# Category - Hard problems

## K Centers Problem | Set 1 (Greedy Approximate Algorithm)

K Centers Problem - Greedy Approximate Algorithm - Let OPT be the maximum distance of a city from a center in the Optimal solution. We need to show that

## java program – Vertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)

java program - Vertex Cover Problem - Introduction and Approximate Algorithm - It can be proved that the above approximate algorithm never finds a vertex

## C Programming – Vertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)

C Programming - Vertex Cover Problem - Introduction and Approximate Algorithm - It can be proved that the above approximate algorithm never finds a vertex

## java programming – Backtracking | Set 6 (Hamiltonian Cycle)

java programming - Backtracking - Hamiltonian Cycle - Create an empty path array and add vertex 0 to it. Add other vertices, starting from the vertex 1.

## C Programming – Backtracking | Set 6 (Hamiltonian Cycle)

C Programming - Backtracking - Hamiltonian Cycle - Create an empty path array and add vertex 0 to it. Add other vertices, starting from the vertex 1

## Travelling Salesman Problem | Set 2 (Approximate using MST)

Travelling Salesman Problem - Approximate using MST - The cost of the output produced by the above algorithm is never more than twice the cost of best

## Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming)

Travelling Salesman Problem - Naive and Dynamic Programming - Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair

## java programming – Graph Coloring | Set 2 (Greedy Algorithm)

java programming - Graph Coloring - Greedy Algorithm - there is no efficient algorithm available for coloring a graph with minimum number of colors

## C programming – Graph Coloring | Set 2 (Greedy Algorithm)

C programming - Graph Coloring | Set 2 (Greedy Algorithm) - Graph Algorithms - It doesn’t guarantee to use minimum colors, but it guarantees an upper bound

## Graph Coloring

Graph Coloring - Graph Cycle - Graph coloring problem is to assign colors to certain elements of a graph subject to certain constraints.