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NP-Hard Class

Last Updated: 23 July 2025

A 'P' problem is said to be NP-Hard when all 'Q' belonging in NP can be reduced in polynomial time (n^k where k is some constant) to 'P' assuming a solution for 'P' takes ...read more

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Analysis of Algorithms

DSA

NPHard

Quadratic Assignment Problem (QAP)

Last Updated: 17 November 2023

The Quadratic Assignment Problem (QAP) is an optimization problem that deals with assigning a set of facilities to a set of locations, considering the pairwise distances a...read more

Last Updated: 23 July 2025

Problem Description:The Art Gallery Problem is formulated in geometry as the minimum number of guards that need to be placed in an n-vertex simple polygon such that all po...read more

DSA

NPHard

Set cover is NP Complete

Last Updated: 15 July 2025

Problem: Given a ground Set X, an integer k, and a collection of subsets Si of X, the problem is to identify if there exists a collection of subsets whose union is X, with...read more

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Misc

Analysis of Algorithms

DSA

NPHard

NP Complete

Hitting Set problem is NP Complete

Last Updated: 15 July 2025

Prerequisite: NP CompleteProblem: Given a ground set X of elements and also a grouping collection C of subsets available in X and an integer k, the task is to find the sma...read more

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Misc

Analysis of Algorithms

DSA

NPHard

NP Complete

Proof that Subgraph Isomorphism problem is NP-Complete

Last Updated: 15 July 2025

Subgraph Isomorphism Problem: We have two undirected graphs G1 and G2. The problem is to check whether G1 is isomorphic to a subgraph of G2.Graph Isomorphism: Two graphs A...read more

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DSA

NPHard

Algorithms-NP Complete

NP Complete

Proof that Clique Decision problem is NP-Complete

Last Updated: 15 July 2025

Prerequisite: NP-CompletenessA clique is a subgraph of a graph such that all the vertices in this subgraph are connected with each other that is the subgraph is a complete...read more

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DSA

NPHard

Algorithms-NP Complete

NP Complete

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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Graph

Analysis of Algorithms

Advanced Data Structure

DSA

NPHard

NP Complete

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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Graph

Analysis of Algorithms

Greedy

Advanced Data Structure

DSA

NPHard

Proof that Clique Decision problem is NP-Complete | Set 2

Last Updated: 12 July 2025

Prerequisite: NP-Completeness, Clique problem.A clique in a graph is a set of vertices where each vertex shares an edge with every other vertex. Thus, a clique in a graph ...read more

Algorithms-NP Complete

NP Complete

Proof that Independent Set in Graph theory is NP Complete

Last Updated: 29 September 2025

Prerequisite:NP-Completeness, Independent set. An Independent Set S of graph G = (V, E) is a set of vertices such that no two vertices in S are adjacent to each other. I...read more

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DSA

NPHard

Algorithms-NP Complete

NP Complete

Proof that Hamiltonian Cycle is NP-Complete

Last Updated: 12 July 2025

Prerequisite: NP-Completeness, Hamiltonian cycle.Hamiltonian Cycle:A cycle in an undirected graph G=(V, E) traverses every vertex exactly once.Problem Statement: Given a g...read more

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DSA

NPHard

Algorithms-NP Complete

NP Complete

Difference between NP hard and NP complete problem

Last Updated: 25 February 2025

All NP Complete Problems are NP-Hard but vice versa is not true. NP-Complete problems are subset of NP Problems. NP Problems : NP problems are a class of computational p...read more

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DSA

NPHard

Algorithms-NP Complete

Traveling Salesman Problem (TSP) Implementation

Last Updated: 26 November 2024

Given a 2d matrix cost[][] of size n where cost[i][j] denotes the cost of moving from city i to city j. The task is to complete a tour from city 0 (0-based index) to all o...read more

Implementation of Exact Cover Problem and Algorithm X using DLX

Last Updated: 10 January 2023

In the article Exact Cover Problem and Algorithm X | Set 1 we discussed the Exact Cover problem and Algorithm X to solve the Exact cover problem. In this article, we’ll di...read more

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C++

NPHard

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