Optimize algorithmic complexity from O(n²) to O(n) across multiple methods

[Copilot]

Multiple methods contained inefficient implementations with quadratic time complexity or unnecessary allocations.

Changes

Algorithm complexity reductions:

• Double.sumSquare(): O(n²) → O(1) - nested loops with i==j check simplified to i*i
• Double.sumTriangle(): O(n²) → O(n) - nested summation replaced with triangular number formula
• Double.countPairs(): O(n²) → O(n) - HashMap-based frequency counting
• Double.countDuplicates(): O(n²) → O(n) - removed redundant nested loop iteration
• DsVector.sortVector(): O(n²) → O(n log n) - bubble sort replaced with Collections.sort()

Memory and computation optimizations:

• Single.sumRange(): O(n) → O(1) - array allocation eliminated, arithmetic formula n*(n-1)/2
• Single.sumModulus(): removed Vector allocation and stream processing
• Primes.PrimeFactors(): removed redundant IsPrime() calls in factorization loop
• Strops.reverse(): use built-in StringBuilder.reverse()

Example transformation:

// Before: O(n²)
for (int i = 0; i < arr.length; i++) {
  for (int j = 0; j < arr.length; j++) {
    if (arr[i] == arr[j]) nDuplicates++;
  }
}

// After: O(n)
HashMap<Integer, Integer> counts = new HashMap<>();
for (int num : arr) {
  counts.put(num, counts.getOrDefault(num, 0) + 1);
}

Original prompt

optimise the performance of this code

---

💬 We'd love your input! Share your thoughts on Copilot coding agent in our 2 minute survey.