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Kth smallest element in an array that contains A[i] exactly B[i] times
• Difficulty Level : Basic
• Last Updated : 18 Jun, 2021

Given two arrays A[] and B[] consisting of N positive integers and an integer K, the task is to find the Kth smallest element in the array formed by taking the ith element from the array A[] exactly B[i] times. If there exists no such element, then print -1.

Examples:

Input: K = 4, A[] = {1, 2, 3}, B[] = {1, 2, 3}
Output: 3
Explanation:
The array obtained by taking A, B (= 1) time, A, B (= 2) times, A, B( = 3)  times is {1, 2, 2, 3, 3, 3}. Therefore, the 4th element of the array is 3.

Input: K = 4, A[] = {3, 4, 5}, B[] = {2, 1, 3}
Output: 3
Explanation:The array formed is {3, 3, 4, 5, 5, 5}. Therefore, the 4th element of the array i.e 5.

Naive Approach: The simplest approach is to iterate over the range [0, N – 1] and push the element at the ith index of the array, B[i] times into the new array. Finally, print the Kth element of the obtained array after sorting the array in ascending order.

Time Complexity: O(N*log(N)), where N is the number of elements in the new array.
Auxiliary Space: O(N)

Efficient Approach: The above approach can be optimized by using a frequency array to keep the count of every element. Follow the steps below to solve the problem:

• Find the maximum element of the array A[] and store it in a variable, say M.
• Initialize an array, say freq[] of size M + 1 with {0}, to store the frequency of every element.
• Iterate in the range [0, N-1] using the variable i:
• Add B[i] in freq[A[i]].
• Initialize a variable, say sum as 0, to store the prefix sum up to a particular index.
• Iterate over the range [0, N – 1] using a variable, say i:
• Add freq[i] in sum.
• If sum is greater than or equal to K, then return i.
• Finally, return -1.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the Kth smallest element``// that contains A[i] exactly B[i] times``int` `KthSmallest(``int` `A[], ``int` `B[], ``int` `N, ``int` `K)``{` `    ``int` `M = 0;` `    ``// Traverse the given array``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``M = max(A[i], M);``    ``}` `    ``// Stores the frequency``    ``// of every elements``    ``int` `freq[M + 1] = { 0 };` `    ``// Traverse the given array``    ``for` `(``int` `i = 0; i < N; i++) {``        ``freq[A[i]] += B[i];``    ``}` `    ``// Initialize a variable to``    ``// store the prefix sums``    ``int` `sum = 0;` `    ``// Iterate over the range [0, M]``    ``for` `(``int` `i = 0; i <= M; i++) {` `        ``// Increment sum by freq[i]``        ``sum += freq[i];` `        ``// If sum is greater``        ``// than or equal to K``        ``if` `(sum >= K) {` `            ``// Return the current``            ``// element as answer``            ``return` `i;``        ``}``    ``}``    ``// Return -1``    ``return` `-1;``}` `// Driver Code``int` `main()``{` `    ``// Given Input``    ``int` `A[] = { 3, 4, 5 };``    ``int` `B[] = { 2, 1, 3 };``    ``int` `N = ``sizeof``(A) / ``sizeof``(A);``    ``int` `K = 4;` `    ``// Function call``    ``cout << KthSmallest(A, B, N, K);``    ``return` `0;``}`

## Java

 `// Java program for the above approach``public` `class` `GFG_JAVA {` `    ``// Function to find the Kth smallest element``    ``// that contains A[i] exactly B[i] times``    ``static` `int` `KthSmallest(``int` `A[], ``int` `B[], ``int` `N, ``int` `K)``    ``{` `        ``int` `M = ``0``;` `        ``// Traverse the given array``        ``for` `(``int` `i = ``0``; i < N; i++) {` `            ``M = Math.max(A[i], M);``        ``}` `        ``// Stores the frequency``        ``// of every elements``        ``int` `freq[] = ``new` `int``[M + ``1``];` `        ``// Traverse the given array``        ``for` `(``int` `i = ``0``; i < N; i++) {``            ``freq[A[i]] += B[i];``        ``}` `        ``// Initialize a variable to``        ``// store the prefix sums``        ``int` `sum = ``0``;` `        ``// Iterate over the range [0, M]``        ``for` `(``int` `i = ``0``; i <= M; i++) {` `            ``// Increment sum by freq[i]``            ``sum += freq[i];` `            ``// If sum is greater``            ``// than or equal to K``            ``if` `(sum >= K) {` `                ``// Return the current``                ``// element as answer``                ``return` `i;``            ``}``        ``}``        ``// Return -1``        ``return` `-``1``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{ ``// Given Input``        ``int` `A[] = { ``3``, ``4``, ``5` `};``        ``int` `B[] = { ``2``, ``1``, ``3` `};``        ``int` `N = A.length;``        ``int` `K = ``4``;` `        ``// Function call``        ``System.out.println(KthSmallest(A, B, N, K));``    ``}``}``// This code is contributed by abhinavjain194`

## Python3

 `# Python3 program for the above approach` `# Function to find the Kth smallest element``# that contains A[i] exactly B[i] times``def` `KthSmallest(A, B, N, K):` `    ``M ``=` `0` `    ``# Traverse the given array``    ``for` `i ``in` `range``(N):``        ``M ``=` `max``(A[i], M)` `    ``# Stores the frequency``    ``# of every elements``    ``freq ``=` `[``0``] ``*` `(M ``+` `1``)` `    ``# Traverse the given array``    ``for` `i ``in` `range``(N):``        ``freq[A[i]] ``+``=` `B[i]` `    ``# Initialize a variable to``    ``# store the prefix sums``    ``sum` `=` `0` `    ``# Iterate over the range [0, M]``    ``for` `i ``in` `range``(M ``+` `1``):` `        ``# Increment sum by freq[i]``        ``sum` `+``=` `freq[i]` `        ``# If sum is greater``        ``# than or equal to K``        ``if` `(``sum` `>``=` `K):` `            ``# Return the current``            ``# element as answer``            ``return` `i``            ` `    ``# Return -1``    ``return` `-``1` `# Driver Code``if` `__name__ ``=``=` `"__main__"` `:` `    ``# Given Input``    ``A ``=` `[ ``3``, ``4``, ``5` `]``    ``B ``=` `[ ``2``, ``1``, ``3` `]``    ``N ``=` `len``(A)``    ``K ``=` `4` `    ``# Function call``    ``print``(KthSmallest(A, B, N, K))``   ` `# This code is contributed by AnkThon`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find the Kth smallest element``// that contains A[i] exactly B[i] times``static` `int` `KthSmallest(``int` `[]A, ``int` `[]B,``                       ``int` `N, ``int` `K)``{``    ``int` `M = 0;` `    ``// Traverse the given array``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``M = Math.Max(A[i], M);``    ``}` `    ``// Stores the frequency``    ``// of every elements``    ``int` `[]freq = ``new` `int``[M + 1];` `    ``// Traverse the given array``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``freq[A[i]] += B[i];``    ``}` `    ``// Initialize a variable to``    ``// store the prefix sums``    ``int` `sum = 0;` `    ``// Iterate over the range [0, M]``    ``for``(``int` `i = 0; i <= M; i++)``    ``{``        ` `        ``// Increment sum by freq[i]``        ``sum += freq[i];` `        ``// If sum is greater``        ``// than or equal to K``        ``if` `(sum >= K)``        ``{``            ` `            ``// Return the current``            ``// element as answer``            ``return` `i;``        ``}``    ``}``    ` `    ``// Return -1``    ``return` `-1;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{  ``    ` `    ``// Given Input``    ``int` `[]A = { 3, 4, 5 };``    ``int` `[]B = { 2, 1, 3 };``    ``int` `N = A.Length;``    ``int` `K = 4;` `    ``// Function call``    ``Console.Write(KthSmallest(A, B, N, K));``}``}` `// This code is contributed by shivanisinghss2110`
Output:
`5`

Time Complexity: O(N), where N is the size of arrays A[] and B[].
Auxiliary Space: O(M), where M is the maximum element of the array A[].

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