searching

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Find Intersection of Two Arrays

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.

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Find First and Last Position of Element in Sorted Array

Given an array of integers sorted in ascending order, write a program to find the first and last occurrence of a given element. Our goal should be to design an algorithm with O(log n) time complexity. Note: This is an excellent question to learn problem-solving using binary search. Here we need to apply binary search twice to solve this problem.

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AVL Tree

AVL Trees is a height-balanced BST named after its inventors, Adelson-Velsky and Landis. This is a variation of binary search trees, also known as self-balancing BST. The property of AVL Trees: The absolute difference of height between left and right subtree is at max 1, which could help us to perform bst operations in O(logn) time complexity.

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Pair sum in an array

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.

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Hashing in Data Structure

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.

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Searching in Binary Search Tree (BST)

We start searching from root node and traverse a path downward in binary search tree. For each node in the path, compare target key k with the node key. If equal, search is successful. If k < node key, go to the left subtree. Similarly, if k > node key, go to the right subtree. In this blog, we have discussed recursive and iterative implementations of searching in BST.

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N Repeated Element in Size 2N 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.

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Binary Search Algorithm

Binary search is an efficient algorithm to search a value in the sorted array using divide and conquer approach. It compares target value with value at mid-index and repeatedly reduces search interval by half. Searching continues until value is found or subarray size gets reduced to 0 (unsuccessful search). Time complexity of binary search is O(logn).

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Search in a 2D Matrix

You have given row-wise and column-wise sorted 2d matrix and integer k, write a program to search k in 2d matrix, i.e. find whether k is present or not. Each row is sorted from left to right, and the first integer of each row is greater than the last integer of the previous row. Note: This is an excellent problem to learn problem solving binary search in a 2d matrix.

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Equilibrium Index of an Array

Write a program to find equilibrium index of an array. An array's equilibrium index is an index such that the sum of elements at lower indexes equals the sum of elements at higher indexes. Note: This is an excellent coding question to learn time and space complexity optimization using prefix array and a single loop using variables.

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Find Minimum and Maximum Element in Array

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.

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Find Maximum Element in a Bitonic Array

You are given an array of n integers that is first increasing and then decreasing. Write a program to find the maximum value in the array. Our goal should be to solve this problem using O(logn) time complexity. Note: This is an excellent problem to learn problem solving using binary search, where we modify binary search to get an efficient solution.

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Introduction to Trie Data Structure

We mainly use trie data structure to process strings efficiently. It is a tree where each node represents a prefix or end of a word. The best thing is that the time complexity of trie operations depends on string length, which is independent of number of strings. Applications of trie: Autocomplete search, longest prefix matching, spell checker, etc.

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Hash Functions in Data Structure

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.

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A* Search Algorithm

A* search algorithm is a popular technique for finding the shortest path in a graph from a given initial node to a destination node. For example, in video games, pathfinding can be used to move objects from their initial place to their destination via shortest route. So implementation of a star algorithm is popular in tile or map-based games.

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Kth Smallest Element

Given an array and a positive integer k, write a program to find the kth smallest element in the array. This is an excellent problem to learn problem-solving using the max and min heap data structure. The quick-select approach (divide and conquer) is also worth exploring because it helps to optimize time complexity to O(n) time average.

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Check Equal Arrays

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.

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Row With Max 1s

Given a boolean 2D array, where each row is sorted. Find the row with the maximum number of 1s. This is an excellent matrix problem that can be solved in linear time complexity. The best part is — we are using the sorted order property and nested loops to improve the solution over the binary search approach.

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