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Chapter 5: Problem 34

List three more applications of backtracking.

Short Answer

Expert verified
Three more applications of backtracking are Sudoku solvers, The Knight’s tour problem, and Maze solving.

Step by step solution

01

Application 1: Sudoku Solver

One of the widely known applications of backtracking is in solving Sudoku puzzles. Backtracking helps to find a solution by filling the cells sequentially. If we encounter a problem, we clear the cell and move to the previous one, continuing this process until we find a solution.
02

Application 2: The Knight’s Tour Problem

The Knight’s tour problem is another classic example where backtracking is used. The problem challenges us to move a knight on an n x n chessboard such that it visits every square once. If we reach a point where a move is not possible, we backtrack and try other possibilities.
03

Application 3: Maze Solver

Backtracking is used for maze solving. Starting at a point, we explore a path. If we hit a dead end, we backtrack to find another path. This process continues until the exit of the maze is found.

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Most popular questions from this chapter

Suppose we have a solution to the \(n\) -Queens Problem instance in which \(n=4,\) Can we extend this solution to find a solution to the problem instance in which \(n=5,\) then use the solutions for \(n=4\) and \(n=5\) to construct a solution to the instance in which \(n=6,\) and continue this dynamic programming approach to find a solution to any instance in which \(n>4 ?\) Justify your answer.

Suppose that to color a graph properly we choose a starting vertex and a color to color as many vertices as possible. Then we select a new color and a new uncolored vertex to color as many more vertices as possible. We repeat this process until all the vertices of the graph are colored or all the colors are exhausted. Write an algorithm for this greedy approach to color a graph of \(n\) vertices. Analyze this algorithm and show the results using order notation.

Use the Backtracking Algorithm for the Sum-of-Subsets Problem (Algorithm 5.4) to find all combinations of the following numbers that sum to \(W=52\) \(w_{1}=2 \quad w_{2}=10 \quad w_{3}=13 \quad w_{4}=17 \quad w_{3}=22 \quad w_{6}=42\) Show the actions step by step.

List some of the practical applications that are representable in terms of the \(m-\) Coloring Problem.

Apply the Backtracking Algorithm for the \(n\) -Quecns Problem (Algorithm 5.1) to the problem instance in which \(n=8\), and show the actions step by step. Draw the pruned state space tree produced by this algorithm up to the point where the first solution is found.
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