LeetCode 2585: Number of Ways to Earn Points Solution

Master LeetCode problem 2585 (Number of Ways to Earn Points), 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.

2585. Number of Ways to Earn Points

Hard

Array Dynamic Programming

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming. We will create a 2D array dp where dp[i][j] represents the number of ways to earn exactly j points using the first i types of questions. We initialize dp[0][0] to 1 as there is one way to earn 0 points with 0 types of questions.

For each type of question, we iterate over the possible number of questions of that type that can be used to earn points. We update the dp array accordingly for each type and cumulative points.

Finally, the answer will be stored in dp[n][target] where n is the total number of types of questions.

Time Complexity: The time complexity of this approach is O(n * target) where n is the number of types of questions and target is the target number of points.

Space Complexity: The space complexity is O(n * target) for the dp array.

Solution Code

class Solution {
    public int numWays(int target, int[][] types) {
        int mod = 1000000007;
        int n = types.length;
        int[][] dp = new int[n + 1][target + 1];
        dp[0][0] = 1;
        
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j <= target; j++) {
                for (int k = 0; k <= types[i - 1][0]; k++) {
                    if (j - k * types[i - 1][1] >= 0) {
                        dp[i][j] = (dp[i][j] + dp[i - 1][j - k * types[i - 1][1]]) % mod;
                    }
                }
            }
        }
        
        return dp[n][target];
    }
}

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