Sort Four Numbers in Descending Order

🧠 Understanding the Elimination Logic

Why This Approach is Clever:

// Traditional approach: Compare all pairs (6 comparisons)
// a vs b, a vs c, a vs d, b vs c, b vs d, c vs d

// Elimination approach: Find extremes, then exclude them
// Step 1: Find largest (2 comparisons in nested max)
// Step 2: Find smallest (2 comparisons in nested min)
// Step 3: Find middle values by elimination

// This is more intuitive and easier to understand!

How Elimination Works:

// Given: a=2, b=0, c=4, d=1
// max1 = 4, max4 = 0

// Finding max2:
if ((a != max1 && a != max4))  // Is a NOT 4 AND NOT 0?
    max2 = a;                        // Yes! a=2 ✓

// Finding max3:
if ((a != max1 && a != max4 && a != max2))  // Is a NOT 4, 0, or 2?
    max3 = a;                                     // No, a=2 is max2
else if ((b != max1 && b != max4 && b != max2)) // Is b NOT 4, 0, or 2?
    max3 = b;                                     // No, b=0 is max4
else if ((c != max1 && c != max4 && c != max2)) // Is c NOT 4, 0, or 2?
    max3 = c;                                     // No, c=4 is max1
else
    max3 = d;                                     // Yes! d=1 ✓

🔢 Understanding Nested min() and max()

Finding the Largest of Four Numbers:

// max() only works with 2 arguments at a time
// To find max of 4 numbers: nest the calls

max1 = max(max(a, b), max(c, d));
       ↓
       max(  max(a,b)  ,  max(c,d)  )
           ↓              ↓
       max of first   max of second
       two numbers    two numbers
           ↓
       Final: max of both results

// Example: a=2, b=0, c=4, d=1
max1 = max(max(2, 0), max(4, 1))
     = max(2, 4)
     = 4 ✓

Finding the Smallest of Four Numbers:

// Same logic with min()
max4 = min(min(a, b), min(c, d));

// Example: a=2, b=0, c=4, d=1
max4 = min(min(2, 0), min(4, 1))
     = min(0, 1)
     = 0 ✓

Why Variable Names are max1, max2, max3, max4:

• max1: 1st position in descending order (largest)
• max2: 2nd position in descending order (2nd largest)
• max3: 3rd position in descending order (3rd largest)
• max4: 4th position in descending order (smallest)

🔍 Handling Edge Cases

Case 1: All Numbers Equal

// Input: 5 5 5 5
max1 = 5  // largest
max4 = 5  // smallest (same as largest!)

// Finding max2: none of a,b,c,d satisfy (x != 5 && x != 5)
// Falls through to else: max2 = d = 5 ✓

// Finding max3: similarly falls through to else: max3 = 5 ✓

// Output: 5 > 5 > 5 > 5

Case 2: Two Numbers Equal

// Input: 3 3 1 5
max1 = 5
max4 = 1

// Both a and b are 3 (neither is max1 or max4)
// First if catches: max2 = a = 3
// Second if-else finds: max3 = b = 3

// Output: 5 > 3 > 3 > 1 ✓

Case 3: Negative Numbers

// Input: -5 -10 -2 -8
max1 = max(max(-5, -10), max(-2, -8))
     = max(-5, -2)
     = -2  // least negative = largest ✓

max4 = min(min(-5, -10), min(-2, -8))
     = min(-10, -8)
     = -10 // most negative = smallest ✓

// Output: -2 > -5 > -8 > -10

🔑 Key Concepts Learned

• Elimination Strategy: Finding values by excluding what they're NOT
• Nested Functions: Using function results as arguments to other functions
• Descending Order: Arranging from largest to smallest
• Compound Conditions: Using && to check multiple conditions
• If-Else Chains: Sequential checking until a condition matches
• Algorithm Library: Using min() and max() from <algorithm>

🔄 Alternative Sorting Approaches

Using std::sort() (Professional Approach):

#include <iostream>
#include <algorithm>
using namespace std;

int main() {
    long long arr[4];
    for(int i=0; i<4; i++) cin >> arr[i];
    
    sort(arr, arr+4, greater<long long>()); // descending
    
    cout << arr[0] << " > " << arr[1] << " > " 
         << arr[2] << " > " << arr[3] << endl;
    
    return 0;
}

↕️ Ascending vs Descending Order

🌍 Real-world Applications

• Leaderboards: Ranking players by score (highest first)
• Product Sorting: "Price: High to Low" in e-commerce
• News Feeds: Most recent posts first (descending by timestamp)
• Stock Markets: Top gainers/losers (descending by percentage)
• Search Results: Most relevant results first (descending by relevance score)
• Grade Reports: Highest performing students first
• Sales Reports: Best-selling products at the top
• Ranking Systems: Any system that needs "best first" ordering

🎯 What You'll Learn

• Understanding elimination-based sorting strategies
• Working with nested min() and max() functions
• Implementing descending order sorting
• Handling edge cases (equal values, negatives)
• Using compound logical conditions (&&)
• Building if-else chains for value assignment
• Understanding when to use elimination vs comparison
• Comparing manual logic with library functions

💪 Extension Challenges

• Level 1: Modify to sort in ascending order instead
• Level 2: Sort 5 numbers using the same elimination technique
• Level 3: Implement using only if-else (no min/max functions)
• Level 4: Rewrite using arrays and std::sort()
• Level 5: Add median calculation (average of max2 and max3)
• Level 6: Implement bubble sort for 4 numbers
• Level 7: Create a function that sorts N numbers using elimination
• Bonus: Compare execution time of different sorting methods

💡 Practice Tips

• Trace by Hand: Write out the values and elimination steps on paper
• Test Edge Cases: All equal, two equal, negatives, zeros
• Understand Nesting: Draw diagrams showing how nested max/min work
• Compare Methods: Implement using different approaches and compare
• Use Debugger: Step through to see how max2 and max3 are found
• Modify Output: Try different separators (commas, arrows, etc.)
• Experiment: What happens if you swap max1 and max4 in output?
• Learn std::sort(): Research how to use the standard sorting algorithm