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ques-minor-2paper

Iterative Backtracking Algorithm

Backtracking is a problem-solving algorithmic technique that involves finding a solution incrementally by trying different options and undoing them if they lead to a dead end.

It uses recursive calling to find a solution set by building a solution step by step, increasing levels with time. In order to find these solutions, a search tree named state-space tree is used. In a state-space tree, each branch is a variable, and each level represents a solution.

A backtracking algorithm uses the depth-first search method.

Diagram:

A diagram can be represented as a tree where each node represents a decision point and each branch represents a possible choice. The backtracking algorithm explores these choices until a solution is found or the search space is exhausted.

mathematicaCopy code
               A
             / | \\
            B  C  D
           /|  |
          E F  G
            |
          H

In this example, each letter represents a decision point, and the branches represent the choices at each point. The algorithm explores the tree until it finds a solution or backtracks when a dead-end is reached.

1**. Initialization:**

• Start with an initial state or an empty partial solution.
• Push the initial state onto the stack.

2. Iterative Loop:

• While the stack is not empty:
  • Pop the top state from the stack.
  • If the state is a solution, return it.
  • Otherwise, generate all possible next states from the current state.

3. Decision Making: