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Minimum Coins to Reach an Amount Coding / DSA Interview

Given a set of coin denominations and a target amount, find the minimum number of coins (with unlimited supply of each denomination) needed to make exactly that amount, or report it is impossible.

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1. Problem Statement

You are given a list of coin denominations and a target amount. Each denomination has unlimited supply. Find the minimum number of coins needed to make exactly the target amount, or -1 if it cannot be made.

2. Live Coding Format

Work in the provided coding workspace while explaining your decisions to the live interviewer. Validation may use inline tests, examples, comments, or a verbal walkthrough.

3. Key Focus Areas

  • 1
    Problem clarification and contract
  • 2
    Approach exploration and optimality
  • 3
    Think-aloud communication and pacing
  • 4
    Implementation correctness
  • 5
    Code quality and language fluency
  • 6
    Handwritten tests and dry run
  • 7
    Debugging and self-correction
  • 8
    Complexity analysis
  • 9
    Follow-up performance

4. What Strong Candidates Should Demonstrate

  • ✓Clarify coin supply, denomination properties, and impossible-case behavior before coding.
  • ✓Explain a naive recursive baseline and improve to bottom-up dynamic programming.
  • ✓Think aloud while implementing careful DP state transitions.
  • ✓Validate with explicit expected outputs and a top-to-bottom handwritten dry run.
  • ✓Analyze time and space complexity and handle a bounded follow-up modification.

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Core Concepts

Dynamic ProgrammingArraysComplexity Analysis

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