Leetcode Problem 879. Profitable Schemes

879. Profitable Schemes

Leetcode Solutions

Bottom-Up Dynamic Programming Approach

  1. Initialize a DP table dp with dimensions [M+1][N+1][minProfit+1] to 0.
  2. Set dp[M][j][0] to 1 for all j from 0 to N, as there is always 1 way to achieve 0 profit regardless of the number of members.
  3. Loop over each crime in reverse (from M-1 to 0), each member count (from 0 to N), and each profit level (from 0 to minProfit).
  4. For each state (i, j, k), update dp[i][j][k] by adding the number of ways to achieve k profit without the current crime (dp[i+1][j][k]) and, if possible, the number of ways to achieve k-profit[i] profit with the current crime (dp[i+1][j-group[i]][max(0, k-profit[i])]).
  5. Ensure that the member count does not exceed N when adding the current crime.
  6. Return dp[0][0][minProfit] as the final answer.
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Top-Down Dynamic Programming Approach

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