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DSA / Algorithms / Analysis of Algorithms

Analysis of Algorithms

187+ posts

3-coloring is NP Complete

Last Updated: 15 July 2025

Prerequisite: NP-Completeness, Graph ColoringGraph K-coloring Problem: A K-coloring problem for undirected graphs is an assignment of colors to the nodes of the graph such...read more

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Analysis of Algorithms

Rearrange and update array elements as specified by the given queries

Last Updated: 15 July 2025

Given an array arr[] of size N and queries Q[][], the task is to perform the following types of queries on the given array. 0: Left shift the array by one position.1: Righ...read more

Analysis of Algorithms

Advanced Data Structure

array-range-queries

array-rearrange

Big O vs Theta Θ vs Big Omega Ω Notations

Last Updated: 15 July 2025

1. Big O notation (O):It defines an upper bound on order of growth of time taken by an algorithm or code with input size. Mathematically, if f(n) describes the running tim...read more

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Analysis of Algorithms

Difference Between

Determine winner of the Game by arranging balls in a row

Last Updated: 01 April 2021

Given the number of small and large balls N and M respectively, the task is to find which player wins if both the player X and Y play optimally by making the following two...read more

Analysis of Algorithms

Check if a large number is divisible by a number which is a power of 2

Last Updated: 11 May 2021

Given a large number in the form of a string str and a number K, the task is to check if the number formed by string str is divisible by the K or not, where K is a power o...read more

Analysis of Algorithms

Count of subarrays of size K having at least one pair with absolute difference divisible by K-1

Last Updated: 15 July 2025

Given an arr[] consisting of N elements, the task is to count all subarrays of size K having atleast one pair whose absolute difference is divisible by K - 1.Examples:Inpu...read more

Analysis of Algorithms

Pigeonhole Principle

Check if given permutation of 1 to N can be counted in clockwise or anticlockwise direction

Last Updated: 30 May 2022

Given an integer array arr of size N which contains distinct elements from 1 to N. The task is to check if a position in the array can be found such that all numbers from ...read more

Analysis of Algorithms

Print all Strong numbers less than or equal to N

Last Updated: 15 July 2025

Given a number N, print all the Strong Numbers less than or equal to N.Strong number is a special number whose sum of the factorial of digits is equal to the original numb...read more

Analysis of Algorithms

Count of pairs in a given range with sum of their product and sum equal to their concatenated number

Last Updated: 01 June 2021

Given two numbers A and B, the task is to find the count of pairs (X, Y) in range [A, B], such that (X * Y) + (X + Y) is equal to the number formed by concatenation of X a...read more

Analysis of Algorithms

Write From Home

array-range-queries

Natural Numbers

Last digit of a number raised to last digit of N factorial

Last Updated: 15 July 2025

Given two number X and N, the task is to find the last digit of X raised to last digit of N factorial, i.e.X^{\left ( N! \right )mod 10}.Examples:Input: X = 5, N = 2Output...read more

Analysis of Algorithms

Minimum sprinklers required to water a rectangular park

Last Updated: 25 September 2022

Given N * M rectangular park having N rows and M columns, each cell of the park is a square of unit area and boundaries between the cells is called hex and a sprinkler can...read more

Analysis of Algorithms

square-rectangle

Proof that Dominant Set of a Graph is NP-Complete

Last Updated: 15 July 2025

Pre-requisite: Dominant Set of a Graph, NP-CompleteA dominating set in a graph G = (V, E) is a subset of vertices V’ following the condition that the vertices not belongin...read more

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Analysis of Algorithms

Advanced Data Structure

Proof that traveling salesman problem is NP Hard

Last Updated: 15 July 2025

Pre-requisite: Travelling Salesman Problem, NP HardGiven a set of cities and the distance between each pair of cities, the travelling salesman problem finds the path betw...read more

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Analysis of Algorithms

Advanced Data Structure

Number of cycles formed by joining vertices of n sided polygon at the center

Last Updated: 28 June 2022

Given an N-sided regular polygon, we have connected all the vertices at the center of the polygon, thus dividing the polygon into N equal parts. Our task is to the Count o...read more

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Analysis of Algorithms

Pattern Searching

Complexity analysis of various operations of Binary Min Heap

Last Updated: 15 July 2025

A Min Heap is a Complete Binary Tree in which the children nodes have a higher value (lesser priority) than the parent nodes, i.e., any path from the root to the leaf node...read more

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Analysis of Algorithms

time complexity

Data Structures-Heap

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