What is the Coin Change problem and how do you solve it?
This problem asks for the minimum number of coins needed to make a certain amount. It tests dynamic programming and knapsack variations.
Why Interviewers Ask This
Interviewers use this to test DP table construction and state transitions. They want to see if you can break down the problem into smaller subproblems. It demonstrates optimization and recurrence relation skills.
How to Answer This Question
Explain the DP state: dp[i] represents the minimum coins for amount i. Initialize dp[0] = 0 and others to infinity. For each coin, update the dp array for all amounts from coin value to target. The recurrence is dp[i] = min(dp[i], dp[i - coin] + 1). Handle cases where the amount cannot be formed. Discuss time complexity.
Key Points to Cover
- DP state definition
- Initialization strategy
- Recurrence relation
- Impossible case handling
Sample Answer
I solve this using dynamic programming where dp[i] stores the minimum coins needed for amount i. I initialize dp[0] to 0 and all other entries to infinity. I iterate through each coin denomination and update the dp array…
Common Mistakes to Avoid
- Incorrect initialization of base cases
- Iterating coins and amounts in wrong order
- Forgetting to check for impossibility
Sound confident on this question in 5 minutes
Answer once and get a 30-second AI critique of your structure, content, and delivery. First attempt is free — no signup needed.