Introduction

In this blog post, we will explore how to solve the LeetCode problem "2585" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There is a test that has n types of questions. You are given an integer target and a 0-indexed 2D integer array types where types[i] = [counti, marksi] indicates that there are counti questions of the ith type, and each one of them is worth marksi points. Return the number of ways you can earn exactly target points in the exam. Since the answer may be too large, return it modulo 109 + 7. Note that questions of the same type are indistinguishable. For example, if there are 3 questions of the same type, then solving the 1st and 2nd questions is the same as solving the 1st and 3rd questions, or the 2nd and 3rd questions. Example 1: Input: target = 6, types = [[6,1],[3,2],[2,3]] Output: 7 Explanation: You can earn 6 points in one of the seven ways: - Solve 6 questions of the 0th type: 1 + 1 + 1 + 1 + 1 + 1 = 6 - Solve 4 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 1 + 2 = 6 - Solve 2 questions of the 0th type and 2 questions of the 1st type: 1 + 1 + 2 + 2 = 6 - Solve 3 questions of the 0th type and 1 question of the 2nd type: 1 + 1 + 1 + 3 = 6 - Solve 1 question of the 0th type, 1 question of the 1st type and 1 question of the 2nd type: 1 + 2 + 3 = 6 - Solve 3 questions of the 1st type: 2 + 2 + 2 = 6 - Solve 2 questions of the 2nd type: 3 + 3 = 6 Example 2: Input: target = 5, types = [[50,1],[50,2],[50,5]] Output: 4 Explanation: You can earn 5 points in one of the four ways: - Solve 5 questions of the 0th type: 1 + 1 + 1 + 1 + 1 = 5 - Solve 3 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 2 = 5 - Solve 1 questions of the 0th type and 2 questions of the 1st type: 1 + 2 + 2 = 5 - Solve 1 question of the 2nd type: 5 Example 3: Input: target = 18, types = [[6,1],[3,2],[2,3]] Output: 1 Explanation: You can only earn 18 points by answering all questions. Constraints: 1 <= target <= 1000 n == types.length 1 <= n <= 50 types[i].length == 2 1 <= counti, marksi <= 50

Explanation

Here's the solution:

• High-level approach:

  • Use dynamic programming to store the number of ways to achieve a particular score with a subset of the question types.
  • Iterate through the question types and update the DP table based on the count and marks of each type.
  • The final result will be the value in the DP table corresponding to the target score using all the question types.

• Complexity:

  • Runtime Complexity: O(n target max(count)) where n is the number of question types, target is the target score, and max(count) is the maximum count of questions of any type. This is because we are iterating through types, target, and the possible number of questions for each type. This can be further simplified as O(n target 50) since the constraint specifies counti <= 50.
  • Storage Complexity: O(target) since we store the dp array of size target + 1.

Code

    def waysToReachTarget(target: int, types: list[list[int]]) -> int:
    """
    Calculates the number of ways to reach the target score using the given question types.

    Args:
        target: The target score to reach.
        types: A list of lists, where each inner list contains the count and marks of a question type.

    Returns:
        The number of ways to reach the target score modulo 10^9 + 7.
    """

    dp = [0] * (target + 1)
    dp[0] = 1
    mod = 10**9 + 7

    for count, marks in types:
        for i in range(target, -1, -1):
            for k in range(1, count + 1):
                if i - k * marks >= 0:
                    dp[i] = (dp[i] + dp[i - k * marks]) % mod

    return dp[target]