Given a sorted array and a value x, the floor of x is the largest element in array smaller than or equal to x. Write efficient functions to find floor of x.
Examples:
Input : arr[] = {1, 2, 8, 10, 10, 12, 19}, x = 5 Output : 2 2 is the largest element in arr[] smaller than 5. Input : arr[] = {1, 2, 8, 10, 10, 12, 19}, x = 20 Output : 19 19 is the largest element in arr[] smaller than 20. Input : arr[] = {1, 2, 8, 10, 10, 12, 19}, x = 0 Output : -1 Since floor doesn't exist, output is -1.
Method 1 (Simple)
A simple solution is linearly traverse input sorted array and search for the first element greater than x. The element just before the found element is floor of x.
C++
// C/C++ program to find floor of a given number // in a sorted array #include<stdio.h> /* An inefficient function to get index of floor of x in arr[0..n-1] */ int floorSearch( int arr[], int n, int x) { // If last element is smaller than x if (x >= arr[n-1]) return n-1; // If first element is greater than x if (x < arr[0]) return -1; // Linearly search for the first element // greater than x for ( int i=1; i<n; i++) if (arr[i] > x) return (i-1); return -1; } /* Driver program to check above functions */ int main() { int arr[] = {1, 2, 4, 6, 10, 12, 14}; int n = sizeof (arr)/ sizeof (arr[0]); int x = 7; int index = floorSearch(arr, n-1, x); if (index == -1) printf ( "Floor of %d doesn't exist in array " , x); else printf ( "Floor of %d is %d" , x, arr[index]); return 0; } |
Java
// Java program to find floor of a given number // in a sorted array import java.io.*; import java.util.*; import java.lang.*; class GFG { /* An inefficient function to get index of floor of x in arr[0..n-1] */ static int floorSearch( int arr[], int n, int x) { // If last element is smaller than x if (x >= arr[n- 1 ]) return n- 1 ; // If first element is greater than x if (x < arr[ 0 ]) return - 1 ; // Linearly search for the first element // greater than x for ( int i= 1 ; i<n; i++) if (arr[i] > x) return (i- 1 ); return - 1 ; } // Driver Code public static void main(String[] args) { int arr[] = { 1 , 2 , 4 , 6 , 10 , 12 , 14 }; int n = arr.length; int x = 7 ; int index = floorSearch(arr, n- 1 , x); if (index == - 1 ) System.out.print( "Floor of " + x + " doesn't exist in array " ); else System.out.print( "Floor of " + x + " is " + arr[index]); } } // This code is contributed // by Akanksha Rai(Abby_akku) |
Python3
# Python3 program to find floor of a # given number in a sorted array # Function to get index of floor # of x in arr[low..high] def floorSearch(arr, low, high, x): # If low and high cross each other if (low > high): return - 1 # If last element is smaller than x if (x > = arr[high]): return high # Find the middle point mid = int ((low + high) / 2 ) # If middle point is floor. if (arr[mid] = = x): return mid # If x lies between mid-1 and mid if (mid > 0 and arr[mid - 1 ] < = x and x < arr[mid]): return mid - 1 # If x is smaller than mid, # floor must be in left half. if (x < arr[mid]): return floorSearch(arr, low, mid - 1 , x) # If mid-1 is not floor and x is greater than # arr[mid], return floorSearch(arr, mid + 1 , high, x) # Driver Code arr = [ 1 , 2 , 4 , 6 , 10 , 12 , 14 ] n = len (arr) x = 7 index = floorSearch(arr, 0 , n - 1 , x) if (index = = - 1 ): print ( "Floor of" , x, "doesn't exist in array ", end = " ") else : print ( "Floor of" , x, "is" , arr[index]) # This code is contributed by Smitha Dinesh Semwal. |
PHP
<?php // PHP program to find floor of // a given number in a sorted array /* An inefficient function to get index of floor of x in arr[0..n-1] */ function floorSearch( $arr , $n , $x ) { // If last element is smaller // than x if ( $x >= $arr [ $n - 1]) return $n - 1; // If first element is greater // than x if ( $x < $arr [0]) return -1; // Linearly search for the // first element greater than x for ( $i = 1; $i < $n ; $i ++) if ( $arr [ $i ] > $x ) return ( $i - 1); return -1; } // Driver Code $arr = array (1, 2, 4, 6, 10, 12, 14); $n = sizeof( $arr ); $x = 7; $index = floorSearch( $arr , $n - 1, $x ); if ( $index == -1) echo "Floor of " , $x , "doesn't exist in array " ; else echo "Floor of " , $x , " is " , $arr [ $index ]; // This code is contributed by ajit ?> |
Output:
Floor of 7 is 6.
Time Complexity : O(n)
Method 2 (Efficient)
The idea is to use Binary Search.
C++
// A C/C++ program to find floor of a given number // in a sorted array #include<stdio.h> /* Function to get index of floor of x in arr[low..high] */ int floorSearch( int arr[], int low, int high, int x) { // If low and high cross each other if (low > high) return -1; // If last element is smaller than x if (x >= arr[high]) return high; // Find the middle point int mid = (low+high)/2; // If middle point is floor. if (arr[mid] == x) return mid; // If x lies between mid-1 and mid if (mid > 0 && arr[mid-1] <= x && x < arr[mid]) return mid-1; // If x is smaller than mid, floor must be in // left half. if (x < arr[mid]) return floorSearch(arr, low, mid-1, x); // If mid-1 is not floor and x is greater than // arr[mid], return floorSearch(arr, mid+1, high, x); } /* Driver program to check above functions */ int main() { int arr[] = {1, 2, 4, 6, 10, 12, 14}; int n = sizeof (arr)/ sizeof (arr[0]); int x = 7; int index = floorSearch(arr, 0, n-1, x); if (index == -1) printf ( "Floor of %d doesn't exist in array " , x); else printf ( "Floor of %d is %d" , x, arr[index]); return 0; } |
Java
// Java program to find floor of // a given number in a sorted array import java.io.*; class GFG { /* Function to get index of floor of x in arr[low..high] */ static int floorSearch( int arr[], int low, int high, int x) { // If low and high cross each other if (low > high) return - 1 ; // If last element is smaller than x if (x >= arr[high]) return high; // Find the middle point int mid = (low+high)/ 2 ; // If middle point is floor. if (arr[mid] == x) return mid; // If x lies between mid-1 and mid if (mid > 0 && arr[mid- 1 ] <= x && x < arr[mid]) return mid- 1 ; // If x is smaller than mid, floor // must be in left half. if (x < arr[mid]) return floorSearch(arr, low, mid - 1 , x); // If mid-1 is not floor and x is // greater than arr[mid], return floorSearch(arr, mid + 1 , high, x); } /* Driver program to check above functions */ public static void main(String[] args) { int arr[] = { 1 , 2 , 4 , 6 , 10 , 12 , 14 }; int n = arr.length; int x = 7 ; int index = floorSearch(arr, 0 , n - 1 , x); if (index == - 1 ) System.out.println( "Floor of " + x + " dosen't exist in array " ); else System.out.println( "Floor of " + x + " is " + arr[index]); } } // This code is contributed by Prerna Saini |
Python3
# Python3 program to find floor of a # given number in a sorted array # Function to get index of floor # of x in arr[low..high] def floorSearch(arr, low, high, x): # If low and high cross each other if (low > high): return - 1 # If last element is smaller than x if (x > = arr[high]): return high # Find the middle point mid = int ((low + high) / 2 ) # If middle point is floor. if (arr[mid] = = x): return mid # If x lies between mid-1 and mid if (mid > 0 and arr[mid - 1 ] < = x and x < arr[mid]): return mid - 1 # If x is smaller than mid, # floor must be in left half. if (x < arr[mid]): return floorSearch(arr, low, mid - 1 , x) # If mid-1 is not floor and x is greater than # arr[mid], return floorSearch(arr, mid + 1 , high, x) # Driver Code arr = [ 1 , 2 , 4 , 6 , 10 , 12 , 14 ] n = len (arr) x = 7 index = floorSearch(arr, 0 , n - 1 , x) if (index = = - 1 ): print ( "Floor of" , x, "doesn't exist in array ", end = " ") else : print ( "Floor of" , x, "is" , arr[index]) # This code is contributed by Smitha Dinesh Semwal. |
C#
// C# program to find floor of // a given number in a sorted array using System; class GFG { /* Function to get index of floor of x in arr[low..high] */ static int floorSearch( int []arr, int low, int high, int x) { // If low and high cross each other if (low > high) return -1; // If last element is smaller than x if (x >= arr[high]) return high; // Find the middle point int mid = (low + high) / 2; // If middle point is floor. if (arr[mid] == x) return mid; // If x lies between mid-1 and mid if (mid > 0 && arr[mid-1] <= x && x < arr[mid]) return mid - 1; // If x is smaller than mid, floor // must be in left half. if (x < arr[mid]) return floorSearch(arr, low, mid - 1, x); // If mid-1 is not floor and x is // greater than arr[mid], return floorSearch(arr, mid + 1, high, x); } /* Driver program to check above functions */ public static void Main() { int []arr = {1, 2, 4, 6, 10, 12, 14}; int n = arr.Length; int x = 7; int index = floorSearch(arr, 0, n - 1, x); if (index == -1) Console.Write( "Floor of " + x + " dosen't exist in array " ); else Console.Write( "Floor of " + x + " is " + arr[index]); } } // This code is contributed by nitin mittal. |
Output:
Floor of 7 is 6.
Time Complexity : O(Log n)
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