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Problem solution · Java

Find the Maximum Factor Score of Array

Find the Maximum Factor Score of Array: 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
66 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 Find the Maximum Factor Score of Array, 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

  • 66 lines of Java from the credited upstream file 3334.java.
  • The implementation visibly relies on sequence storage.
  • 3 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 codeFind the Maximum Factor Score of Array · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public long maxScore(int[] nums) {    final int n = nums.length;    // prefixGcd[i] := GCD of nums[0..i]    // prefixLcm[i] := LCM of nums[0..i]    long[][] prefix = getPrefix(nums);    long[] prefixGcd = prefix[0];    long[] prefixLcm = prefix[1];    // suffixGcd[i] := GCD of nums[i..n - 1]    // suffixLcm[i] := LCM of nums[i..n - 1]    long[][] suffix = getSuffix(nums);    long[] suffixGcd = suffix[0];    long[] suffixLcm = suffix[1];    long ans = suffixGcd[0] * suffixLcm[0];     for (int i = 0; i < n; ++i) {      final long gcd1 = i > 0 ? prefixGcd[i - 1] : 0;      final long gcd2 = i + 1 < n ? suffixGcd[i + 1] : 0;      final long lcm1 = i > 0 ? prefixLcm[i - 1] : 1;      final long lcm2 = i + 1 < n ? suffixLcm[i + 1] : 1;      final long score = gcd(gcd1, gcd2) * lcm(lcm1, lcm2);      ans = Math.max(ans, score);    }     return ans;  }   // Returns the prefix GCD and LCM arrays.  private long[][] getPrefix(int[] nums) {    long[] prefixGcd = new long[nums.length];    long[] prefixLcm = new long[nums.length];    long currGcd = 0;    long currLcm = 1;    for (int i = 0; i < nums.length; ++i) {      currGcd = gcd(currGcd, nums[i]);      currLcm = lcm(currLcm, nums[i]);      prefixGcd[i] = currGcd;      prefixLcm[i] = currLcm;    }    return new long[][] {prefixGcd, prefixLcm};  }   // Returns the suffix GCD and LCM arrays.  private long[][] getSuffix(int[] nums) {    long[] suffixGcd = new long[nums.length];    long[] suffixLcm = new long[nums.length];    long currGcd = 0;    long currLcm = 1;    for (int i = nums.length - 1; i >= 0; --i) {      currGcd = gcd(currGcd, nums[i]);      currLcm = lcm(currLcm, nums[i]);      suffixGcd[i] = currGcd;      suffixLcm[i] = currLcm;    }    return new long[][] {suffixGcd, suffixLcm};  }   private long gcd(long a, long b) {    return b == 0 ? a : gcd(b, a % b);  }   private long lcm(long a, long b) {    return a * (b / gcd(a, b));  }}

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