Array Access and Update at Index in DSA Java - Time & Space Complexity

Time Complexity: Array Access and Update at Index

O(1)

Understanding Time Complexity

We want to understand how fast we can get or change a value in an array by its position.

The question is: how does the time to access or update an element grow as the array gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int[] arr = new int[1000];

// Access element at index 500
int value = arr[500];

// Update element at index 500
arr[500] = 42;
    

This code accesses and updates a single element in the array by its index.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Direct access to an array element by index.
• How many times: Exactly once for each access or update.

How Execution Grows With Input

Accessing or updating an element by index takes the same amount of time no matter how big the array is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time stays constant even if the array size grows.

Final Time Complexity

Time Complexity: O(1)

This means accessing or updating an element by index takes the same fixed time regardless of array size.

Common Mistake

[X] Wrong: "Accessing an element by index takes longer if the array is bigger."

[OK] Correct: Arrays allow direct jumps to any position, so the time does not depend on size.

Interview Connect

Knowing that array access and update are constant time helps you choose the right data structure for fast lookups and changes.

Self-Check

"What if we had to search for a value instead of accessing by index? How would the time complexity change?"

Practice

1. What does the expression arr[2] do in a Java array named arr?

easy

A. Deletes the element at index 2

B. Adds a new element at index 2

C. Accesses the element at index 2 of the array

D. Returns the length of the array

Solution

1. Step 1: Understand array indexing

   In Java, arrays use zero-based indexing, so arr[2] accesses the third element.

2. Step 2: Identify the operation

   The expression reads the value stored at index 2 without modifying the array.

3. Final Answer:

   Accesses the element at index 2 of the array -> Option C

4. Quick Check:

   arr[2] means get element at index 2 [OK]

Hint: Remember arrays start at index 0, so arr[2] is third element [OK]

Common Mistakes:

• Thinking arr[2] adds or deletes elements
• Confusing index with array length
• Assuming indexing starts at 1

2. Which of the following is the correct syntax to update the element at index 1 of an integer array nums to 10?

easy

A. nums(1) = 10;

B. nums[1] = 10;

C. nums{1} = 10;

D. nums.1 = 10;

Solution

1. Step 1: Recall Java array update syntax

   In Java, array elements are accessed and updated using square brackets: array[index] = value;

2. Step 2: Match correct syntax

   Only nums[1] = 10; uses correct brackets and assignment.

3. Final Answer:

   nums[1] = 10; -> Option B

4. Quick Check:

   Use square brackets for array index update [OK]

Hint: Use square brackets [] to access or update array elements [OK]

Common Mistakes:

• Using parentheses () instead of brackets []
• Using curly braces {} which are invalid for arrays
• Trying to access with dot notation

3. What will be the output of the following Java code?

int[] arr = {5, 10, 15, 20};
arr[2] = 25;
System.out.println(arr[2]);

medium

A. 25

B. 15

C. 20

D. 10

Solution

1. Step 1: Understand initial array values

   The array arr starts as [5, 10, 15, 20].

2. Step 2: Update element at index 2

   We set arr[2] = 25; changing the third element from 15 to 25.

3. Step 3: Print updated element

   System.out.println(arr[2]); prints the updated value 25.

4. Final Answer:

   25 -> Option A

5. Quick Check:

   arr[2] updated to 25, so output is 25 [OK]

Hint: Remember updates change the element before printing [OK]

Common Mistakes:

• Printing old value before update
• Confusing index 2 with index 3
• Assuming array is unchanged

4. Identify the error in the following code snippet:

int[] numbers = {1, 2, 3};
numbers[3] = 4;

medium

A. ArrayIndexOutOfBoundsException at runtime

B. Syntax error due to missing semicolon

C. Compilation error: invalid array declaration

D. No error, code runs fine

Solution

1. Step 1: Check array size and valid indices

   The array numbers has length 3, valid indices are 0, 1, 2.

2. Step 2: Analyze index used for update

   Attempting numbers[3] = 4; accesses index 3, which is out of bounds.

3. Step 3: Identify error type

   This causes a runtime ArrayIndexOutOfBoundsException.

4. Final Answer:

   ArrayIndexOutOfBoundsException at runtime -> Option A

5. Quick Check:

   Index 3 invalid for length 3 array [OK]

Hint: Array indices go from 0 to length-1 only [OK]

Common Mistakes:

• Assuming index 3 is valid for length 3 array
• Confusing compile-time and runtime errors
• Ignoring zero-based indexing

5. Given the array int[] data = {2, 4, 6, 8, 10};, which code snippet correctly doubles the value at index 3 and then prints the entire array?

hard

A. data[4] = data[4] * 2;
for(int i = 0; i < data.length; i++) {
System.out.print(data[i] + " ");
}

B. data[3] *= 2;
for(int i = 1; i <= data.length; i++) {
System.out.print(data[i] + " ");
}

C. data[3] = data[3] + 2;
for(int i = 0; i < data.length; i++) {
System.out.print(data[i] + " ");
}

D. data[3] = data[3] * 2;
for(int i = 0; i < data.length; i++) {
System.out.print(data[i] + " ");
}

Solution

1. Step 1: Identify correct index and operation

   Index 3 corresponds to the fourth element (value 8). Doubling means multiplying by 2.

2. Step 2: Check loop correctness for printing

   The loop must run from 0 to data.length - 1 to print all elements without error.

3. Step 3: Verify each option

   data[3] = data[3] * 2; for(int i = 0; i < data.length; i++) { System.out.print(data[i] + " "); } correctly doubles data[3] and loops from 0 to length-1. data[3] *= 2; for(int i = 1; i <= data.length; i++) { System.out.print(data[i] + " "); } uses invalid loop bounds and will cause runtime error. data[3] = data[3] + 2; for(int i = 0; i < data.length; i++) { System.out.print(data[i] + " "); } adds 2 instead of doubling. data[4] = data[4] * 2; for(int i = 0; i < data.length; i++) { System.out.print(data[i] + " "); } doubles wrong index (4).

4. Final Answer:

   data[3] = data[3] * 2; for(int i = 0; i < data.length; i++) { System.out.print(data[i] + " "); } -> Option D

5. Quick Check:

   Correct index and loop bounds ensure proper update and print [OK]

Hint: Use index 3 for 4th element; loop from 0 to length-1 [OK]

Common Mistakes:

• Using wrong index for update
• Incorrect loop bounds causing errors
• Adding instead of multiplying