Python Program for k-th missing element in sorted array

Last Updated : 08 May, 2023

Given an increasing sequence a[], we need to find the K-th missing contiguous element in the increasing sequence which is not present in the sequence. If no k-th missing element is there output -1.

Examples :

Input : a[] = {2, 3, 5, 9, 10};   
        k = 1;
Output : 1
Explanation: Missing Element in the increasing 
sequence are {1,4, 6, 7, 8}. So k-th missing element
is 1

Input : a[] = {2, 3, 5, 9, 10, 11, 12};       
        k = 4;
Output : 7
Explanation: missing element in the increasing 
sequence are {1, 4, 6, 7, 8}  so k-th missing 
element is 7

Approach 1: Start iterating over the array elements, and for every element check if the next element is consecutive or not, if not, then take the difference between these two, and check if the difference is greater than or equal to given k, then calculate ans = a[i] + count, else iterate for next element.

Python3

# Function to find k-th 
# missing element
def missingK(a, k, n) :

    difference = 0
    ans = 0
    count = k
    flag = 0
    
    # iterating over the array
    for i in range (0, n-1) : 
        difference = 0
        
        # check if i-th and 
        # (i + 1)-th element 
        # are not consecutive
        if ((a[i] + 1) != a[i + 1]) :
        
            
            # save their difference
            difference += (a[i + 1] - a[i]) - 1
            
            # check for difference
            # and given k
            if (difference >= count) :
                    ans = a[i] + count
                    flag = 1
                    break
            else :
                count -= difference     
    
    # if found
    if(flag) :
        return ans
    else :
        return -1

# Driver code
# Input array
a = [1, 5, 11, 19]

# k-th missing element 
# to be found in the array
k = 11
n = len(a)

# calling function to
# find missing element
missing = missingK(a, k, n)

print(missing)

# This code is contributed by 
# Manish Shaw (manishshaw1)

Output

Time Complexity :O(n), where n is the number of elements in the array.

Space Complexity: O(1) as no extra space has been used.

Approach 2:

Apply a binary search. Since the array is sorted we can find at any given index how many numbers are missing as arr[index] - (index+1). We would leverage this knowledge and apply binary search to narrow down our hunt to find that index from which getting the missing number is easier.

Below is the implementation of the above approach:

Python3

# Python3 program for above approach

# Function to find 
# kth missing number
def missingK(arr, k):
  n = len(arr)
  l = 0
  u = n - 1
  mid = 0 
  while(l <= u):
    mid = (l + u)//2;
    numbers_less_than_mid = arr[mid] - (mid + 1);
    
    # If the total missing number 
    # count is equal to k we can iterate
    # backwards for the first missing number
    # and that will be the answer.
    if(numbers_less_than_mid == k):
      
      # To further optimize we check 
      # if the previous element's
      # missing number count is equal 
      # to k. Eg: arr = [4,5,6,7,8]
      # If you observe in the example array, 
      # the total count of missing numbers for all
      # the indices are same, and we are
      # aiming to narrow down the 
      # search window and achieve O(logn)
      # time complexity which 
      # otherwise would've been O(n).
      if(mid > 0 and (arr[mid - 1] - (mid)) == k):    
        u = mid - 1;
        continue;
      
      # Else we return arr[mid] - 1.
      return arr[mid]-1;
      
    # Here we appropriately 
    # narrow down the search window.
    if(numbers_less_than_mid < k):    
      l = mid + 1;
    elif(k < numbers_less_than_mid):
      u = mid - 1;

  # In case the upper limit is -ve 
  # it means the missing number set
  # is 1,2,..,k and hence we directly return k.
  if(u < 0):
    return k;
  
  # Else we find the residual count 
  # of numbers which we'd then add to
  # arr[u] and get the missing kth number.
  less = arr[u] - (u + 1);
  k -= less;
  
  # Return arr[u] + k
  return arr[u] + k;

# Driver Code
if __name__=='__main__':

    arr = [2,3,4,7,11];
    k = 5;
  
    # Function Call
    print("Missing kth number = "+ str(missingK(arr, k)))
    
# This code is contributed by rutvik_56.