Write a program to swap two numbers without using a third variable.

Exercises · Q15

Q. Write a program to swap two numbers without using a third variable.

Sikkim CbseNCERTSubjective· 2mImportance★★★★★est

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Concept understanding — Variable Assignment Order

Variable Assignment Order — First Principles

Imagine you are following a recipe. The recipe says: "Take the number of eggs, call it $x$ . Then take $x$ , add 2, and call the result $y$ ." You would never dream of using $y$ before you have defined $x$ — that would be nonsense. Variable assignment order is simply the rule that a variable must be given a value before it can be used in any expression that defines another variable.

The Intuition

Think of a variable as a labelled box. You cannot take something out of a box that is empty. When you write:

x = 5

y = x + 3

you first put the number 5 into box $x$ , then you look into box $x$ , take out the 5, add 3, and put the result (8) into box $y$ . The order is: define first, use second.

Now consider what happens if you reverse the order:

y = x + 3

x = 5

At the moment you try to compute $y$ , box $x$ is empty. The expression $x + 3$ has no meaning — it is like asking "what is nothing plus 3?" In most programming languages and in mathematical reasoning, this is an error. The variable $x$ has not yet been assigned.

The Precise Statement

Important

Variable Assignment Order: In any sequence of assignments (or definitions), a variable must appear on the left-hand side of an assignment (i.e., be defined) before it appears on the right-hand side of any later assignment (i.e., before it is used). Violating this order produces an undefined variable error.

Formally, for a sequence of statements $S_1, S_2, \dots, S_n$ , if a variable $v$ is used in $S_k$ (on the right-hand side), then there must exist some $S_j$ with $j < k$ where $v$ appears on the left-hand side.

Why This Matters in Exams

In Indian board exams (CBSE, ICSE, state boards), especially in Computer Science and Mathematics, you will encounter questions that test this concept in two ways:

Tracing code: Given a sequence of assignments, you must compute the final values. The order is everything.
Spotting errors: A question may present a jumbled or incorrect sequence and ask you to identify why it fails.

A Worked Example

Consider this sequence:

a = 10
b = a + c
c = 5

At the second line, $c$ is used but has never been assigned. This violates assignment order. The correct order would be:

a = 10
c = 5
b = a + c

Now $b$ becomes $10 + 5 = 15$ .

A Common Pitfall …

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Python can swap in one statement with simultaneous (tuple) assignment — both right-hand values are evaluated first, then assigned together:

num1 = int(input("Enter first number: "))
num2 = int(input("Enter second number: "))
print("Before swapping:", num1, num2)
num1, num2 = num2, num1
print("After swapping: ", num1, num2)

Sample run (5 and 10):

Before swapping: 5 10
After swapping:  10 5
``` …

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Python's simultaneous assignment num1, num2 = num2, num1 swaps two variables in a single statement, no helper variable needed — 5 and 10 become 10 and 5.

The concept: in a tuple (simultaneous) assignment, Python evaluates the entire right-hand side first — capturing the current values (num2, num1) — and only then assigns them to the left-hand names. Nothing is overwritten prematurely, so no temporary variable is needed.

# Swap two numbers WITHOUT a third variable
num1 = int(input("Enter first number: "))
num2 = int(input("Enter second number: "))
print("Before swapping:", num1, num2)

num1, num2 = num2, num1   # simultaneous assignment

print("After swapping: ", num1, num2)

Sample run:

Enter first number: 5
Enter second number: 10
Before swapping: 5 10
After swapping:  10 5

An alternative that also avoids a third variable — the arithmetic method — is worth knowing for exams:

num1 = num1 + num2   # num1 now holds the sum (15)
num2 = num1 - num2   # 15 - 10 = 5  -> old num1
num1 = num1 - num2   # 15 - 5  = 10 -> old num2
``` …

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Q.Write a program to swap two numbers without using a third variable.

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