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LectureON Backtracking V.Radhesyam Assistant professor Department of IT:VRSEC
What is Backtracking • Backtracking is a design technique used to solve problems with large search space. • Build a solution incrementally, one piece at a time, removing those solutions that fail to satisfy the constraints of the problem at any point of time. • Backtracking uses a data structure called state space tree.
What is 4-Queens Problem • The 4-Queens Problem consists in placing four queens on a 4 x 4 chessboard so that no two queens can attack each other. • That is, no two queens are allowed to be placed on the same row, the same column or the same diagonal. • This problem can be solved by backtracking
Solution: State space Tree x1=1 means Q1 Placed in first column
Types of nodes • Live node: A node which is generated and the children are not yet generated is called live node. • E-node: The node whose children are currently generated is called E-node. • Dead node: A node which cannot further extended is called dead node.
Graph coloring • The problem is, given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color. • This number is called chromatic number
Hamilton cycles • Hamiltonian Path in an undirected graph is a path that visits each vertex exactly once. A Hamiltonian cycle is a Hamiltonian Path such that there is an edge (in graph) from the last vertex to the first vertex of the Hamiltonian Path
