You are given two sorted arrays, each of size n. Give as efficient an algorithm as possible to find the k-th smallest element in the union of the two arrays. What is the running time of your algorithm as a function of k and n?

# Program to find kth element  

# from two sorted arrays  

def kth(arr1, arr2, m, n, k):  

sorted1 = [0] * (m + n)  

i = 0

j = 0

d = 0

while (i < m and j < n):  

 if (arr1[i] < arr2[j]):  

 sorted1[d] = arr1[i]  

 i += 1

 else:  

 sorted1[d] = arr2[j]  

 j += 1

 d += 1

while (i < m):  

 sorted1[d] = arr1[i]  

 d += 1

 i += 1

while (j < n):  

 sorted1[d] = arr2[j]  

 d += 1

 j += 1

return sorted1[k - 1]  

# driver code  

arr1 = [2, 3, 6, 7, 9]  

arr2 = [1, 4, 8, 10]  

k = 5;  

print(kth(arr1, arr2, 5, 4, k))  

The running time will be  O(n)  and O(log k)

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