Solved DP-1

[pratikb0501]

No description provided.

[super30admin]

The Coin Change (Problem_1.py)

Your solution is comprehensive, showing progression from brute-force to memoization to tabulation. The tabulation solution is correct and efficient. Here are some points for improvement:

• Space Optimization: You can reduce the space complexity from O(n * amount) to O(amount) by using a 1D DP array. Since the recurrence for index i only depends on the next coin index (for not_choose) and the same index for smaller amounts (for choose), you can use a single array dp[target] of size amount+1. Initialize dp with INF for all targets except dp[0]=0. Then for each coin, update the dp array for targets from the coin value to amount. This would be more efficient in space.

• Initialization: In your tabulation code, you initialize memo[n][target] = INF for target>=1. But note that memo[n][0] should be 0, which is already handled by your initialization (since you set all to 0 initially). However, when you create the 2D array with [[0] * (amount+1)], it sets all values to 0. So for index=n, you then set for target from 1 to amount to INF. This is correct.

• Edge Case Handling: Your solution handles amount=0 correctly by returning 0. Also, if no combination is found, it returns -1. This is good.

• Code Clarity: The code is clear and well-commented. However, you might consider adding a brief explanation of the tabulation approach for better understanding.

Overall, your solution is correct and efficient. The space optimization is a minor improvement that can be made.

VERDICT: PASS

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House Robber (Problem_2.py)

Your solution demonstrates a strong understanding of dynamic programming and its optimizations. You have correctly implemented the brute force, memoization, tabulation, and space-optimized versions. The final solution is optimal in both time and space.

Strengths:

• You have considered multiple approaches and provided implementations for each, showing a deep understanding of the problem.
• The code is clean, well-commented, and easy to follow.
• You have achieved the optimal time and space complexity with the final solution.

Areas for Improvement:

• While it's great to show multiple approaches, in a production or interview setting, you might want to present only the most efficient solution. The commented code could be removed to keep the submission concise.
• Ensure that the solution is self-contained and does not include test code at the bottom if it's meant to be submitted to an online judge. For example, the lines nums = [2,7,9,3,1], sl = Solution(), and print(sl.rob(nums)) should not be included in the submitted code.
• Consider adding more comments to explain the space-optimized approach for clarity, especially for readers who might not be familiar with the technique.

Overall, excellent work!

VERDICT: PASS