If number is divisible by 3, we store “Fizz”. If number is divisible by 5, we store “Buzz”. If number is divisible by both 3 and 5, we store “FizzBuzz”. Hint: This is an excellent puzzle to learn coding concepts like conditional statements, loops, etc.

Given two strings, str1 and str2, of size m and n, write a program to check whether two strings are an anagram of each other or not. A string str1 is an anagram of str2 if characters of str1 can be rearranged to form str2. Note: This is an excellent string problem to learn problem-solving and optimization using direct address table.

Given an array X[] of n integers, write a program to find the length of largest continuous subarray with zero sum. The subarray length starting from index i and ending at index j will be j - i + 1. So in other words, for all j > i, find max (j - i + 1) among all subarrays with zero sum.. Note: This is an excellent question to learn problem-solving using hash table.

Given two integer arrays X[] and Y[], write a program to check if arrays are equal or not. Two arrays are equal if they have the same elements in any order. If there are repeated elements, then counts of repeated elements must also be the same for both arrays. Note: This is an excellent problem to learn problem solving using a hash table.

Given an array of n integers, find the length of the longest consecutive elements sequence. We need to find the length of the longest subsequence such that elements in the subsequence are consecutive integers. The consecutive numbers can be in any order. Note: This is an excellent problem to learn problem-solving using sorting and hash table.

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.

The least recently used (LRU) cache is one of the popular caching strategies, which defines the policy to discard the least recently used items first from the cache and make room for new elements when the cache is full. It is used to organize items in order of their use, which allows identifying items that have not been used for a long time.

The least frequently used (LFU) is a cache algorithm used to manage memory within a computer. In this method, the system keeps track of the number of times a block is referenced in memory, and when the cache is full, our system removes the item with the lowest reference frequency. LFU cache get and put operation works in O(1) average time complexity.

Bloom filter is a space-efficient data structure that tells whether an element may be in a set (either a false positive or true positive) or definitely not present in a set (True negative). It will take O(1) space, regardless of the number of items inserted. However, their accuracy decreases as more elements are added.

Hashing is a technique to map (key, value) pairs into the hash table using a hash function. It uses an array of size proportional to the number of keys and calculates an array index from the key using a hash function. We use hashing/hash tables in several real life applications and solve various coding questions efficiently in data structures.

Given a string S[], write a program to sort string S in decreasing order based on the frequency of characters. The frequency of a character is the number of times it appears in the string. If two characters have the same frequency, whichever occurs earliest in S, must come first. In other words, frequency based sorting must be stable.

We use hash functions to distribute keys in the hash table uniformly. In other words, a good hash function satisfies the assumption of uniform hashing, where each key is equally likely to hash to any slots in the hash table. This blog has discussed the design and properties of some popular hash functions used in algorithm and data structure.