Problem1 added

[megharaykar]

No description provided.

[super30admin]

The Coin Change (Problem1.py)

Your solutions show a good progression from recursive to optimized DP. Here are some points for improvement:

1. Solution 1 (Recursive):

   • Instead of using a class variable self.minimum, consider returning the value from the recursive function. This makes the code more modular and easier to understand.
   • The recursive solution might be correct for small inputs, but it is inefficient. You can add memoization to avoid repeated calculations. However, for the coin change problem, the recursive approach with memoization might still be inefficient compared to iterative DP.
   • Note: The problem constraints (amount up to 10^4) make the recursive approach infeasible.

2. Solution 2 (2D DP):

   • Instead of using 99999, use float('inf') or a constant value like MAX = 10**5 to represent infinity. This is more robust and clear.
   • The initialization of the first row is correct, but you can also set dp[0][0] = 0 and then for j>=1, set to infinity. Your code sets the first row for j>=1 to 99999, which is correct.

3. Solution 3 (1D DP):

   • You can optimize the inner loop by starting j from coins[i-1] to avoid the condition check. For example:
     for i in range(m):
     for j in range(coins[i], amount+1):
     dp[j] = min(dp[j], 1 + dp[j - coins[i]])
   • This avoids the unnecessary condition and makes the code slightly faster and cleaner.

4. General:

   • Always consider edge cases: amount=0 should return 0. Your DP solutions handle this correctly because dp[0] is initialized to 0.
   • In Solution 3, the line dp[j] = dp[j] when j < coins[i-1] is redundant and can be skipped.

Overall, your DP solutions are excellent and meet the requirements. The recursive solution needs improvement, but since you have provided optimal solutions, it's acceptable.

VERDICT: PASS

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House Robber

Your solutions for the Coin Change problem are well thought out, showing a progression from a recursive exhaustive approach to optimized dynamic programming solutions. However, you have submitted this code for the House Robber problem, which is entirely different. This indicates a possible misunderstanding of the task or a mix-up in files.

For the House Robber problem, you need to design a solution that maximizes the amount robbed without robbing adjacent houses. The recursive approach for House Robber would involve considering two cases at each house: rob it and skip the next, or skip it and move to the next. This is similar to the recursive structure you used in Coin Change, but with different parameters.

Here are steps to correct this:

1. Understand the problem: House Robber requires you to choose a subset of non-adjacent houses to maximize the sum.
2. Implement a recursive solution: Similar to your Coin Change Solution 1, but for House Robber, you would have:
   • Base case: If index is beyond the array, return 0.
   • Recursive cases:
     case0 = rob from next house (skip current)
     case1 = rob current + rob from house after next
   • Return max(case0, case1)
3. Optimize with memoization or DP: Since the recursive solution is exponential, you can use DP to store results for subproblems.

Your Coin Change solutions demonstrate good understanding of DP, so you can apply similar optimization to House Robber. For example, you can use a 1D DP array where dp[i] represents the maximum amount that can robbed from houses i to the end.

VERDICT: NEEDS_IMPROVEMENT