feat: Optimise hasPairWithSum function

Author: JanefrancessC

Sprint-1/JavaScript/hasPairWithSum/hasPairWithSum.js

@@ -1,21 +1,24 @@
 /**
  * Find if there is a pair of numbers that sum to a given target value.
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Time Complexity: O(n^2)
+ * Space Complexity:O(1)
+ * Optimal Time Complexity: O(n)
  *
  * @param {Array<number>} numbers - Array of numbers to search through
  * @param {number} target - Target sum to find
  * @returns {boolean} True if pair exists, false otherwise
  */
 export function hasPairWithSum(numbers, target) {
+  const seenNumbers = new Set();
   for (let i = 0; i < numbers.length; i++) {
-    for (let j = i + 1; j < numbers.length; j++) {
-      if (numbers[i] + numbers[j] === target) {
-        return true;
-      }
+    // initial solution iterates twice, having outer and inner loop which gives us a time complexity of O(n**2). To optimise this, using a set to store seen numbers, then check whether the complement(target - number) for each num in the array has been seen and in the set. This gives a complexity of O(n)
+    let complement = target - numbers[i];
+
+    if (seenNumbers.has(complement)) {
+      return true;
     }
+    seenNumbers.add(numbers[i]);
   }
   return false;
 }