Find missing elements of a range

1.7

Given an array arr[0..n-1] of distinct elements and a range [low, high], find all numbers that are in range, but not in array. The missing elements should be printed in sorted order.

Examples:

Input: arr[] = {10, 12, 11, 15}, 
       low = 10, hight = 15
Output: 13, 14

Input: arr[] = {1, 14, 11, 51, 15}, 
       low = 50, hight = 55
Output: 50, 52, 53, 54

There can be following two approaches to solve the problem.

  1. Use Sorting : Sort the array, then do binary search for ‘low’. Once location of low is find, start traversing array from that location and keep printing all missing numbers.

    C++

    // A sorting based C++ program to find missing
    // elements from an array
    #include<bits/stdc++.h>
    using namespace std;
    
    // Print all elements of range [low, high] that
    // are not present in arr[0..n-1]
    void printMissing(int arr[], int n, int low,
                                       int high)
    {
       // Sort the array
       sort(arr, arr+n);
    
       // Do binary search for 'low' in sorted
       // array and find index of first element
       // which either equal to or greater than
       // low.
       int *ptr = lower_bound(arr, arr+n, low);
       int index = ptr - arr;
    
       // Start from the found index and linearly
       // search every range element x after this
       // index in arr[]
       int i = index, x = low;
       while (i < n && x<=high)
       {
           // If x doesn't math with current element
           // print it
           if (arr[i] != x)
              cout << x << " ";
    
           // If x matches, move to next element in arr[]
           else
              i++;
    
           // Move to next element in range [low, high]
           x++;
       }
    
       // Print range elements thar are greater than the
       // last element of sorted array.
       while (x <= high)
         cout << x++ << " ";
    }
    
    // Driver program
    int main()
    {
       int arr[] = {1, 3, 5, 4};
       int n = sizeof(arr)/sizeof(arr[0]);
       int low = 1, high = 10;
       printMissing(arr, n, low, high);
       return 0;
    }
    

    Java

    // A sorting based Java program to find missing
    // elements from an array
    
    import java.util.Arrays;
    
    public class PrintMissing 
    {
        // Print all elements of range [low, high] that
        // are not present in arr[0..n-1]
        static void printMissing(int ar[], int low, int high) 
        {
            Arrays.sort(ar);
            // Do binary search for 'low' in sorted
            // array and find index of first element
            // which either equal to or greater than
            // low.
            int index = ceilindex(ar, low, 0, ar.length - 1);
            int x = low;
    
            // Start from the found index and linearly
            // search every range element x after this
            // index in arr[]
            while (index < ar.length && x <= high) 
            {
                // If x doesn't math with current element
                // print it
                if (ar[index] != x) 
                {
                    System.out.print(x + " ");
                }
                
                // If x matches, move to next element in arr[]
                else
                    index++;
                // Move to next element in range [low, high]
                x++;
            }
            
            // Print range elements thar are greater than the
            // last element of sorted array.
            while (x <= high) 
            {
                System.out.print(x + " ");
                x++;
            }
    
        }
        
        // Utility function to find ceil index of given element
        static int ceilindex(int ar[], int val, int low, int high) 
        {
    
            if (val < ar[0])
                return 0;
            if (val > ar[ar.length - 1])
                return ar.length;
    
            int mid = (low + high) / 2;
            if (ar[mid] == val)
                return mid;
            if (ar[mid] < val) 
            {
                if (mid + 1 < high && ar[mid + 1] >= val)
                    return mid + 1;
                return ceilindex(ar, val, mid + 1, high);
            } 
            else 
            {
                if (mid - 1 >= low && ar[mid - 1] < val)
                    return mid;
                return ceilindex(ar, val, low, mid - 1);
            }
    
        }
    
        // Driver program to test above function
        public static void main(String[] args) 
        {
            int arr[] = { 1, 3, 5, 4 };
            int low = 1, high = 10;
            printMissing(arr, low, high);
        }
    }
    
    // This code is contributed by Rishabh Mahrsee
    


    Output:
    2 6 7 8 9 10 
  2. Use Hashing : Create a hash table and insert all array items into the hash table. Once all items are in hash table, traverse through the range and print all missing elements.

    C++

    // A hashing based C++ program to find missing
    // elements from an array
    #include<bits/stdc++.h>
    using namespace std;
    
    // Print all elements of range [low, high] that
    // are not present in arr[0..n-1]
    void printMissing(int arr[], int n, int low,
                                       int high)
    {
       // Insert all elements of arr[] in set
       unordered_set<int> s;
       for (int i=0; i<n; i++)
          s.insert(arr[i]);
    
       // Traverse throught the range an print all
       // missing elements
       for (int x=low; x<=high; x++)
          if (s.find(x) == s.end())
             cout << x << " ";
    }
    
    // Driver program
    int main()
    {
       int arr[] = {1, 3, 5, 4};
       int n = sizeof(arr)/sizeof(arr[0]);
       int low = 1, high = 10;
       printMissing(arr, n, low, high);
       return 0;
    }
    

    Java

    // A hashing based Java program to find missing
    // elements from an array
    
    import java.util.Arrays;
    import java.util.HashSet;
    
    public class Print 
    {
        // Print all elements of range [low, high] that
        // are not present in arr[0..n-1]
        static void printMissing(int ar[], int low, int high) 
        {
            HashSet<Integer> hs = new HashSet<>();
            
            // Insert all elements of arr[] in set
            for (int i = 0; i < ar.length; i++)
                hs.add(ar[i]);
            
            // Traverse throught the range an print all
            // missing elements
            for (int i = low; i <= high; i++) 
            {
                if (!hs.contains(i)) 
                {
                    System.out.print(i + " ");
                }
            }
        }
    
        // Driver program to test above function
        public static void main(String[] args) 
        {
            int arr[] = { 1, 3, 5, 4 };
            int low = 1, high = 10;
            printMissing(arr, low, high);
        }
    }
    
    // This code is contributed by Rishabh Mahrsee
    


    Output:
    2 6 7 8 9 10 

Which approach is better?
Time complexity of first approach is O(nLogn + k) where k is number of missing elements (Note that k may be more than nLogn if array is small and range is big)

Time complexity of second solution is O(n + (high-low+1)).

If the given array has almost elements of range i.e., n is close to value of (high-low+1), then second approach is definitely better as there is no Log n factor. But if n is much smaller than range, then first approach is better as it doesn’t require extra space for hashing. We can also modify first approach to print adjacent missing elements as range to save time. For example if 50, 51, 52, 53, 54, 59 are missing, we can print them as 50-54, 59 in first method. And if printing this way is allowed, the first approach takes only O(n Log n) time.

This article is contributed by Piyush Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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