Introduction to Algorithms
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 33.4, Problem 3E
Program Plan Intro

To alter the closestpair program to use L1 distance, also called as the Manhattan distance .

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An approximation to the integral of a function f(x) over an interval [a, b] can              be found by first approximating f(x) by the straight line that goes through the              end points (a, f(a)) and (b, f(b)), and then finding the area under the straight              line, which is the area of a trapezoid.              Write a function trapezint(f, a, b) that returns this approximation to the                                       integral. Test your code by integrating cos(x) and sin(x) from 0 to π.
Algorithms Question Three points P, Q, and R are said to be collinear if they are on a single line. To check whether the 3 points lie on the same line, we use the distance formula. If P, Q and R are three collinear points, then: Distance from P to Q + Distance from Q to R = Distance from P to R PQ + QR = PR The distance between two points (x1, y1) and (x2, y2) is given by Hence, we can easily find the distance between the points P, Q and R, with the help of this formula.  Design an algorithm (pseudocode) to check whether three points are collinear. In your solution include the input and the output.
Q10: Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential equation. 1. The charge Q(t) on the capacitor in the electrical circuit shown satisfies the differential equation where d²Q dQ 1 +R- + √ √e dt2 dt L = 0.5 R = 6.0 C= 0.02 and V(t) is the applied voltage. V(t) = V(t), henrys is the coil's inductance ohms is the resistor's resistance farads is the capacitor's capacitance ellee (i) Is the circuit oscillatory? (ii) If V(t) = 24 sin(10r) volts and Q(0) = 0 = Q'(0), find Q(t). (iii) Sketch the transient solution, the steady state solution, and the full solution Q(t).
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