Consider a 2 × n grid graph with nodes (x, y) where x ∈ {0, 1} and y ∈ {1, 2, · · · , n}. The initial graph has 3n - 2 edges connecting all pairs of adjacent nodes.
You need to maintain the graph with two types of different adjustments. The first one, denoted by “1 $x_0$ $y_0$ $x_1$ $y_1$”,adds an new edge between the nodes ($x_0, y_0$) and ($x_1, y_1$) which was not exist. The second one, denoted by“2 $x_0$ $y_0$ $x_1$ $y_1$”, erases an existed edge between the nodes ($x_0, y_0$) and ($x_1, y_1$).
It is sure that, for each adjustment, ($x_0, y_0$) and ($x_1, y_1$) were adjacent in the original grid graph. That is say thateither they share the same x coordinate and |$y_0 - y_1$| = 1, or they share the same y coordinate and |$x_0 - x_1$| = 1.
After each adjustment, we guarantee the connectedness of the graph and you need to calculate the number of bridges in the current graph.