This is a premium problem. We're working on making it available for free soon.
Explore Free ProblemsUse these hints if you're stuck. Try solving on your own first.
Use dynamic programming.
Store whether the last element was even or odd.
Solutions for this premium problem will be available for free soon.
Browse Free ProblemsWatch expert explanations and walkthroughs
Jot down your thoughts, approach, and key learnings
Problems involving counting arrays with constraints and dynamic programming transitions are common in FAANG-style interviews. Variations that combine combinatorics and DP are frequently used to test problem decomposition and state design skills.
The optimal approach uses dynamic programming to track how many ways an array can be formed while maintaining a specific count of even numbers. By defining states based on array length and the number of evens used so far, transitions can efficiently compute the total valid arrays.
A 2D dynamic programming table or a rolling 1D DP array is typically used. These structures help store intermediate counts for different lengths and even-number counts, enabling efficient state transitions.
Yes. Instead of storing the entire DP table, you can keep only the previous state and update a rolling array. This reduces the space complexity from O(n × k) to O(k) while preserving the same time complexity.