How does backtracking compare to dynamic programming?

Can you explain how backtracking differs from dynamic programming?

Sure! Backtracking is a technique for solving problems incrementally, trying partial solutions and abandoning them if they don't lead to a valid solution. Dynamic programming, on the other hand, solves problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations.

What types of problems are best suited for each method?

Backtracking is great for combinatorial problems like puzzles and games, where you explore all possibilities. Dynamic programming is ideal for optimization problems, like finding the shortest path or calculating Fibonacci numbers, where overlapping subproblems exist.

Can you give an example of a problem that uses backtracking?

A classic example is the N-Queens problem, where you need to place N queens on an N×N chessboard so that no two queens threaten each other. Backtracking helps explore all possible placements.

And what about dynamic programming?

An example of dynamic programming is the Knapsack problem, where you want to maximize the value of items in a knapsack without exceeding its weight limit. It uses a table to store the maximum value for each weight limit.