How to get better optimizations from Cursor

1// Cursor Chat prompt (Cmd+L):
2// Write a function that finds all pairs of numbers in an
3// array that sum to a target value. Return an array of
4// [index1, index2] pairs.
5
6// Cursor's first attempt (typically O(n^2)):
7function findPairs(nums: number[], target: number): number[][] {
8  const pairs: number[][] = [];
9  for (let i = 0; i < nums.length; i++) {
10    for (let j = i + 1; j < nums.length; j++) {
11      if (nums[i] + nums[j] === target) {
12        pairs.push([i, j]);
13      }
14    }
15  }
16  return pairs;
17}

1// Follow-up prompt in the SAME chat session:
2// What is the time and space complexity of this solution?
3// Can you identify any performance bottlenecks for large
4// input arrays (100,000+ elements)?

1// Follow-up prompt:
2// Generate an optimized O(n) version using a hash map.
3// Keep the same function signature and return type.
4// Show both solutions side by side with their complexities.
5
6// Cursor generates:
7function findPairsOptimized(nums: number[], target: number): number[][] {
8  const pairs: number[][] = [];
9  const seen = new Map<number, number[]>(); // value -> indices
10  for (let i = 0; i < nums.length; i++) {
11    const complement = target - nums[i];
12    if (seen.has(complement)) {
13      for (const j of seen.get(complement)!) {
14        pairs.push([j, i]);
15      }
16    }
17    const existing = seen.get(nums[i]) || [];
18    existing.push(i);
19    seen.set(nums[i], existing);
20  }
21  return pairs;
22}
23// Time: O(n), Space: O(n)

1// Follow-up prompt:
2// The hash map version uses O(n) extra space. Can you
3// generate a version that uses O(1) extra space? It is
4// acceptable to be O(n log n) time if it saves memory.
5// Explain the tradeoff.

1// Composer prompt (Cmd+I):
2// @src/utils/arrayUtils.ts Replace the findPairs function
3// with the O(n) hash map version from our chat discussion.
4// Keep all existing exports and tests passing. Add a JSDoc
5// comment noting the O(n) time and O(n) space complexity.