Union basics in C++ - Time & Space Complexity

Time Complexity: Union basics

O(1)

Understanding Time Complexity

When working with unions in C++, it's helpful to understand how operations on them scale as data changes.

We want to see how the time to access or modify union members grows with input size.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

union Data {
    int i;
    float f;
    char str[20];
};

void setInt(Data &d, int value) {
    d.i = value;
}

int getInt(const Data &d) {
    return d.i;
}
    

This code defines a union with different types and functions to set and get an integer value.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Direct assignment and access of union members.
• How many times: Each operation happens once per function call, no loops or recursion.

How Execution Grows With Input

Accessing or setting a union member takes the same time regardless of input size.

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

Pattern observation: The time stays constant no matter how big the input is.

Final Time Complexity

Time Complexity: O(1)

This means accessing or setting a union member takes the same amount of time no matter what.

Common Mistake

[X] Wrong: "Accessing different union members takes longer as the union grows."

[OK] Correct: A union shares memory for all members, so accessing any member is a simple direct operation that does not depend on union size.

Interview Connect

Understanding that unions provide constant-time access helps you explain memory-efficient data handling clearly and confidently.

Self-Check

What if we added a loop to copy each character of the union's string member? How would the time complexity change?

Practice

1. What is the main characteristic of a union in C++?

easy

A. All members share the same memory location

B. Each member has its own separate memory

C. Unions can only store integers

D. Unions automatically initialize all members

Solution

1. Step 1: Understand union memory sharing

   A union allocates one shared memory block for all its members, so they overlap.

2. Step 2: Compare with other data structures

   Unlike structs, unions do not allocate separate memory for each member.

3. Final Answer:

   All members share the same memory location -> Option A

4. Quick Check:

   Union memory sharing = All members share the same memory location [OK]

Hint: Remember: union members overlap in memory [OK]

Common Mistakes:

• Thinking each member has separate memory
• Assuming unions initialize all members
• Believing unions only store one data type

2. Which of the following is the correct syntax to define a union named Data with an int and a float member?

easy

A. union Data = { int i; float f; };

B. struct Data { int i; float f; };

C. union Data ( int i; float f; );

D. union Data { int i; float f; };

Solution

1. Step 1: Recall union declaration syntax

   Unions are declared using the keyword union, followed by the name and braces with members inside.

2. Step 2: Check each option

   union Data { int i; float f; }; uses correct syntax with braces and semicolons. Options B, C, and D have syntax errors or wrong keywords.

3. Final Answer:

   union Data { int i; float f; }; -> Option D

4. Quick Check:

   Correct union syntax = union Data { int i; float f; }; [OK]

Hint: Use 'union Name { members; };' syntax [OK]

Common Mistakes:

• Using struct keyword instead of union
• Using parentheses instead of braces
• Assigning values in declaration

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

union Number {
  int i;
  float f;
};

Number n;
n.i = 65;
std::cout << n.f << std::endl;

medium

A. A floating-point number representing the bits of 65

B. 65.0

C. 0

D. Compilation error

Solution

1. Step 1: Understand union memory sharing and type punning

   Assigning to n.i sets the bits of the union. Reading n.f interprets those bits as a float.

2. Step 2: Predict output

   The bits for integer 65 do not represent 65.0 as a float, so output is a float number corresponding to those bits, not 65.0.

3. Final Answer:

   A floating-point number representing the bits of 65 -> Option A

4. Quick Check:

   Union type punning = A floating-point number representing the bits of 65 [OK]

Hint: Union shares bits; int bits read as float show strange value [OK]

Common Mistakes:

• Expecting output 65.0
• Assuming union members hold independent values
• Thinking code causes compile error

4. Identify the error in this union usage:

union Data {
  int i;
  char c;
};

Data d;
d.i = 100;
d.c = 'A';
std::cout << d.i << std::endl;

medium

A. Output will be 100

B. Error: Cannot assign to union members separately

C. No error; output will be 65

D. Compilation error due to missing semicolon

Solution

1. Step 1: Understand union member assignment

   Assigning to d.i then to d.c overwrites the same memory because union members share memory.

2. Step 2: Determine final value of d.i

   After d.c = 'A', the first byte of d.i is set to ASCII 65, so printing d.i shows 65.

3. Final Answer:

   No error; output will be 65 -> Option C

4. Quick Check:

   Union last write wins = No error; output will be 65 [OK]

Hint: Last assigned union member overwrites memory [OK]

Common Mistakes:

• Thinking union members hold values independently
• Expecting output 100 after assigning 'A'
• Assuming syntax error

5. You want to store either an int, a float, or a char in the same memory space efficiently. Which union definition and usage correctly allows this, and how do you safely read the stored value?

hard

A. union Value { int i; float f; char c; }; Value v; v.i = 10; std::cout << v.c << std::endl;

B. union Value { int i; float f; char c; }; Value v; v.f = 3.14f; std::cout << v.f << std::endl;

C. union Value { int i; float f; char c; }; Value v; v.c = 'Z'; std::cout << v.i << std::endl;

D. union Value { int i; float f; char c; }; Value v; std::cout << v.i << std::endl;

Solution

1. Step 1: Check union definition and assignment

   union Value { int i; float f; char c; }; Value v; v.f = 3.14f; std::cout << v.f << std::endl; defines a union with int, float, char and assigns a float value correctly.

2. Step 2: Verify safe reading of stored value

   union Value { int i; float f; char c; }; Value v; v.f = 3.14f; std::cout << v.f << std::endl; reads the same member v.f that was assigned, ensuring correct interpretation.

3. Step 3: Analyze other options

   Other options either assign to one member and read a different one, leading to unexpected values, or read uninitialized memory.

4. Final Answer:

   union Value { int i; float f; char c; }; Value v; v.f = 3.14f; std::cout << v.f << std::endl; -> Option B

5. Quick Check:

   Read the same union member you wrote [OK]

Hint: Always read the union member you last wrote [OK]

Common Mistakes:

• Reading a different member than assigned
• Using uninitialized union members
• Assuming union members hold independent values