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.
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To solve this problem, we can use a recursive approach to generate all possible combinations of cars, tricycles, and bicycles that would exhaust the given number of tires fairly.
Here's an example program in Python that implements this solution:
```python
def generate_combinations(n, current_combination):
if n == 0:
# We have exhausted all the tires, so we print the current combination
print_combination(current_combination)
return
if n >= 4:
# We have enough tires to add a car
current_combination.append("car")
generate_combinations(n - 4, current_combination)
current_combination.pop() # Backtrack by removing the car
if n >= 3:
# We have enough tires to add a tricycle
current_combination.append("tricycle")
generate_combinations(n - 3, current_combination)
current_combination.pop() # Backtrack by removing the tricycle
if n >= 2:
# We have enough tires to add a bicycle
current_combination.append("bicycle")
generate_combinations(n - 2, current_combination)
current_combination.pop() # Backtrack by removing the bicycle
def print_combination(combination):
# Prints the generated combination
count = {}
for obj in combination:
count[obj] = count.get(obj, 0) + 1
print(count)
def main():
n = int(input("Enter the number of tires: "))
current_combination = []
generate_combinations(n, current_combination)
if __name__ == "__main__":
main()
```
Explanation:
1. The `generate_combinations` function is defined to generate all possible combinations. It takes two parameters: `n` (the number of tires remaining) and `current_combination` (the current combination of objects being generated).
2. When `n == 0`, we have exhausted all the tires. So, we print the current combination using the `print_combination` function and return.
3. We start by checking if we have enough tires (`n >= 4`) to add a car. If so, we add a car to the current combination, decrement the tire count by 4, and recursively call `generate_combinations` with the updated tire count and current combination. After that, we backtrack by removing the car from the current combination.
4. Similarly, we check for tricycles (`n >= 3`) and bicycles (`n >= 2`) and perform the same steps as with the car.
5. The `print_combination` function takes the current combination and prints it in the desired format (e.g., counting the number of each object).
6. In the `main` function, we take the input for the number of tires (`n`), initialize an empty `current_combination`, and call `generate_combinations` to start generating the combinations.
By running this program, you will see all the combinations of cars, tricycles, and bicycles that could exhaust the given number of tires, ensuring a fair share among objects with shared tires.