Solving Questions With Brainpower

Solving Questions With Brainpower

What is this problem about?

"Solving Questions With Brainpower" is a dynamic programming problem that simulates a test-taking scenario with a twist. You are presented with a series of questions, each having a specific point value and a "brainpower" cost. If you choose to solve a question, you gain its points, but you must skip the next several questions based on its brainpower cost. Alternatively, you can choose to skip the current question and move to the next one without any penalty.

The goal is to determine the maximum number of points you can accumulate by strategically choosing which questions to solve and which to skip. It’s a classic optimization problem where a decision made at the current step affects the options available in future steps.

Why is this asked in interviews?

This interview question is a favorite at companies like Microsoft, Meta, and Google because it tests a candidate's ability to model dependencies in a sequence. It’s a perfect introduction to 1D Dynamic Programming. Unlike simpler problems, this one requires you to think about how a choice "jumps" you forward in the array. It evaluates your skill in defining state transitions and your ability to choose between a top-down (memoization) or bottom-up (tabulation) approach.

Algorithmic pattern used

The primary algorithmic pattern is Dynamic Programming (DP). Since the decision to solve a question at index $i$ depends on the maximum points we can get starting from index $i + \text{brainpower} + 1$, we can build the solution from the end of the array to the beginning (bottom-up).

• Let dp[i] be the maximum points we can get from questions $i$ to $n-1$.
• dp[i] = max(solve_current, skip_current)
• solve_current = points[i] + dp[i + brainpower[i] + 1] (if the jump is within bounds)
• skip_current = dp[i + 1]

Example explanation

Suppose we have three questions:

1. Points: 3, Brainpower: 2
2. Points: 4, Brainpower: 3
3. Points: 4, Brainpower: 4

• If we solve Q1, we get 3 points but must skip Q2 and Q3. Total = 3.
• If we skip Q1 and solve Q2, we get 4 points but must skip Q3. Total = 4.
• If we skip Q1 and Q2 and solve Q3, we get 4 points. Total = 4. The maximum points for this solving questions with brainpower coding problem would be 4.

Common mistakes candidates make

One common mistake is trying to use a greedy approach (always picking the question with the most points or the least brainpower). Greedy fails because a high-point question might force you to skip even higher-point questions later. Another mistake is incorrect indexing during the "jump"—forgetting that if you are at index $i$ and have brainpower $k$, the next available question is at index $i + k + 1$. Finally, failing to handle the base cases (the end of the array) can lead to out-of-bounds errors.

Interview preparation tip

To master this Solving Questions With Brainpower interview question, practice other "house robber" style DP problems. The key is to recognize the "Include/Exclude" pattern. When you decide to include an element, calculate how it restricts your future choices. Drawing a recursion tree for a small example can help you visualize the overlapping subproblems, which is the hallmark of a DP-solvable challenge.