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

Floor and Ceil in Sorted Array

📖 Scenario: You are working with 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 given number (floor) and the closest house number that is greater than or equal to that number (ceil).

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

📋 What You'll Learn

Create a sorted array of integers called houses with exact values

Create an integer variable called target for the number to find floor and ceil

Write a function findFloorAndCeil that takes houses and target and returns two integers: 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 need closest matches in sorted data.

💼 Career

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

1

Create the sorted array of house numbers

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

DSA Go

# Create the sorted array houses with the exact values
# Your code here

Hint

Use houses := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91} to create the array.

2

Set the target number to find floor and ceil

Create an integer variable called target and set it to 20

DSA Go

package main

func main() {
    houses := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    // Create target variable and set to 20
    // Your code here
}

Hint

Use target := 20 to create the variable.

3

Write the function to find floor and ceil

Write a function called findFloorAndCeil that takes houses []int and target int and returns two integers: floor and ceil. Use a simple loop to find the floor (largest number ≤ target) and ceil (smallest number ≥ target).

DSA Go

package main

func findFloorAndCeil(houses []int, target int) (int, int) {
    // Your code here
}

func main() {
    houses := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    target := 20
}

Hint

Loop through houses. Update floor if house ≤ target. Set ceil to first house ≥ target and break.

4

Print the floor and ceil values

Call findFloorAndCeil with houses and target. Print the floor and ceil values in the format: Floor: X, Ceil: Y

DSA Go

package main

func findFloorAndCeil(houses []int, target int) (int, int) {
    floor := -1
    ceil := -1
    for _, house := range houses {
        if house = target && ceil == -1 {
            ceil = house
            break
        }
    }
    return floor, ceil
}

func main() {
    houses := []int{2, 5, 8, 12, 16, 23, 38, 56, 72, 91}
    target := 20
    // Call findFloorAndCeil and print the result
    // Your code here
}

Hint

Use floor, ceil := findFloorAndCeil(houses, target) and fmt.Printf("Floor: %d, Ceil: %d\n", floor, ceil).

Practice

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

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 the floor definition

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

2. Step 2: Compare options with definition

   The greatest element less than or equal to the number matches this definition exactly, while 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 ≤ number, pick greatest such element [OK]

Common Mistakes:

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

2. Which Go code snippet correctly declares a function to find the floor in a sorted array?

easy

A. func floor(arr int[], x int) int { /* code */ }

B. func floor(arr []int, x int) int { /* code */ }

C. function floor(arr []int, x int) int { /* code */ }

D. func floor(arr []int, x int) void { /* code */ }

Solution

1. Step 1: Check Go function syntax

   In Go, functions are declared with func, parameter types follow names, and return type is after parameters.

2. Step 2: Validate each option

   func floor(arr []int, x int) int { /* code */ } uses correct Go syntax: func floor(arr []int, x int) int. func floor(arr int[], x int) int { /* code */ } uses incorrect array syntax, C uses wrong keyword, D has wrong return type.

3. Final Answer:

   func floor(arr []int, x int) int { /* code */ } -> Option B

4. Quick Check:

   Go func syntax = func floor(arr []int, x int) int { /* code */ } [OK]

Hint: Go arrays use []type, func keyword, return type after params [OK]

Common Mistakes:

• Using 'function' keyword instead of 'func'
• Incorrect array type syntax
• Wrong return type declaration

3. What is the output of the following Go code snippet?

arr := []int{1, 3, 5, 7, 9}
x := 6
floor := -1
for _, val := range arr {
    if val <= x {
        floor = val
    } else {
        break
    }
}
fmt.Println(floor)

medium

A. 5

B. 6

C. 7

D. -1

Solution

1. Step 1: Trace the loop over array elements

   The loop checks each element: 1 ≤ 6 (floor=1), 3 ≤ 6 (floor=3), 5 ≤ 6 (floor=5), 7 ≤ 6? No, break loop.

2. Step 2: Determine final floor value

   Last floor assigned is 5, so printed output is 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Floor of 6 in arr = 5 [OK]

Hint: Floor is last element ≤ x before break [OK]

Common Mistakes:

• Assuming floor equals x if not present
• Not breaking loop early
• Confusing floor with ceil

4. Identify the bug in this Go code to find the ceil of x in a sorted array arr:

func ceil(arr []int, x int) int {
    ceil := -1
    for _, val := range arr {
        if val >= x {
            ceil = val
        }
    }
    return ceil
}

medium

A. It uses wrong comparison operator

B. It initializes ceil with -1 incorrectly

C. It returns ceil before loop ends

D. It does not break after finding first valid ceil

Solution

1. Step 1: Analyze loop behavior for ceil

   The loop updates ceil whenever val ≥ x, but does not stop after first valid ceil, so it ends with the last such value, which may not be the smallest ceil.

2. Step 2: Identify correct fix

   To find the smallest ceil, the loop should break immediately after first val ≥ x is found.

3. Final Answer:

   It does not break after finding first valid ceil -> Option D

4. Quick Check:

   Ceil needs first ≥ x, break loop [OK]

Hint: Break loop on first val ≥ x for correct ceil [OK]

Common Mistakes:

• Not breaking loop early
• Confusing ceil with floor logic
• Incorrect initialization of ceil

5. Given a sorted array arr := []int{2, 4, 6, 8, 10} and a number x = 5, write a Go function that returns both floor and ceil of x. What is the correct output of floor and ceil?

hard

A. Floor: -1, Ceil: -1

B. Floor: 6, Ceil: 4

C. Floor: 4, Ceil: 6

D. Floor: 5, Ceil: 5

Solution

1. Step 1: Find floor of 5 in arr

   Floor is greatest element ≤ 5. Elements ≤ 5 are 2 and 4, greatest is 4.

2. Step 2: Find ceil of 5 in arr

   Ceil is smallest element ≥ 5. Elements ≥ 5 are 6, 8, 10, smallest is 6.

3. Final Answer:

   Floor: 4, Ceil: 6 -> Option C

4. Quick Check:

   Floor ≤ x ≤ Ceil = 4 ≤ 5 ≤ 6 [OK]

Hint: Floor ≤ x ≤ Ceil in sorted array [OK]

Common Mistakes:

• Swapping floor and ceil values
• Assuming floor or ceil equals x if not present
• Returning -1 when valid floor or ceil exists