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# #Medium #Top_100_Liked_Questions #Array #Dynamic_Programming #Matrix
# #Dynamic_Programming_I_Day_16 #Udemy_Dynamic_Programming #Big_O_Time_O(m*n)_Space_O(m*n)
# #2024_08_02_Time_285_ms_(100.00%)_Space_79.9_MB_(100.00%)

defmodule Solution do
    @spec min_path_sum(grid :: [[integer]]) :: integer
    def min_path_sum(grid) do
        traverse(grid, [0 | List.duplicate(20000, 199)])
    end

    defp traverse([], prev_row), do: Enum.at(prev_row, -1)
    defp traverse([[first | row] | rows], [prev_row_head | prev_row]) do
        prev_row = traverse_row(row, prev_row, [first + prev_row_head])
        traverse(rows, prev_row)
    end

    defp traverse_row([], _prev_row, acc), do: Enum.reverse(acc)
    defp traverse_row([head | tail], [top | prev_row], [prev | _rest] = acc) do
        traverse_row(tail, prev_row, [head + min(prev, top) | acc])
    end
end