Longest subsequence whose average is less than K - GeeksforGeeks

31 Jan, 2022
Given an array of N positive integers and Q queries consisting of an integer K, the task is to print the length of the longest subsequence whose average is less than K. Examples:  
Input: a[] = {1, 3, 2, 5, 4} Query1: K = 3 Query2: K = 5Output: 4 5 Query1: The subsequence is: {1, 3, 2, 4} or {1, 3, 2, 5} Query2: The subsequence is: {1, 3, 2, 5, 4}  
 
A Naive Approach is to generate all subsequences using power-set and check for the longest subsequence whose average is less than K. Time Complexity: O(2N * N ) An efficient approach is to sort the array elements and find the average of elements starting from the left. Insert the average of elements computed from the left into the container(vector or arrays). Sort the container’s element and then use binary search to search for the number K in the container. The length of the longest subsequence will thus be the index number which upper_bound() returns for every query.Below is the implementation of the above approach.  
C++
Java
Python3
C#
Javascript
// C++ program to perform Q queries// to find longest subsequence whose// average is less than K#include <bits/stdc++.h>using namespace std; // Function to print the length for every queryint longestSubsequence(int a[], int n, int q[], int m){     // sort array of N elements    sort(a, a + n);    int sum = 0;     // Array to store average from left    int b[n];     for (int i = 0; i < n; i++) {        sum += a[i];        double av = (double)(sum) / (double)(i + 1);        b[i] = ((int)(av + 1));    }     // Sort array of average    sort(b, b + n);     // number of queries     for (int i = 0; i < m; i++) {        int k = q[i];         // print answer to every query        // using binary search        int longest = upper_bound(b, b + n, k) - b;         cout << "Answer to Query" << i + 1 << ": "             << longest << endl;    }} // Driver Codeint main(){    int a[] = { 1, 3, 2, 5, 4 };    int n = sizeof(a) / sizeof(a[0]);     // 4 queries    int q[] = { 4, 2, 1, 5 };    int m = sizeof(q) / sizeof(q[0]);     longestSubsequence(a, n, q, m);    return 0;}
// Java program to perform Q queries// to find longest subsequence whose// average is less than Kimport java.util.Arrays; class GFG{     // Function to print the length for every query    static void longestSubsequence(int a[], int n,                                    int q[], int m)    {         // sort array of N elements        Arrays.sort(a);        int sum = 0;         // Array to store average from left        int []b = new int[n];         for (int i = 0; i < n; i++)        {            sum += a[i];            double av = (double)(sum) / (double)(i + 1);            b[i] = ((int)(av + 1));        }         // Sort array of average        Arrays.sort(b);         // number of queries         for (int i = 0; i < m; i++)        {            int k = q[i];             // print answer to every query            // using binary search            int longest = upperBound(b,0, n, k);             System.out.println("Answer to Query" + (i + 1) +": "                + longest);        }    }    private static int upperBound(int[] a, int low, int high, int element)    {        while(low < high)        {            int middle = low + (high - low)/2;            if(a[middle] > element)                high = middle;            else                low = middle + 1;        }        return low;    }         // Driver Code    public static void main(String[] args)    {        int a[] = { 1, 3, 2, 5, 4 };        int n = a.length;         // 4 queries        int q[] = { 4, 2, 1, 5 };        int m = q.length;         longestSubsequence(a, n, q, m);    }} /* This code contributed by PrinciRaj1992 */
# Python3 program to perform Q queries to find# longest subsequence whose average is less than Kimport bisect # Function to print the length for every querydef longestSubsequence(a, n, q, m):      # sort array of N elements    a.sort()    Sum = 0     # Array to store average from left    b = [None] * n     for i in range(0, n):         Sum += a[i]        av = Sum // (i + 1)        b[i] = av + 1     # Sort array of average    b.sort()     # number of queries     for i in range(0, m):         k = q[i]         # print answer to every query        # using binary search        longest = bisect.bisect_right(b, k)         print("Answer to Query", i + 1, ":", longest) # Driver Codeif __name__ == "__main__":      a = [1, 3, 2, 5, 4]     n = len(a)     # 4 queries    q = [4, 2, 1, 5]     m = len(q)     longestSubsequence(a, n, q, m)     # This code is contributed by Rituraj Jain
// C# program to perform Q queries// to find longest subsequence whose// average is less than Kusing System; class GFG{         // Function to print the length for every query    static void longestSubsequence(int []a, int n,                                    int []q, int m)    {         // sort array of N elements        Array.Sort(a);        int sum = 0;         // Array to store average from left        int []b = new int[n];         for (int i = 0; i < n; i++)        {            sum += a[i];            double av = (double)(sum) / (double)(i + 1);            b[i] = ((int)(av + 1));        }         // Sort array of average        Array.Sort(b);         // number of queries         for (int i = 0; i < m; i++)        {            int k = q[i];             // print answer to every query            // using binary search            int longest = upperBound(b,0, n, k);             Console.WriteLine("Answer to Query" + (i + 1) +": "                + longest);        }    }         private static int upperBound(int[] a, int low,                                    int high, int element)    {        while(low < high)        {            int middle = low + (high - low)/2;            if(a[middle] > element)                high = middle;            else                low = middle + 1;        }        return low;    }         // Driver Code    static public void Main ()    {        int []a = { 1, 3, 2, 5, 4 };        int n = a.Length;         // 4 queries        int []q = { 4, 2, 1, 5 };        int m = q.Length;         longestSubsequence(a, n, q, m);    }}     /* This code contributed by ajit */
<script>     // Javascript program to perform Q queries    // to find longest subsequence whose    // average is less than K         // Function to print the length for every query    function longestSubsequence(a, n, q, m)    {           // sort array of N elements        a.sort(function(a, b){return a - b});        let sum = 0;           // Array to store average from left        let b = new Array(n);           for (let i = 0; i < n; i++)        {            sum += a[i];            let av = parseInt((sum) / (i + 1), 10);            b[i] = (av + 1);        }           // Sort array of average        b.sort(function(a, b){return a - b});           // number of queries           for (let i = 0; i < m; i++)        {            let k = q[i];               // print answer to every query            // using binary search            let longest = upperBound(b,0, n, k);               document.write("Answer to Query" +            (i + 1) +": "                + longest + "</br>");        }    }           function upperBound(a, low, high, element)    {        while(low < high)        {            let middle = low +            parseInt((high - low)/2, 10);            if(a[middle] > element)                high = middle;            else                low = middle + 1;        }        return low;    }         let a = [ 1, 3, 2, 5, 4 ];    let n = a.length;     // 4 queries    let q = [ 4, 2, 1, 5 ];    let m = q.length;     longestSubsequence(a, n, q, m);     </script>
Output:  
Answer to Query1: 5
Answer to Query2: 2
Answer to Query3: 0
Answer to Query4: 5
Time Complexity: O(N*log N + M*log N) Auxiliary Space: O(N) 
rituraj_jain
Code_r
princiraj1992
jit_t
divyeshrabadiya07
avtarkumar719
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