# Category: Backtracking

## All combinations of elements satisfying given constraints

Given a positive number N, find all combinations of 2*N elements such that every element from 1 to N appears exactly twice and distance between its two appearances is exactly equal to value of the element.

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## Print All Hamiltonian Path present in a graph

Given an undirected graph, print all Hamiltonian paths present in it. Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once.

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## Find Longest Possible Route in a Matrix

Given a rectangular path in the form of binary matrix, find the length of longest possible route from source to destination position of the matrix by moving to only non-zero adjacent positions i.e. route can be formed from positions having their value as 1. Note there should not be any cycles in the output path.

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## Find Shortest Path in Maze

Given a maze in the form of the binary rectangular matrix, find length of the shortest path in maze from given source to given destination. The path can only be constructed out of cells having value 1 and at any given moment, we can only move one step in one of the four directions.

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## Magnet Puzzle

We are given set of bipolar magnets each domino-shaped. The objective is to place magnets on a M X N board which should meet a set of conditions where both N and M are not odd.