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5 An Example: Quicksort Let us now give an example that demonstrates the definitions given earlier. Consider the following algorithm, called quicksort [192, 314, 410]. The algorithm is given a sequence Pl, ... ,Pn of n numbers. It picks the ith number Pi as a partitioning number. It constructs two subsequences of numbers of p: the sequence p< containing all numbers less than Pi, and the sequence p> containing all numbers greater than Pi. The sequences p< and p> are sorted recursively. Finally, the results are concatenated with Pi to yield the sorted output sequence.

II, •• • . 10: Five standard cells, represented as logic diagrams and by their mask layouts. (a) Inverter, (b) two-input NOR-gate, (c) fourinput NOR-gate, (d) master-slave flipflop (courtesy XEROX PARe). Chapter 1. J~ . ~, - .... =- '=:= ~ I'! 11: The layout of a small condition-code circuit made up completely of standard cells. The cells are arranged in three rows (courtesy XEROX PARe). standard cells. Today, standard-cell layout is in the process of being superseded by other layout styles, such as full-custom or sea of gates.

In the subsequent routing phase, the course of the wires is determined. Most often, the routing phase is itself split into two phases-global routing and detailed routing. The global-routing phase determines how a wire maneuvers around and through the cells. The detailed-routing phase does not change the result of the globalrouting phase, but simply computes the exact paths the wires take through the grid. ) For a restricted set of detailed-routing problems, the channel-routing problems (see Chapter 9), there are ways of minimizing the routing area in the topological domain.

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