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Find range of values for S in given Array with values satisfying [ arr[i] = floor((i*S)/K) ]

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  • Last Updated : 29 Sep, 2021
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Given an array arr[] of N positive integers and a positive integer K, the task is to find the range [L, R] such that for all the elements in this range, say S each array element arr[i] is floor((i*S)/K).

Examples:

Input: N = 5, K = 10, arr[] = {2, 4, 6, 9, 11}
Output: 23 23
Explanation: 
When S = 23, substituting in the equation gives the same array values:
arr[1] = floor((1*23)/10) = 2
arr[2] = floor((2*23/10)) = 4
arr[3] = floor((3*23/10)) = 6
arr[4] = floor((4*23/10)) = 9
arr[5] = floor((5*23/10)) = 11

Input: N = 5, K = 100, arr[] = {0, 0, 0, 0, 1}
Output: 20 24

Approach: Follow the below steps to solve the given problem:

  • Initialize two variables say L and R as INT_MIN and INT_MAX that stores the value of the left range and the right range respectively.
  • Traverse the given array arr[] and perform the following steps:
    • Find the possible value of the left range for the ith array element as ceil(1.0*arr[i]*K/(i + 1)).
    • Find the possible value of the right range for the ith array element as ceil((1.0 + arr[i])*K/(i + 1)) – 1.
    • Update the value of L as max(L, l) and the value of R as min(R, r).
  • After completing the above steps, print the values of L and R as the resultant range.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the range of values
// for S in a given array that satisfies
// the given condition
void findRange(int arr[], int N, int K)
{
 
    // Stores the left range value
    int L = INT_MIN;
 
    // Stores the right range value
    int R = INT_MAX;
 
    for (int i = 0; i < N; i++) {
        // Find the current left range
        // value for S
        int l = (int)ceil(1.0 * arr[i] * K / (i + 1));
 
        // Find the current right range
        // value for S
        int r = (int)ceil((1.0 + arr[i]) * K / (i + 1)) - 1;
 
        // Updating L value
        L = max(L, l);
 
        // Updating R value
        R = min(R, r);
    }
 
    cout << L << " " << R;
}
 
// Driver Code
int main()
{
 
    int arr[] = { 2, 4, 6, 9, 11 };
    int K = 10;
    int N = sizeof(arr) / sizeof(int);
 
    findRange(arr, N, K);
    return 0;
}
 
// This code is contributed by Potta Lokesh


Java




// Java program for the above approach
 
import java.util.*;
import java.lang.*;
 
class Codechef {
 
    // Function to find the range of values
    // for S in a given array that satisfies
    // the given condition
    static void findRange(int arr[], int N,
                          int K)
    {
 
        // Stores the left range value
        int L = Integer.MIN_VALUE;
 
        // Stores the right range value
        int R = Integer.MAX_VALUE;
 
        for (int i = 0; i < N; i++) {
            // Find the current left range
            // value for S
            int l = (int)Math.ceil(
                1.0 * arr[i] * K / (i + 1));
 
            // Find the current right range
            // value for S
            int r = (int)Math.ceil(
                        (1.0 + arr[i]) * K / (i + 1))
                    - 1;
 
            // Updating L value
            L = Math.max(L, l);
 
            // Updating R value
            R = Math.min(R, r);
        }
 
        System.out.println(L + " " + R);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int arr[] = { 2, 4, 6, 9, 11 };
        int K = 10;
        int N = arr.length;
 
        findRange(arr, N, K);
    }
}


Python3




# Python 3 program for the above approach
from math import ceil,floor
import sys
 
# Function to find the range of values
# for S in a given array that satisfies
# the given condition
def findRange(arr, N, K):
   
    # Stores the left range value
    L = -sys.maxsize-1
 
    # Stores the right range value
    R = sys.maxsize
 
    for i in range(N):
       
        # Find the current left range
        # value for S
        l = ceil(1.0 * arr[i] * K / (i + 1))
 
        # Find the current right range
        # value for S
        r = ceil((1.0 + arr[i]) * K / (i + 1) - 1)
 
        # Updating L value
        L = max(L, l)
 
        # Updating R value
        R = min(R, r)
 
    print(L,R)
 
# Driver Code
if __name__ == '__main__':
    arr = [2, 4, 6, 9, 11]
    K = 10
    N = len(arr)
    findRange(arr, N, K)
     
    # This code is contributed by SURENDRA_GANGWAR.


C#




// C# program for the above approach
 
using System;
 
class GFG {
 
    // Function to find the range of values
    // for S in a given array that satisfies
    // the given condition
    static void findRange(int[] arr, int N, int K)
    {
 
        // Stores the left range value
        int L = Int32.MinValue;
 
        // Stores the right range value
        int R = Int32.MaxValue;
 
        for (int i = 0; i < N; i++)
        {
           
            // Find the current left range
            // value for S
            int l = (int)Math.Ceiling(1.0 * arr[i] * K
                                      / (i + 1));
 
            // Find the current right range
            // value for S
            int r = (int)Math.Ceiling((1.0 + arr[i]) * K
                                      / (i + 1))
                    - 1;
 
            // Updating L value
            L = Math.Max(L, l);
 
            // Updating R value
            R = Math.Min(R, r);
        }
 
        Console.WriteLine(L + " " + R);
    }
 
    // Driver Code
    public static void Main()
    {
        int[] arr = { 2, 4, 6, 9, 11 };
        int K = 10;
        int N = arr.Length;
 
        findRange(arr, N, K);
    }
}
 
// This code is contributed by subham348.


Javascript




<script>
// JavaScript program for the above approach
 
// Function to find the range of values
// for S in a given array that satisfies
// the given condition
function findRange(arr,  N,  K)
{
 
    // Stores the left range value
    let L = Number.MIN_VALUE;
 
    // Stores the right range value
    let R = Number.MAX_VALUE;
 
    for (let i = 0; i < N; i++) {
        // Find the current left range
        // value for S
        let l = Math.ceil(1.0 * arr[i] * K / (i + 1));
 
        // Find the current right range
        // value for S
        let r = Math.ceil((1.0 + arr[i]) * K / (i + 1)) - 1;
 
        // Updating L value
        L = Math.max(L, l);
 
        // Updating R value
        R = Math.min(R, r);
    }
 
    document.write(L  + " " + R);
}
 
    // Driver code
    let  arr = [ 2, 4, 6, 9, 11 ];
    let K = 10;
    let N = arr.length;
 
    findRange(arr, N, K);
 
// This code is contributed by AnkThon
</script>


Output: 

23 23

 

Time Complexity: O(N)
Auxiliary Space: O(1)


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