The Coin Change (coin_change.java)

Your solution is excellent! You have successfully implemented the optimized dynamic programming approach for the coin change problem. Here are some strengths and areas for improvement:

Strengths:

• You used a 1D DP array which is space-efficient.
• The code is clean, well-commented, and easy to understand.
• You correctly handled the base case and the recurrence relation.
• You provided time and space complexity analysis, which is good practice.

Areas for Improvement:

• While using Integer.MAX_VALUE - 10 is safe in this context (because the maximum amount is 10^4, so the maximum coins needed is 10^4, which is less than 2^15), it's generally better to use Integer.MAX_VALUE and then check for Integer.MAX_VALUE in the result. Alternatively, you can set the initial value to amount + 1 (which is an upper bound for the number of coins needed) to avoid potential issues with integer overflow. For example, you could initialize dp[i] = amount + 1 for all i > 0, since it's impossible to use more than amount coins (if all coins are at least 1).
• You might want to consider adding a check for amount == 0 at the beginning to return 0 immediately, but it's not necessary because your dp[0] is already set to 0.

Minor Note:

• In the inner loop, you start from j = coins[i-1] which is efficient. However, you could also iterate from j = 0 to n and add a condition to skip if j < coins[i-1], but your way is better.

Overall, great job! Your solution is optimal and correct.

VERDICT: PASS

House Robber (house_robber.java)

Now, evaluate the student's solution.

VERDICT: NEEDS_IMPROVEMENT