5. Find Minimum of Two Numbers

Using if-else to find minimum:

if (a < b)
  min = a;
else
  min = b;

How it works:

1. Compare two numbers: a < b
2. If TRUE → a is smaller, store it in min
3. If FALSE → b is smaller or equal, store it in min

✅ Why learn this approach?

• Builds fundamental understanding of comparison logic
• Essential for interviews and problem-solving
• Forms the foundation for more complex algorithms
• You understand exactly what's happening

💡 Edge case: When both numbers are equal (a == b), either can be the minimum. Our else handles this by choosing b.

Using the built-in min() function:

#include <cmath>
cout << "Minimum is " << min(a, b);

How it works:

The min(a, b) function takes two values and returns the smaller one.

min(10, 200) → Returns 10

min(50, 50) → Returns 50

✅ Advantages:

• Shorter, more concise code
• Less chance of making mistakes
• Optimized by the compiler
• Industry-standard approach

❌ Disadvantage:

• You don't build the comparison logic yourself
• Less understanding of how it works internally

Alternative solution using min():

// Commented line in our code:
cout << "Minimum of " << a << " and " << b << " is " << min(a,b);

The <cmath> library provides mathematical functions and constants.

To use it:

#include <cmath>

Common functions in <cmath>:

• min(a, b) → Returns minimum of two values
• max(a, b) → Returns maximum of two values
• abs(x) → Returns absolute value (removes negative sign)
• pow(x, y) → Returns x raised to power y (x^y)
• sqrt(x) → Returns square root of x
• ceil(x) → Rounds up to nearest integer
• floor(x) → Rounds down to nearest integer
• round(x) → Rounds to nearest integer

Examples:

• min(5, 10) → 5
• max(5, 10) → 10
• abs(-25) → 25
• pow(2, 3) → 8 (2³)
• sqrt(16) → 4
• ceil(4.2) → 5
• floor(4.8) → 4
• round(4.5) → 5

Use Logic-Building Approach when:

• 🎓 Learning fundamentals and building problem-solving skills
• 📝 In interviews where you need to show your thinking process
• 🧩 Solving complex problems where no built-in function exists
• 🔍 You need to understand exactly how something works

Use Library Functions when:

• ⚡ Building production code (faster, more reliable)
• 🏗️ Working on real-world projects with tight deadlines
• ✅ The logic is straightforward and well-tested
• 📦 You want cleaner, more maintainable code

💡 Best practice: Learn the logic first (like we're doing!), then use library functions for efficiency. This way you understand what's happening under the hood.

Example with a=10, b=200:

1. Declare variables: long long a, b, min;
2. Read input: a = 10, b = 200
3. Check condition: if (10 < 200) → TRUE
4. Execute: min = a; → min = 10
5. Print: "Minimum of 10 and 200 is 10"

Example with a=100, b=20:

1. Declare variables: long long a, b, min;
2. Read input: a = 100, b = 20
3. Check condition: if (100 < 20) → FALSE
4. Go to else: min = b; → min = 20
5. Print: "Minimum of 100 and 20 is 20"

Example with a=50, b=50:

1. Declare variables: long long a, b, min;
2. Read input: a = 50, b = 50
3. Check condition: if (50 < 50) → FALSE (equal, not less)
4. Go to else: min = b; → min = 50
5. Print: "Minimum of 50 and 50 is 50" ✅

You might notice we include <cmath> but don't use it in the solution.

Reason:

This demonstrates that there are two approaches to solving the problem:

1. Logic-based approach (what we used) - Better for learning
2. Library function approach (commented out) - More practical

The commented line shows the alternative:

// cout << "Minimum of " << a << " and " << b << " is " << min(a,b);

✅ Including the library prepares you to use min(a, b) if needed, but we choose the manual approach to build stronger problem-solving skills.

💡 In competitive programming or interviews, showing you can build the logic manually is often more impressive than just using a library function!