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Greedy Mobile Grid Layout

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Your question is Greedy Mobile Grid Layout. Start with the requirements on the right.

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Problem

At PixelFlow, a mobile screen must display identical rectangular cards in a grid. Write a function that calculates the optimal layout for a given screen width, card minimum width, gap size, and number of cards.

The goal is to place as many columns as possible while ensuring each card is at least min_card_width pixels wide. Among all valid layouts, choose the one with the maximum number of columns. Then compute the resulting card width and the number of rows needed.

Formal Specification

Implement a function that receives:

  • screen_width: integer total width of the screen in pixels
  • min_card_width: integer minimum allowed width for each card
  • gap: integer horizontal gap between adjacent cards
  • item_count: integer number of cards to place

Return a list [columns, card_width, rows] where:

  • columns is the chosen number of columns
  • card_width is the integer width of each card after distributing available space evenly
  • rows is the number of rows required to place all cards

If item_count is 0, return [0, 0, 0].

Constraints

  • 0 <= item_count <= 10^5
  • 1 <= min_card_width <= screen_width <= 10^9
  • 0 <= gap <= 10^6
  • At least one column is always possible when item_count > 0

Function Signature

def optimal_layout(screen_width, min_card_width, gap, item_count):
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