LeetCode 879: Profitable Schemes Solution

Master LeetCode problem 879 (Profitable Schemes), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

879. Profitable Schemes

Hard

Array Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We can create a 3D DP array dp[i][j][k] where i represents the number of crimes considered, j represents the total profit obtained so far, and k represents the total number of members used so far. We iterate through each crime one by one and update the DP array accordingly. The final answer will be the sum of all the DP values where the profit is at least minProfit and the total number of members used is at most n.

Algorithm:

Initialize a 3D DP array dp where dp[i][j][k] represents the number of schemes that can be chosen with i crimes considered, j total profit obtained, and k total number of members used.
Initialize dp[0][0][0] = 1, as there is 1 way to make a profit of 0 with 0 members and 0 crimes.
Iterate through each crime:
- For each crime, update the DP array based on the current crime's profit and group size.
Calculate the final result by summing up all the DP values where profit is at least minProfit and the total number of members used is at most n.
Return the final result modulo 10^9 + 7.

Time Complexity:

The time complexity of this solution is O(n * minProfit * group.length) where n is the total number of members, minProfit is the minimum profit required, and group.length is the number of crimes.

Space Complexity:

The space complexity of this solution is O(n * minProfit * group.length) for the DP array.

Solution Code

class Solution {
    public int profitableSchemes(int n, int minProfit, int[] group, int[] profit) {
        int MOD = 1000000007;
        int[][][] dp = new int[group.length + 1][n + 1][minProfit + 1];
        dp[0][0][0] = 1;

        for (int i = 1; i <= group.length; i++) {
            int g = group[i - 1];
            int p = profit[i - 1];

            for (int j = 0; j <= n; j++) {
                for (int k = 0; k <= minProfit; k++) {
                    dp[i][j][k] = dp[i - 1][j][k];
                    if (j >= g) {
                        dp[i][j][k] += dp[i - 1][j - g][Math.max(0, k - p)];
                    }
                    dp[i][j][k] %= MOD;
                }
            }
        }

        int total = 0;
        for (int j = 0; j <= n; j++) {
            total = (total + dp[group.length][j][minProfit]) % MOD;
        }

        return total;
    }
}

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