@@ -1,20 +1,22 @@
 /**
  * Find if there is a pair of numbers that sum to a given target value.
  *
- * Time Complexity:
- * Space Complexity:
- * Optimal Time Complexity:
+ * Time Complexity:To using nested loop for compare elements time complexity will be ---> O(n*n)
+ * Space Complexity:We only use few variables -->O(1)
+ * Optimal Time Complexity:Iterate array only once and use a Set for O(1) lookups / total----->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 seen = 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;
-      }
+    const neededNumber = target - numbers[i];
+    if (seen.has(neededNumber)) {
+      return true;
+    } else {
+      seen.add(numbers[i]);
     }
   }
   return false;