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 26.1, Problem 4E
Program Plan Intro
To prove the flows in a network form a convex set.
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Students have asked these similar questions
We have learned the mid-point and trapezoidal rule for
numercial intergration in the tutorials. Now you are asked to
implement the Simpson rule, where we approximate the
integration of a non-linear curve using piecewise quadratic
functions.
Assume f(x) is continuous over [a, b] . Let [a, b] be
divided into N subintervals, each of length Ax, with
endpoints at P = x0, x1, x2,..
Xn,..., XN. Each
interval is Ax = (b − a)/N.
The equation for the Simpson numerical integration rule is
derived as:
f f(x) dx
N-1
Ax [ƒ(x0) + 4 (Σ1,n odd f(xn))
ƒ(x₂)) + f(xx)].
N-2
+ 2 (n=2,n even
Now complete the Python function InterageSimpson (N, a,
b) below to implement this Simpson rule using the above
equation.
The function to be intergrate is ƒ(x) = 2x³ (Already
defined in the function, no need to change).
Let f be a flow of flow network G and f' a flow of residual network Gf . Show that f +f' is a flow of G.
We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions.
Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1,x2,..., X., XN. Each interval is Ax = (b − a)/N.
The equation for the Simpson numerical integration rule is derived as:
f f(x)dx ≈
[ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)].
Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation.
The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change).
*Complete the function given the variables N, a,b and return the value as "TotalArea"."
"Don't change the predefined content' only fill your code in the region *YOUR CODE""
from math import *
def InterageSimpson (N, a,…
Chapter 26 Solutions
Introduction to Algorithms
Ch. 26.1 - Prob. 1ECh. 26.1 - Prob. 2ECh. 26.1 - Prob. 3ECh. 26.1 - Prob. 4ECh. 26.1 - Prob. 5ECh. 26.1 - Prob. 6ECh. 26.1 - Prob. 7ECh. 26.2 - Prob. 1ECh. 26.2 - Prob. 2ECh. 26.2 - Prob. 3E
Ch. 26.2 - Prob. 4ECh. 26.2 - Prob. 5ECh. 26.2 - Prob. 6ECh. 26.2 - Prob. 7ECh. 26.2 - Prob. 8ECh. 26.2 - Prob. 9ECh. 26.2 - Prob. 10ECh. 26.2 - Prob. 11ECh. 26.2 - Prob. 12ECh. 26.2 - Prob. 13ECh. 26.3 - Prob. 1ECh. 26.3 - Prob. 2ECh. 26.3 - Prob. 3ECh. 26.3 - Prob. 4ECh. 26.3 - Prob. 5ECh. 26.4 - Prob. 1ECh. 26.4 - Prob. 2ECh. 26.4 - Prob. 3ECh. 26.4 - Prob. 4ECh. 26.4 - Prob. 5ECh. 26.4 - Prob. 6ECh. 26.4 - Prob. 7ECh. 26.4 - Prob. 8ECh. 26.4 - Prob. 9ECh. 26.4 - Prob. 10ECh. 26.5 - Prob. 1ECh. 26.5 - Prob. 2ECh. 26.5 - Prob. 3ECh. 26.5 - Prob. 4ECh. 26.5 - Prob. 5ECh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Prob. 6P
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