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# Abstract Data Types

ADTs classify data structures based on usage and behavior, providing an understanding of the interface and responses.

Consider the standard algorithm for converting a decimal number (**base 10**) into a binary number (**base 2**). This algorithm makes use of a single stack.

How many times will an item be pushed to this stack if the number to be converted is \(1048596\)?

Given a contiguous histogram each of integer height and unit width, write a program that finds the maximum possible rectangular area.

For the histogram above, the maximum area is \(6\times4=24\). What is the maximum area for the following data table?

**Note**

There are many ways to approach this question, but an efficient way of solving this is using stacks.

A *polish expression* or *postfix expression* is a notational form for logic, arithmetic, and algebra which places operators to the left of their operands. What is the value of the *polish expression* below when evaluated?

\[\large{35\ 17\ 40\ 9\ - * + 7 - }\]

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