What is the Coin Change problem and how do you solve it?

DSA
Medium
69.9K views

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

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