Coin Change Problem Concepts

The video tutorial covers the classic dynamic programming problem of coin change, where the goal is to find the minimum number of coins needed to make a given amount. It explores various approaches, including greedy, brute force, backtracking, top-down memoization, and bottom-up dynamic programming. The tutorial explains why the greedy approach fails and how dynamic programming provides an efficient solution. It concludes with a code implementation and analysis of time and space complexity.

What is the main objective of the coin change problem?

• To use only one type of coin to reach a target amount.

• To use the fewest number of coins to reach a target amount.

• To use all available coins to reach a target amount.

• To use the maximum number of coins to reach a target amount.

Why does the greedy approach fail in the coin change problem?

• It only works when there is one type of coin.

• It doesn't consider all possible combinations of coins.

• It requires sorting the coins first.

• It always uses the smallest coin first.

What is a brute force solution in the context of the coin change problem?

• A solution that uses the largest coin first.

• A solution that ignores the target amount.

• A solution that uses only one type of coin.

• A solution that tries all possible combinations of coins.

What is meant by overlapping subproblems in dynamic programming?

• Subproblems that are larger than the original problem.

• Subproblems that appear multiple times in the solution process.

• Subproblems that can be solved independently.

• Subproblems that have the same solution.

What is the key difference between top-down memoization and bottom-up dynamic programming?

• Top-down is faster than bottom-up.

• Top-down solves the problem recursively, bottom-up solves it iteratively.

• Top-down uses iteration, bottom-up uses recursion.

• Top-down starts with the smallest subproblem, bottom-up starts with the largest.

In the bottom-up dynamic programming solution, what is the base case for the dp array?

• dp[0] = -1

• dp[0] = 1

• dp[0] = infinity

• dp[0] = 0

What is the time complexity of the dynamic programming solution for the coin change problem?

• O(amount * number of coins)

• O(n^2)

• O(log n)

• O(n)