Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 32.4, Problem 7E
Program Plan Intro
To give a linear-time
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Write a regular expression for the set of strings over the alphabet {a, b} that have at least one a andat least one b. For example, aaaba and bbaba are strings in the set, but aaaa and bbb are not.
Given a string s, find the length of the longest substring without repeating characters.
For example, if the input is "abcabcbb", the output should be 3, because the longest substring without repeating characters is "abc". If the input is "bbbbb", the output should be 1, because the longest substring without repeating characters is "b".
The coordinates of a polygon can be represented as a list of tuples: [(x1, y1), (x2, y2), .., (xn, yn)], where (x1, y1), ., (xn, yn) are points of the polygon in a counterclockwise order.
Find the area of such a polygon using using shoelace formula. It is no longer required to take absolute value.
п-1
п—1
A =
> xi+1Yi ) – x1Yn
i=1
i=1
1
x142 + x2Y3 + + xn-1Yn + xnY1 - x2y1 – X3Y2 – ··- xn Yn-1 – x1Yn|
>>> area ([(0,0), (1,0), (0,1)])
0.5
>>> area ([(0,0), (1,0),(1,1),(0,1)])
1.0
>> area([(0,0),(2,0), (2,2),(1,2), (0,1)])
3.5
Write the function area(C) to find the area of a triangle with vertices at c = [(x1, y1), (x2, y2),..., (xn, yn)].
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