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, 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;
}
Python3
# Python3 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]
def 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 in range(1, n):
if (arr[i] > x):
return (i - 1)
return -1
# Driver Code
arr = [1, 2, 4, 6, 10, 12, 14]
n = len(arr)
x = 7
index = floorSearch(arr, 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
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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Improved By : nitin mittal
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