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. n-1 n-1 1 A = 2 (Σ (Σ XiYi+1 ) Xi+1Yi) - x1Yn i=1 i=1 142 +x2Y3 +...+ xn-1Yn + xny1 - x2Y1 - 23Y2 - .. 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)]. 1/2

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. n-1 n-1 1 A = 2 (Σ (Σ XiYi+1 ) Xi+1Yi) - x1Yn i=1 i=1 142 +x2Y3 +...+ xn-1Yn + xny1 - x2Y1 - 23Y2 - .. 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)]. 1/2

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.

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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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