Floor and Ceil in Sorted Array in DSA Java - Build from Scratch

Floor and Ceil in Sorted Array

📖 Scenario: Imagine you have a sorted list of house numbers on a street. You want to find the closest house number that is less than or equal to a visitor's number (floor), and the closest house number that is greater than or equal to the visitor's number (ceil).

🎯 Goal: Build a Java program that finds the floor and ceil values for a given number in a sorted array of integers.

📋 What You'll Learn

Create a sorted integer array named houses with exact values

Create an integer variable named visitorNumber with a specific value

Write a method findFloorAndCeil that takes the array and visitor number and returns floor and ceil

Print the floor and ceil values in the format: Floor: X, Ceil: Y

💡 Why This Matters

🌍 Real World

Finding floor and ceil values is useful in real estate, pricing, and scheduling where you want to find closest matches or limits.

💼 Career

Understanding floor and ceil concepts helps in algorithm design, data searching, and optimization tasks common in software development.

1

Create the sorted array of house numbers

Create a sorted integer array called houses with these exact values: 2, 5, 8, 12, 16, 23, 38, 56, 72, 91

DSA Java

// Create the sorted array houses with given values
// Your code here

Hint

Use int[] houses = { ... }; to create the array with the exact numbers.

2

Set the visitor's house number

Create an integer variable called visitorNumber and set it to 20

DSA Java

int[] houses = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
// Create visitorNumber and set it to 20
// Your code here

Hint

Use int visitorNumber = 20; to store the visitor's number.

3

Write the method to find floor and ceil

Write a method called findFloorAndCeil that takes int[] houses and int visitorNumber as parameters and returns an integer array of size 2 where the first element is the floor and the second is the ceil. Use a for loop to find the floor and ceil values.

DSA Java

int[] houses = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
int visitorNumber = 20;

// Write findFloorAndCeil method below
// Your code here

Hint

Use a for-each loop to check each house number. Update floor if house is less than or equal to visitorNumber. Set ceil when you find the first house greater than or equal to visitorNumber.

4

Print the floor and ceil values

Call the method findFloorAndCeil with houses and visitorNumber, store the result in result, and print the floor and ceil values in the format: Floor: X, Ceil: Y

DSA Java

int[] houses = {2, 5, 8, 12, 16, 23, 38, 56, 72, 91};
int visitorNumber = 20;

public static int[] findFloorAndCeil(int[] houses, int visitorNumber) {
    int floor = -1;
    int ceil = -1;
    for (int house : houses) {
        if (house = visitorNumber && ceil == -1) {
            ceil = house;
        }
    }
    return new int[]{floor, ceil};
}

// Call the method and print the result
// Your code here

Hint

Call findFloorAndCeil(houses, visitorNumber), save the result, and print using System.out.println.

Practice

1. What does the floor of a number mean in a sorted array context?

easy

A. The greatest element less than or equal to the number

B. The smallest element greater than the number

C. The average of all elements less than the number

D. The smallest element less than the number

Solution

1. Step 1: Understand floor definition in sorted array

   The floor of a number is the greatest element in the array that is less than or equal to the number.

2. Step 2: Compare options with definition

   The greatest element less than or equal to the number matches the definition exactly, others describe different concepts.

3. Final Answer:

   The greatest element less than or equal to the number -> Option A

4. Quick Check:

   Floor = greatest ≤ number [OK]

Hint: Floor is always ≤ target, pick greatest such element [OK]

Common Mistakes:

• Confusing floor with ceil
• Thinking floor is strictly less than the number
• Mixing floor with average or median

2. Which of the following is the correct Java method signature to find the floor of a number in a sorted integer array?

easy

A. int findFloor(int arr[], target)

B. public int findFloor(int[] arr, int target, int size)

C. static int findFloor(int[] arr, int target) throws Exception

D. public static int findFloor(int[] arr, int target)

Solution

1. Step 1: Check Java method signature syntax

   Java methods must specify access modifier, return type, method name, and parameter types.

2. Step 2: Validate each option

   public static int findFloor(int[] arr, int target) is correct: public static int findFloor(int[] arr, int target). int findFloor(int arr[], target) misses access modifier and parameter type for target. static int findFloor(int[] arr, int target) throws Exception unnecessarily throws Exception. public int findFloor(int[] arr, int target, int size) has extra parameter 'size' not needed.

3. Final Answer:

   public static int findFloor(int[] arr, int target) -> Option D

4. Quick Check:

   Correct Java method signature = public static int findFloor(int[] arr, int target) [OK]

Hint: Java method needs access modifier, return type, parameters [OK]

Common Mistakes:

• Omitting access modifier
• Missing parameter types
• Adding unnecessary throws clause

3. Given the sorted array int[] arr = {1, 3, 5, 7, 9} and target = 6, what is the floor and ceil of 6?

medium

A. Floor = 7, Ceil = 9

B. Floor = 3, Ceil = 5

C. Floor = 5, Ceil = 7

D. Floor = 6, Ceil = 6

Solution

1. Step 1: Identify floor of 6 in array

   Floor is greatest element ≤ 6. Elements ≤ 6 are 1, 3, 5. Greatest is 5.

2. Step 2: Identify ceil of 6 in array

   Ceil is smallest element ≥ 6. Elements ≥ 6 are 7, 9. Smallest is 7.

3. Final Answer:

   Floor = 5, Ceil = 7 -> Option C

4. Quick Check:

   Floor ≤ 6 = 5, Ceil ≥ 6 = 7 [OK]

Hint: Floor ≤ target, ceil ≥ target; pick closest values [OK]

Common Mistakes:

• Choosing floor greater than target
• Choosing ceil less than target
• Assuming target must be in array

4. Consider this Java method to find floor in a sorted array:

public static int findFloor(int[] arr, int target) {
    int low = 0, high = arr.length - 1;
    int floor = -1;
    while (low <= high) {
        int mid = (low + high) / 2;
        if (arr[mid] == target) return arr[mid];
        else if (arr[mid] < target) {
            floor = arr[mid];
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    return floor;
}

What is the bug if the array is empty?

medium

A. Returns -1 correctly as floor does not exist

B. Throws ArrayIndexOutOfBoundsException at mid calculation

C. Returns 0 incorrectly as floor

D. Infinite loop occurs

Solution

1. Step 1: Analyze behavior with empty array

   If array is empty, arr.length = 0, so high = -1. Condition low <= high is false initially, so loop never runs.

2. Step 2: Check return value when loop doesn't run

   Variable floor initialized to -1 and returned as is, indicating no floor found.

3. Final Answer:

   Returns -1 correctly as floor does not exist -> Option A

4. Quick Check:

   Empty array returns -1 floor [OK]

Hint: Check loop condition before accessing array [OK]

Common Mistakes:

• Assuming mid calculation causes error on empty array
• Expecting exception instead of -1 return
• Missing initialization of floor variable

5. You have a sorted array int[] arr = {2, 4, 6, 8, 10}. You want to find the floor and ceil for target = 1 and target = 11. What are the correct floor and ceil values for these targets?

hard

A. For 1: Floor = -1, Ceil = 2; For 11: Floor = -1, Ceil = -1

B. For 1: Floor = -1, Ceil = 2; For 11: Floor = 10, Ceil = -1

C. For 1: Floor = -1, Ceil = -1; For 11: Floor = 10, Ceil = 10

D. For 1: Floor = 2, Ceil = -1; For 11: Floor = -1, Ceil = 10

Solution

1. Step 1: Find floor and ceil for target = 1

   Floor is greatest element ≤ 1. No elements ≤ 1, so floor = -1 (not found). Ceil is smallest element ≥ 1, which is 2.

2. Step 2: Find floor and ceil for target = 11

   Floor is greatest element ≤ 11, which is 10. Ceil is smallest element ≥ 11, none exists, so ceil = -1.

3. Final Answer:

   For 1: Floor = -1, Ceil = 2; For 11: Floor = 10, Ceil = -1 -> Option B

4. Quick Check:

   Floor and ceil outside array bounds handled with -1 [OK]

Hint: Floor or ceil missing means return -1 for that value [OK]

Common Mistakes:

• Returning array ends incorrectly as floor or ceil
• Confusing floor and ceil for out-of-bound targets
• Assuming floor or ceil always exists