Floor and Ceil in Sorted Array in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Find floor and ceil of 7 in a sorted array

Given the sorted array [1, 3, 5, 7, 9], what is the floor and ceil of 7?

DSA Go

arr := []int{1, 3, 5, 7, 9}
num := 7
floor, ceil := -1, -1
for _, v := range arr {
    if v <= num {
        floor = v
    }
    if v >= num && ceil == -1 {
        ceil = v
    }
}
fmt.Printf("Floor: %d, Ceil: %d", floor, ceil)

A Floor: 5, Ceil: 7

B Floor: 7, Ceil: 9

C Floor: 7, Ceil: 7

D Floor: 5, Ceil: 9

💡 Hint

Floor is the greatest element less than or equal to the number; ceil is the smallest element greater than or equal to the number.

Since 7 is present in the array, both floor and ceil are 7.

❓ Predict Output

intermediate

Floor and ceil for a number not in the array

What is the floor and ceil of 6 in the sorted array [1, 3, 5, 7, 9]?

DSA Go

arr := []int{1, 3, 5, 7, 9}
num := 6
floor, ceil := -1, -1
for _, v := range arr {
    if v <= num {
        floor = v
    }
    if v >= num && ceil == -1 {
        ceil = v
    }
}
fmt.Printf("Floor: %d, Ceil: %d", floor, ceil)

A Floor: 7, Ceil: 9

B Floor: 5, Ceil: 7

C Floor: 5, Ceil: 6

D Floor: 6, Ceil: 7

💡 Hint

Floor is the greatest element less than or equal to the number; ceil is the smallest element greater than or equal to the number.

6 is not in the array. The greatest element less than 6 is 5 (floor), and the smallest element greater than 6 is 7 (ceil).

🧠 Conceptual

advanced

Behavior when number is smaller than all elements

If the number is smaller than all elements in a sorted array, what will be the floor and ceil?

A Floor: -1 (no floor), Ceil: smallest element in array

B Floor: smallest element, Ceil: -1 (no ceil)

C Floor and Ceil both are -1

D Floor and Ceil both are the smallest element

💡 Hint

Floor must be less than or equal to the number; if none exists, floor is -1.

If the number is smaller than all elements, no floor exists (-1), but ceil is the smallest element.

🧠 Conceptual

advanced

Floor and ceil when number is greater than all elements

If the number is greater than all elements in a sorted array, what will be the floor and ceil?

A Floor: largest element in array, Ceil: -1 (no ceil)

B Floor: -1 (no floor), Ceil: largest element

C Floor and Ceil both are largest element

D Floor and Ceil both are -1

💡 Hint

Ceil must be greater than or equal to the number; if none exists, ceil is -1.

If the number is greater than all elements, floor is the largest element, but no ceil exists (-1).

🔧 Debug

expert

Identify the error in floor and ceil calculation code

What error does the following Go code produce when finding floor and ceil? arr := []int{2, 4, 6, 8} num := 5 floor, ceil := -1, -1 for _, v := range arr { if v < num { floor = v } if v > num && ceil == -1 { ceil = v } } fmt.Printf("Floor: %d, Ceil: %d", floor, ceil)

DSA Go

arr := []int{2, 4, 6, 8}
num := 5
floor, ceil := -1, -1
for _, v := range arr {
    if v < num {
        floor = v
    }
    if v > num && ceil == -1 {
        ceil = v
    }
}
fmt.Printf("Floor: %d, Ceil: %d", floor, ceil)

A Floor: -1, Ceil: 6

B Floor: 5, Ceil: 6

C Floor: 4, Ceil: -1

D Floor: 4, Ceil: 6

💡 Hint

Check the comparison operators used for floor and ceil conditions.

The code uses '<' and '>' which exclude equality. Since 5 is not in the array, floor is the greatest element less than 5 (4), and ceil is the smallest element greater than 5 (6).

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