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Problem solution · Java

Maximum GCD-Sum of a Subarray

Maximum GCD-Sum of a Subarray: a Java solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Direct simulation
Source
walkccc LeetCode Solutions
Length
40 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Maximum GCD-Sum of a Subarray, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 40 lines of Java from the credited upstream file 2941.java.
  • The implementation visibly relies on sequence storage.
  • 4 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMaximum GCD-Sum of a Subarray · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public long maxGcdSum(int[] nums, int k) {    long ans = 0;    // [(startIndex, gcd of subarray starting at startIndex)]    List<Pair<Integer, Integer>> startIndexAndGcds = new ArrayList<>();    long[] prefix = new long[nums.length + 1];     for (int i = 0; i < nums.length; ++i)      prefix[i + 1] = (long) nums[i] + prefix[i];     for (int i = 0; i < nums.length; ++i) {      List<Pair<Integer, Integer>> nextStartIndexAndGcds = new ArrayList<>();      for (Pair<Integer, Integer> pair : startIndexAndGcds) {        final int startIndex = pair.getKey();        final int gcd = pair.getValue();        final int nextGcd = gcd(gcd, nums[i]);        if (nextStartIndexAndGcds.isEmpty() ||            !nextStartIndexAndGcds.get(nextStartIndexAndGcds.size() - 1)                 .getValue()                 .equals(nextGcd)) // Skip duplicates.          nextStartIndexAndGcds.add(new Pair<>(startIndex, nextGcd));      }      startIndexAndGcds = new ArrayList<>(nextStartIndexAndGcds);      startIndexAndGcds.add(new Pair<>(i, nums[i]));      for (Pair<Integer, Integer> pair : startIndexAndGcds) {        final int startIndex = pair.getKey();        final int gcd = pair.getValue();        if (i - startIndex + 1 >= k)          ans = Math.max(ans, (prefix[i + 1] - prefix[startIndex]) * gcd);      }    }     return ans;  }   private int gcd(int a, int b) {    return b == 0 ? a : gcd(b, a % b);  }}

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