How do you solve Number of Ways to Earn Points on LeetCode?

Number of Ways to Earn Points (LeetCode #2585) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * target) time complexity and O(n) space complexity. Key insight: Dynamic programming effectively reduces redundant calculations by storing intermediate results.

What is the time complexity of Number of Ways to Earn Points?

The optimal solution for Number of Ways to Earn Points runs in O(n * target) time and uses O(n) space. The time complexity is O(n * target) because we iterate through each type and update the DP array for each possible score up to the target.

What is the brute force solution for Number of Ways to Earn Points?

The brute force approach for Number of Ways to Earn Points is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible combinations of questions from each type and checking if their total points equal the target. This method is straightforward but inefficient as it explores all possibilities. The optimal Optimal Solution approach improves this to O(n * target).

What algorithm or data structure is used to solve Number of Ways to Earn Points?

Number of Ways to Earn Points uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Combinatorial Counting.

What are the interview tips for Number of Ways to Earn Points?

Always explain your thought process clearly; it shows understanding. Consider edge cases, such as when the target is 0 or when types are empty. Practice explaining your code as you write it; this helps solidify your understanding.

What are common mistakes when solving Number of Ways to Earn Points?

Failing to consider the modulo operation when counting combinations, leading to overflow. Not properly initializing the DP array or misunderstanding its indexing.

#2585

Number of Ways to Earn Points

Hard

ArrayDynamic ProgrammingDynamic ProgrammingCombinatorial Counting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * target)
Space	O(1)	O(n)

💡

Intuition

Time O(n * target)Space O(n)

The optimal approach uses dynamic programming to build up the number of ways to achieve each possible score up to the target. This is more efficient as it avoids redundant calculations by storing previously computed results.

⚙️

Algorithm

3 steps

1Step 1: Initialize a DP array where dp[i] represents the number of ways to score exactly i points.
2Step 2: For each type of question, update the DP array based on the number of questions and their marks.
3Step 3: Return dp[target] as the result.

solution.py10 lines

1def countWays(target, types):
2    MOD = 10**9 + 7
3    dp = [0] * (target + 1)
4    dp[0] = 1
5    for count, marks in types:
6        for j in range(target, -1, -1):
7            for k in range(1, count + 1):
8                if j >= k * marks:
9                    dp[j] = (dp[j] + dp[j - k * marks]) % MOD
10    return dp[target]

ℹ

Complexity note: The time complexity is O(n * target) because we iterate through each type and update the DP array for each possible score up to the target.

1Dynamic programming effectively reduces redundant calculations by storing intermediate results.
2Understanding how to represent the problem in terms of states (like dp arrays) is crucial for optimization.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.