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Chapter 6 Backtracking Algorithms
Backtracking Algorithm
The Knight’s Tour Problem
Data representation
Given the current coordinate pair <x, y>, there are 8 potential candidates for coordinates <u, v> of the destination. They are
The final refinement
The recursive procedure is initiated by a call with the coordinates x0, y0 , from which the tour is to start. h[x0,y0]:= 1;
The general pattern of backtracking algorithm
The eight queens problem
Rule of chess: A queen can attacks all other queens in either the same column, row or diagonal on the board
Extension: Finding all solutions
In the extended algorithm, to simplify the stopping condition of the selection process, the repeat statement is replaced by a
State space tree
Complexity of backtracking algorithm
Branch-and-bound algorithm
Exhaustive search: Modified DFS to generate all the simple paths
An instance of TSP
Exhaustive search to find all simple paths
From the algorithm generating all simple paths to the algorithm solving TSP
The idea of branch-and-bound
The idea of branch-and-bound (cont.)
Example: Given a Traveling Salesman Problem as in the figure:
References
Nội dung
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