Smallest missing number

Author: mandliya

README.md

@@ -6,8 +6,8 @@
 
 | Current Status|     Stats     |
 | :------------: | :----------: |
-| Total Problems | 146 |
-| Current Streak | 10 days |
+| Total Problems | 147 |
+| Current Streak | 11 days |
 | Longest Streak | 91 ( August 17, 2015 - November 15, 2015 ) |
 
 </center>
@@ -180,6 +180,7 @@ Include contains single header implementation of data structures and some algori
 | Find the common elements in 3 sorted vectors | [commonIn3Arrays.cpp](sort_search_problems/commonIn3Arrays.cpp) |
 | Find all the pairs with a given sum in an unsorted array/vector | [find_pairs_with_sum.cpp](sort_search_problems/find_pairs_with_sum.cpp) |
 | Given an array, find peak element in it. A peak element is an element that is greater than its neighbors.| [peak_element.cpp](sort_search_problems/peak_element.cpp) |
+| Given a sorted array of distinct non-negative integers, find smallest missing element in it.| [smallest_missing.cpp](sort_search_problems/smallest_missing.cpp)|
 
 ### Graph Problems
 | Problem | Solution |

sort_search_problems/smallest_missing.cpp

@@ -0,0 +1,59 @@
+/*
+ * Given a sorted array of distinct non-negative integers, find smallest missing element in it.
+ * For example,
+
+ * Input: A[] = [0, 1, 2, 6, 9, 11, 15]
+ * Output: The smallest missing element is 3
+ 
+ * Input: A[] = [1, 2, 3, 4, 6, 9, 11, 15]
+ * Output: The smallest missing element is 0
+ 
+ * Input: A[] = [0, 1, 2, 3, 4, 5, 6]
+ * Output: The smallest missing element is 7
+ */
+
+#include <iostream>
+#include <vector>
+
+int missingElement(const std::vector<int>& arr, int low, int high)
+{
+    if (low > high)
+    {
+        return low;
+    }
+
+    int mid = low + (high - low)/2;
+
+    // if mid index matches the with the mid element, then smallest
+    // missing element lies on the right of the mid.
+    if (arr[mid] == mid)
+    {
+        return missingElement(arr, mid + 1, high);
+    }
+    else
+    {
+        return missingElement(arr, low, mid - 1);
+    }
+}
+
+
+void print(const std::vector<int>& arr)
+{
+    std::cout << "Contents of array:" << std::endl;
+    for (auto i : arr)
+    {
+        std::cout << i << " ";
+    }
+    std::cout << std::endl;
+}
+
+int main()
+{
+    std::vector<int> arr{0, 1, 2, 3, 4, 6, 7};
+    print(arr);
+    int low = 0;
+    int high = arr.size() -1;
+    std::cout << "Smallest missing element in array is :" << missingElement(arr, low, high)
+        << std::endl;
+    return 0;
+}