Done Competitive-Coding-1

find_missing_number.py

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+#-------------Solution 1-------------
+def find_missing_number_formula(arr, n):
+    """
+    arr: sorted list of n-1 integers from 1 to n
+    n: the upper bound of the range
+    Return the missing integer
+
+    Approach : Taking the difference of Sum of Total array, and Sum of given array.
+    Time Complexity : O(n) 
+    Space Complexity : O(1)
+
+    """
+    # Formula to get the sum of all integers from 1 to n
+    total_sum = n * (n + 1) // 2 
+    arr_sum = sum (arr)
+    missing_no = total_sum - arr_sum
+    return missing_no
+
+#-------------Solution 2-------------
+def find_missing_number_binary(arr, n):
+    """
+    arr: sorted list of n-1 integers from 1 to n
+    n: the upper bound of the range
+    Return the missing integer
+
+    Approach : In sorted array, the difference of index and the element would be exactly 1,
+              If any no is missing the diff of next element would be 2.
+
+    TIme Complexity : O(log n)
+    Space Complexity : O(1)
+    """
+    l , r = 0 , n-2
+    while l <= r:
+        mid = (l + r) // 2
+        print(l, r, mid)
+        diff = arr[mid] - mid
+        if diff == 1:
+            l = mid + 1
+        else:
+            r = mid - 1
+    print("mid:",mid)
+    return arr[r] + 1
+
+
+def main():
+    # Read input
+    # Example input:
+    # 1 2 3 4 6 7 8
+    arr = list(map(int, input("Enter the array elements separated by space: ").split()))
+    # Since one number is missing, n = len(arr) + 1
+    n = len(arr) + 1
+    # Call the function
+    missing = find_missing_number_binary(arr, n)
+    # Print result
+    print("Missing number:", missing)
+if __name__ == "__main__":
+    main()