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 32.1, Problem 4E
Program Plan Intro
To analyze the execution time of a polynomial time
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Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w.
Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal.
In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized.
All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap.
You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line.
Input format
The first line of the input contains an integer, n - denoting the range of numbers…
We consider certain strings of length 6 over the alphabet S = {A,B,C}.
We require that the string contains exactly two As, and exactly two B's, and exactly two C's.
How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?
Imagine you have a strip of highway connecting n towns in a line. Each town is being evaluated as a possible location for building a cellular phone tower. Each cell tower will provide coverage to the town it’s built in, but no other towns. However, due to the way that cell towers interfere with one another, it’s not possible to build cell phone towers in two adjacent towns.Describe an algorithm that, given the populations of each of the towns, reports the maximum number of people you can provide cell phone coverage to, subject to the restriction that no two adjacent towns can each have cell towers in them. Use dynamic programming to dramatically speed up your solution over a na ̈ıve recursive algorithm.
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