Completed Problem1

Problem1.java

@@ -1 +1,37 @@
+//Missing Number in Sorted Array of Natural Numbers
+// Solved it by binary search. intuition is that in an array of numbers starting from 1, the value at each index should be index + 1. If a number is missing, then this will become false. We find the mid and check if
+// arr[mid] - 1 == mid. if it is false we move to the left half else the right half. 
+//Time complexity is O(log n) and space complexity is O(1).
+public class Problem1 {
+    static int missingNumber(int arr[]) {
+        // code here
+        int n = arr.length;
+
+        if (arr[0] != 1) {
+            return 1;
+        }
+
+        if (arr[n - 1] != (n + 1)) {
+            return n + 1;
+        }
+
+        int low = 0;
+        int high = n -1;
+
+        while (low <= high) {
+            int mid = low + (high - low)/2;
+            if (arr[mid] - 1 != mid) {
+                high = mid  - 1;
+            } else {
+                low = mid + 1;
+            }
+        }
+
+        return arr[low] - 1;
+    }
 
+    public static void main(String[] args) {
+        int[] arr = {1, 2, 3, 4, 6, 7, 8};
+        System.out.println(missingNumber(arr));
+    }
+}