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.
Try to answer the query of asking GCD of a subarray in <code>O(1)</code> using sparse tables and preprocessing.
For every index <code>L</code>, let’s find the subarray starting at the index <code>L</code> and maximizing gcd-sum.
Use the fact that if <code>L</code> is fixed, then by adding one more element to the end of a subarray, two things can happen: the gcd remains the same as the last gcd or becomes at least half of the last one.
Now we can use binary search to find the last index <code>R</code> such that gcd of the elements of <code>nums[L..R]</code> would be equal to <code>nums[L]</code>.
Now add <code>nums[R + 1]</code> to the current subarray and continue the process to find the last index that has the same gcd as the current gcd of elements.
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
Prefix sums allow constant-time calculation of any subarray sum. When evaluating multiple subarrays that share gcd states, prefix sums help compute the sum component of the score quickly without recomputing totals repeatedly.
Yes, variations of this problem appear in advanced coding interviews at top tech companies. These problems test knowledge of number theory concepts like gcd, along with optimization techniques for handling subarrays efficiently.
A dynamic list or map storing pairs of gcd values and their corresponding start positions works well. This structure allows you to merge states when the gcd becomes the same and efficiently maintain candidate subarrays.
The optimal approach tracks the gcd values of subarrays ending at each index and compresses them into distinct states. Using prefix sums allows quick computation of subarray sums while evaluating candidates. This avoids checking every subarray explicitly and keeps the complexity near O(n log V).