Given an array arr[], the task is to check if the minimum element in the array is less than or equal to half of every other element. If it is then print “yes” otherwise print “no”.
Note: The minimum number in the given array is always unique.
Examples:
Input: arr = {2, 1, 4, 5}
Output: Yes
Explanation:
1 is the minimum element in the array arr[] and on dividing 2, 4, 5 by 2 we get 1, 2, 2.5 which is greater than or equal to the minimum number. Hence, print “yes”.Input : arr = {2, 4, 5, 3}
Output : No
Explanation:
2 is the minimum element in the array arr[] and on dividing 4, 5, 3 by 2 we get 2, 2.5, 1.5 in which the integer 3 does not return a value which is greater than or equal to the minimum number ( 1.5 < 2). Hence, print “no”.
Method 1:
To solve the problem mentioned above we have to find the smallest element with the help of loops and then scan through the entire array again and check if twice the smallest element is smaller than or equal to every other element. But this solution takes O(N) time using two loops and can be optimized further where only one iteration is involved.
Below is the implementation of the above approach:
// C++ implementation to Check if the minimum element in the // array is greater than or equal to half of every other // elements #include <bits/stdc++.h> using namespace std;
// Function to Check if the minimum element in the array is // greater than or equal to half of every other element bool checkMin( int arr[], int len)
{ // Initialise the variables to store the index of
// smallest element
int smallest = 0;
for ( int i = 0; i < len; i++) {
// Check if current element is smaller than smallest
if (arr[i] < arr[smallest]) {
smallest = i;
}
}
for ( int i = 0; i < len; i++) {
// Check if (current element / 2) is smaller than
// smallest
if (i != smallest && arr[i] / 2 < arr[smallest]) {
return false ;
}
}
return true ;
} // Driver code int main()
{ int arr[] = { 2, 30, 4, 5 };
int len = sizeof (arr) / sizeof (arr[0]);
if (checkMin(arr, len)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
} |
/*package whatever //do not write package name here */ import java.io.*;
class GFG {
public static boolean checkMin( int arr[], int len)
{ // Initialise the variables to store the index of
// smallest element
int smallest = 0 ;
for ( int i = 0 ; i < len; i++) {
// Check if current element is smaller than smallest
if (arr[i] < arr[smallest]) {
smallest = i;
}
}
for ( int i = 0 ; i < len; i++) {
// Check if (current element / 2) is smaller than
// smallest
if (i != smallest && arr[i] / 2 < arr[smallest]) {
return false ;
}
}
return true ;
} public static void main (String[] args) {
int arr[] = { 2 , 30 , 4 , 5 };
int len = arr.length;
if (checkMin(arr, len)) {
System.out.println( "Yes" );
}
else {
System.out.println( "No" );
}
}
} |
class GFG :
@staticmethod
def checkMin( arr, len ) :
# Initialise the variables to store the index of
# smallest element
smallest = 0
i = 0
while (i < len ) :
# Check if current element is smaller than smallest
if (arr[i] < arr[smallest]) :
smallest = i
i + = 1
i = 0
while (i < len ) :
# Check if (current element / 2) is smaller than
# smallest
if (i ! = smallest and int (arr[i] / 2 ) < arr[smallest]) :
return False
i + = 1
return True
@staticmethod
def main( args) :
arr = [ 2 , 30 , 4 , 5 ]
len1 = len (arr)
if (GFG.checkMin(arr, len1)) :
print ( "Yes" )
else :
print ( "No" )
if __name__ = = "__main__" :
GFG.main([])
# This code is contributed by aadityaburujwale.
|
// C# implementation to Check if the minimum element in the // array is greater than or equal to half of every other // elements using System;
class GFG {
// Function to Check if the minimum element in the array
// is greater than or equal to half of every other
// element
static bool checkMin( int [] arr, int len)
{
// Initialise the variables to store the index of
// smallest element
int smallest = 0;
for ( int i = 0; i < len; i++) {
// Check if current element is smaller than
// smallest
if (arr[i] < arr[smallest]) {
smallest = i;
}
}
for ( int i = 0; i < len; i++) {
// Check if (current element / 2) is smaller
// than smallest
if (i != smallest
&& arr[i] / 2 < arr[smallest]) {
return false ;
}
}
return true ;
}
static void Main()
{
int [] arr = { 2, 30, 4, 5 };
int len = arr.Length;
if (checkMin(arr, len) == true ) {
Console.Write( "Yes" );
}
else {
Console.Write( "No" );
}
}
} // This code is contributed by garg28harsh. |
// Javascript implementation to Check if the minimum element // in the array is greater than or equal to half of every // other elements // Function to Check if the minimum element in the array
// is greater than or equal to half of every other
// element
function checkMin(arr, len)
{
// Initialise the variables to store the index of
// smallest element
let smallest = 0;
for (let i = 0; i < len; i++) {
// Check if current element is smaller than smallest
if (arr[i] < arr[smallest]) {
smallest = i;
}
}
for (let i = 0; i < len; i++) {
// Check if (current element / 2) is smaller than
// smallest
if (i != smallest && arr[i] / 2 < arr[smallest]) {
return false ;
}
}
return true ;
} // Driver code let arr = [ 2, 30, 4, 5 ]; let len = arr.length; if (checkMin(arr, len) == true ) {
console.log( "Yes" );
} else {
console.log( "No" );
} // This code is contributed by garg28harsh. |
Yes
Time Complexity: O(N), where N is the length of the given array.
Auxiliary Space: O(1).
Method 2:
To optimize the above solution we can find the smallest as well as the second smallest element in a single iteration itself. Then simply check if twice of the smallest element is smaller than or equal to the second smallest element.
Below is the implementation of the above approach:
// C++ implementation to Check if the minimum element in the // array is greater than or equal to half of every other elements #include <bits/stdc++.h> using namespace std;
// Function to Check if the minimum element in the array is // greater than or equal to half of every other element void checkMin( int arr[], int len)
{ // Initialise the variables to store
// smallest and second smallest
int smallest = INT_MAX, secondSmallest = INT_MAX;
for ( int i = 0; i < len; i++) {
// Check if current element is smaller than smallest,
// the current smallest will become secondSmallest
// and current element will be the new smallest
if (arr[i] < smallest) {
secondSmallest = smallest;
smallest = arr[i];
}
// Check if current element is smaller than
// secondSmallest simply update the latter
else if (arr[i] < secondSmallest) {
secondSmallest = arr[i];
}
}
if (2 * smallest <= secondSmallest)
cout << "Yes" ;
else
cout << "No" ;
} // Driver code int main()
{ int arr[] = { 2, 3, 4, 5 };
int len = sizeof (arr) / sizeof (arr[0]);
checkMin(arr, len);
} |
// Java implementation to check // if the minimum element in the // array is greater than or equal // to half of every other elements import java.util.*;
class GFG{
// Function to Check if the minimum // element in the array is greater // than or equal to half of every // other elements static void checkMin( int arr[], int len)
{ // Initialise the variables to store
// smallest and second smallest
int smallest = Integer.MAX_VALUE;
int secondSmallest = Integer.MAX_VALUE;
for ( int i = 0 ; i < len; i++)
{
// Check if current element is smaller than
// smallest, the current smallest will
// become secondSmallest and current
// element will be the new smallest
if (arr[i] < smallest)
{
secondSmallest = smallest;
smallest = arr[i];
}
// Check if current element is smaller than
// secondSmallest simply update the latter
else if (arr[i] < secondSmallest)
{
secondSmallest = arr[i];
}
}
if ( 2 * smallest <= secondSmallest)
System.out.print( "Yes" );
else
System.out.print( "No" );
} // Driver code public static void main(String[] args)
{ int arr[] = { 2 , 3 , 4 , 5 };
int len = arr.length;
checkMin(arr, len);
} } // This code is contributed by amal kumar choubey |
# Python3 implementation to Check if # the minimum element in the array # is greater than or equal to half # of every other element import math
# Function to Check if the minimum element # in the array is greater than or equal to # half of every other element def checkMin(arr, n):
# Initialise the variables to store
# smallest and second smallest
smallest = math.inf
secondSmallest = math.inf
for i in range (n):
# Check if current element is
# smaller than smallest,
# the current smallest will become
# secondSmallest and current element
# will be the new smallest
if (arr[i] < smallest):
secondSmallest = smallest
smallest = arr[i]
# Check if current element is smaller than
# secondSmallest simply update the latter
elif (arr[i] < secondSmallest):
secondSmallest = arr[i]
if ( 2 * smallest < = secondSmallest):
print ( "Yes" )
else :
print ( "No" )
# Driver code if __name__ = = '__main__' :
arr = [ 2 , 3 , 4 , 5 ]
n = len (arr)
checkMin(arr, n)
# This code is contributed by Shivam Singh. |
// C# implementation to check // if the minimum element in the // array is greater than or equal // to half of every other elements using System;
class GFG{
// Function to Check if the minimum // element in the array is greater // than or equal to half of every // other elements static void checkMin( int []arr, int len)
{ // Initialise the variables to store
// smallest and second smallest
int smallest = int .MaxValue;
int secondSmallest = int .MaxValue;
for ( int i = 0; i < len; i++)
{
// Check if current element is smaller than
// smallest, the current smallest will
// become secondSmallest and current
// element will be the new smallest
if (arr[i] < smallest)
{
secondSmallest = smallest;
smallest = arr[i];
}
// Check if current element is smaller than
// secondSmallest simply update the latter
else if (arr[i] < secondSmallest)
{
secondSmallest = arr[i];
}
}
if (2 * smallest <= secondSmallest)
Console.Write( "Yes" );
else
Console.Write( "No" );
} // Driver code public static void Main(String[] args)
{ int []arr = { 2, 3, 4, 5 };
int len = arr.Length;
checkMin(arr, len);
} } // This code is contributed by amal kumar choubey |
<script> // Javascript implementation to check // if the minimum element in the // array is greater than or equal // to half of every other elements // Function to Check if the minimum // element in the array is greater // than or equal to half of every // other element function checkMin(arr, len)
{ // Initialise the variables to store
// smallest and second smallest
var smallest = Number.INFINITY,
secondSmallest = Number.INFINITY;
for ( var i = 0; i < len; i++)
{
// Check if current element is
// smaller than smallest, the
// current smallest will become
// secondSmallest and current
// element will be the new smallest
if (arr[i] < smallest)
{
secondSmallest = smallest;
smallest = arr[i];
}
// Check if current element is smaller than
// secondSmallest simply update the latter
else if (arr[i] < secondSmallest)
{
secondSmallest = arr[i];
}
}
if (2 * smallest <= secondSmallest)
document.write( "Yes" );
else
document.write( "No" );
} // Driver code var arr = [ 2, 3, 4, 5 ];
var len = 4;
checkMin(arr, len); // This code is contributed by akshitsaxenaa09 </script> |
No
Time Complexity: O(N), where N is the length of the given array.
Auxiliary Space: O(1).