Unit 5-BACKTRACKING- n queens, sum of subset, graph coloring problems
- 2. General Method Backtracking • Many problems which deal with searching for a set of solutions or which ask for an optimal solution Satisfying some constraints can be solved using the backtracking formulation. • The name backtrack was first coined by D.H.Lehmer in the 1950s Early
- 4. General Method Backtracking • Many of the problems we solve using backtracking require that all the Solutions satisfy a complex set of constraints. For any problem these constraints can be divided into two categories : explicit and implicit • Explicit constraints are rules that restrict each Xi to take on values only from a given set • Common examples of explicit constraints are
- 5. General Method Backtracking • The explicit constraints depend on the particular instance I of the problem Being solved. • All tuples that satisfy the explicit constraints define a possible Solution space for I. • The implicit constraints • are rules that determine which of the tuples in the solution space of I satisfy the criterion function. • Thus Implicit constraints describe the way in which the Xi must relate to each other
- 10. Formulation of Backtracking process
- 13. N-Queen Problem
- 14. N-Queen Problem
- 17. SUM OF SUBSET
- 22. GRAPH COLORING
- 32. Example Find the all possible Hamiltonian cycle by using the backtracking approach for a given graph. Draw portion of state space tree generated