Write an algorithm to assist a school canteen which sum up to 12cedis. Displaying your answer in a constant of P

Answer 1

To create an algorithm that helps a school canteen sum up to 12 cedis, we need to define a structure to represent the possible items and their prices. Assuming we have a predefined list of items with their respective prices, the algorithm will generate combinations of these items that sum up to 12 cedis.

Here’s a step-by-step outline of the algorithm:

1. Define Item Prices: Create a list or array containing the prices of various items available in the canteen. For example:

   • Item 1: 2 cedis
   • Item 2: 3 cedis
   • Item 3: 4 cedis
   • Item 4: 5 cedis

2. Initialize Variables:

   • Define an empty list results to store valid combinations.
   • Define a constant P to hold the target sum, which is 12 in this case.

3. Define Recursive Function: Create a recursive function to explore combinations of items:

   • Parameters: Current combination (list), current sum, and the starting index in the items list.
   • Base Case: If the current sum equals 12 (value of P), add the current combination to results.
   • Recursive Case: Loop through the items starting from the current index, adding each item to the current combination and calling the function recursively with the updated sum and index.

4. Call the Function and Display Results: Once the function has completed exploring all combinations, print or display the results.

Here is a Python-like pseudocode that implements the above algorithm:

# Define item prices in cedis
item_prices = [2, 3, 4, 5]  # For example, the prices of items in the canteen
target_sum = 12  # This is our constant P

# Initialize results to store combinations
results = []

# Function to find combinations that sum up to P
def find_combinations(current_combination, current_sum, start_index):
    # Base case: if current sum is equal to the target sum
    if current_sum == target_sum:
        results.append(current_combination.copy())
        return
    # If current sum exceeds the target, stop exploring
    if current_sum > target_sum:
        return
    
    # Recursive case: explore the rest of the items
    for i in range(start_index, len(item_prices)):
        # Include this item and try to find further combinations
        current_combination.append(item_prices[i])
        find_combinations(current_combination, current_sum + item_prices[i], i)  # allow repeat items
        current_combination.pop()  # Backtrack

# Start finding combinations
find_combinations([], 0, 0)

# Display the results
print("Combinations that sum up to", target_sum, "cedis are:")
for combination in results:
    print(combination)

Explanation:

• The algorithm uses recursion to explore all possible combinations of item prices that sum up to the target sum (12 cedis).
• The use of start_index allows the combination to include the same item multiple times (if that is allowed).
• Finally, the combinations that meet the criterion are printed.

This structure can be adjusted to fit the specific items and prices of the school canteen.