Alarm Beams Between Rows

Medium

A warehouse floor plan is given as a list of equal-length strings floor_plan: floor_plan[i] is row i, where 1 marks a sensor and 0 marks an empty spot. Two sensors are linked by a beam if they sit in different rows and no row strictly between them contains any sensor. Each such pair produces its own beam. Count the beams.

Example 1

floor_plan=['1010', '0000', '0110', '1000'] → 6

The empty row 1 is skipped. Rows 0 and 2 give 2 · 2 = 4 beams, rows 2 and 3 give 2 · 1 = 2. That is 6 in total.

Example 2

floor_plan=['111', '000'] → 0

All sensors share one row, and beams only run between different rows.

Example 3

floor_plan=['1', '1', '1'] → 2

Constraints

1 ≤ len(floor_plan) ≤ 500
1 ≤ len(floor_plan[i]) ≤ 500, all rows have the same length
Rows consist only of the characters 0 and 1

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Topics

Array Math String Matrix

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Input

floor_plan=['1010', '0000', '0110', '1000']

Expected

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