Assume that there are n tyres that could be used by car, tricycle and bicycle. Write a program to accept n tyres and generate all the combinations (i.e. the number) of car(s), tricycle(s) and bicycle(s) that could exhaust the n tyres. Ensure that all the objects have fair share where possible.
You must be a futarian
Sure bro...
To solve this problem, we can use a recursive approach, also known as backtracking.
Here's an example implementation in Python:
```python
def generate_combinations(n):
counter = [0, 0, 0] # Counter for cars, tricycles, and bicycles
combinations = []
def backtrack(num):
nonlocal n
if num > n:
combinations.append(counter.copy()) # Add the current combination to the list
return
for i in range(3):
counter[i] += 1 # Add one tire to an object
backtrack(num + 1)
counter[i] -= 1 # Remove one tire from the object
backtrack(1) # Start the recursive process from the first tire
return combinations
# Test the function
n = int(input("Enter the number of tires: "))
result = generate_combinations(n)
print(f"Number of combinations: {len(result)}")
for combination in result:
print(f"Cars: {combination[0]}, Tricycles: {combination[1]}, Bicycles: {combination[2]}")
```
Explanation of the code:
1. We start by defining a helper function called `backtrack`. This function uses the `counter` list to keep track of the number of cars, tricycles, and bicycles for each tire combination.
2. Inside the `backtrack` function, we check if we have exhausted all tires (i.e., `num > n`). If so, we add the current combination (`counter`) to the `combinations` list and return.
3. If we haven't exhausted all tires, we iterate through the three possible objects (cars, tricycles, bicycles) and increment the corresponding counter. Then, we make a recursive call to `backtrack` with the next tire.
4. After the recursive call returns, we need to undo the changes made to the `counter` list to explore other possibilities. We decrement the counter value for the current object.
5. Finally, we call the `backtrack` function with `num=1` to start the recursive process. This will generate all possible combinations of cars, tricycles, and bicycles.
6. The generated combinations are stored in the `combinations` list, which is returned by the `generate_combinations` function.
7. The code then prompts the user to enter the number of tires and prints the number of combinations along with the details of each combination.
Note: This solution assumes that at least one tire should be allocated to each object (car, tricycle, bicycle) for a fair share. If it's possible to have objects with zero tires, you can modify the code accordingly.