EX_03/powerset/README.md

Powerset Exercise - Simple Explanation 🧮

What is this exercise about?

Imagine you have a bag of numbered balls, and you want to find all the different ways you can pick some balls so that the numbers on them add up to a specific target number.

This is exactly what the powerset exercise does!

Real-world example 🎯

Let's say you have these numbered balls: 1, 2, 3, 4, 5

And you want to find all the ways to pick balls that add up to 5.

Here are all the possible ways:

• Pick just ball 5 → 5 = 5 ✅
• Pick balls 1 and 4 → 1 + 4 = 5 ✅
• Pick balls 2 and 3 → 2 + 3 = 5 ✅

So the answer would be:

5
1 4
2 3

How does our program work? 🤖

Step 1: Understanding the input

When you run the program like this:

./powerset 5 1 2 3 4 5

• 5 is our target number (what we want the balls to add up to)
• 1 2 3 4 5 are our numbered balls

Step 2: The magic behind the scenes

Our program is like a smart robot that tries every possible combination:

1. Try no balls at all → sum = 0 (not 5, so skip)
2. Try just ball 1 → sum = 1 (not 5, so skip)
3. Try just ball 2 → sum = 2 (not 5, so skip)
4. Try just ball 3 → sum = 3 (not 5, so skip)
5. Try just ball 4 → sum = 4 (not 5, so skip)
6. Try just ball 5 → sum = 5 ✅ FOUND ONE!
7. Try balls 1 and 2 → sum = 3 (not 5, so skip)
8. Try balls 1 and 3 → sum = 4 (not 5, so skip)
9. Try balls 1 and 4 → sum = 5 ✅ FOUND ANOTHER!
10. Try balls 2 and 3 → sum = 5 ✅ FOUND ANOTHER!

...and so on until it tries every possible combination!

Code explanation 📝

The main parts of our code:

1. Reading the input (main function)

target = atoi(argv[1]);    // Get the target number (5 in our example)
set[i] = atoi(argv[i + 2]); // Get each ball number (1, 2, 3, 4, 5)

2. The smart robot (find_subsets function)

This function is like our robot that tries every combination:

// For each ball, we have 2 choices:
find_subsets(..., index + 1);           // Don't pick this ball
subset[subset_size] = set[index];       // Pick this ball
find_subsets(..., subset_size + 1, ...); // Continue with this ball included

3. Checking if we found a winner (print_subset)

if (current_sum == target)    // If the sum equals our target
    print_subset(subset, subset_size);  // Show this combination!

More examples to understand better 🎲

Example 1: Finding combinations that sum to 3

./powerset 3 1 0 2 4 5 3

What the robot finds:

• Ball 3 alone → 3 ✅
• Balls 0 and 3 → 0 + 3 = 3 ✅
• Balls 1 and 2 → 1 + 2 = 3 ✅
• Balls 1, 0, and 2 → 1 + 0 + 2 = 3 ✅

Output:

3
0 3
1 2
1 0 2

Example 2: Finding the empty combination

./powerset 0 1 -1

What the robot finds:

• No balls picked → sum = 0 ✅ (shows as empty line)
• Balls 1 and -1 → 1 + (-1) = 0 ✅

Output:

1 -1

(Notice the empty line at the top!)

Example 3: When nothing works

./powerset 7 3 8 2

What the robot finds:

• No combination of 3, 8, and 2 can make 7
• So nothing gets printed (empty output)

Important rules 📏

1. Order matters: We always keep balls in the same order as given

   • ✅ Correct: 1 4 (1 comes before 4 in input)
   • ❌ Wrong: 4 1 (this changes the order)

2. No duplicates: Each ball can only be used once per combination

3. Empty combination counts: If target is 0, picking no balls is valid!

How to use the program 🚀

1. Compile it:

   make
   

2. Run tests:

   make test
   

3. Try your own examples:

   ./powerset [target_number] [ball1] [ball2] [ball3] ...
   

4. Clean up:

   make clean    # Remove temporary files
   make fclean   # Remove everything
   

Fun challenge! 🎮

Try to predict what this will output before running it:

./powerset 6 1 2 3 4

Think about it:

• Which combinations of 1, 2, 3, 4 add up to 6?
• Remember: order matters and each number can only be used once!

Answer: 2 4 and 1 2 3 (because 2+4=6 and 1+2+3=6)

---

Now you understand how the powerset exercise works! It's like having a super-smart robot that can instantly try every possible combination of numbers to find the ones that add up to your target. Pretty cool, right? 🤖✨