Count the Cans

Total cans: 33

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Count the Cans: Problem Explanation

The "Count the Cans" problem involves calculating the total number of cans in a pyramid-like structure, with optional additional cans on top.

Key Components:

  • Base cans: The number of cans in the bottom row.
  • Top cans: The number of cans in the top row of the pyramid.
  • Additional cans: Extra cans placed on top of the pyramid.

The Formula:

totalCans = ((base - top + 1) * (top + base)) / 2 + addition

Explanation:

  1. Pyramid calculation: ((base - top + 1) * (top + base)) / 2
    • This uses the formula for the sum of an arithmetic sequence.
    • base - top + 1 is the number of rows.
    • top + base is the sum of the first and last terms.
  2. Additional cans: Simply add the addition value.

This formula efficiently calculates the total number of cans without needing to generate the entire structure in memory.

Note:

Ensure that the top cans are always less than or equal to the base cans for a valid pyramid structure. The additional cans can be any non-negative number.