Prove that if we order the characters in an alphabet so that their frequencies are monotonically decreasing,

Question:

Prove that if we order the characters in an alphabet so that their frequencies are monotonically decreasing, then there exists an optimal code whose codeword lengths are monotonically increasing.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction to Algorithms

ISBN: 978-0262033848

3rd edition

Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest

See More Books

Question Posted: Feb 25, 2020 08:37 AM

See More Questions

In order to transform one source string of text x [1 m] to a target string y [1 n], we can perform various transformation operations. Our goal is, given x and y, to produce a series of...
Prove that if we apply a unit force to node i in a structure and measure the displacement of node j in the direction of the force, then we obtain the same value if we apply the force to node j and...
If A is symmetric and invertible and A = LDLT (with L unit lower triangular and D diagonal), prove that this factorization is unique. That is, prove that if we also have A = L1D1LT1 (with L1 unit...
Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables. OF -; F(u, v) = eu+v, u = x, v = xy
A nitro group( - NO2) effectively stabilizes a negative charge on an adjacent carbon atom through resonance: Two of the following nitrophenols are much more acidic than phenol itself. The third...
Explain why many large airlines operate several hubs.
Identify the four components of an ecosystem. After you do this try to visualize the interactions of these four components of an ecosystem as illustrated by Figure 2. 2 in the textbook. Does this...
The Barberton Municipal Division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Cindy Kramer, road maintenance director, must submit a staffing...
2. 2. A 20 kg child climbs to the top of a slide that is 3 m above the ground level. She starts from rest and slides down the incline. a. Define and model the energy of the system with Energy Bar...
Just hours before they died, Miller, Wantz, and family members met with Kevorkian at the home of Sherry Millers parents on October 22, 1991. Miller, 43, had advanced multiple sclerosis and had...
Describe an efficient algorithm that, given a set x 1, x 2, . . . ,x n of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points....
Suppose we have an optimal prefix code on a set C = {0, 1, . . . n 1} of characters and we wish to transmit this code using as few bits as possible. Show how to represent any optimal prefix code on...
Government must classify investments into one of three categories of input to establish fair value. A government holds the following investments. For each, indicate the category in which it should...
Discuss the importance of the common-size financial statements in strategic evaluation and control process.
Discuss the proposition: 'In times of change, conflict between individuals and groups is inevitable.'
Explain the goals of the training and development function of HRM.
Contrast management, personnel, and HRM.
What activities are involved in the staffing function of HRM?
Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components, 30% contain one defective component, and 20% contain...
Coastal Refining Company operates a refinery with a distillation capacity of 12,000 barrels per day. As a new member of Coastal's management team, you have been given the task of developing a...
Consider an initially empty memory cache consisting of four pages. How many page misses does the FIFO algorithm incur on the following page request sequence: (2,3,4,1,2,5,1,3,5,4,1,2,3)?
Karen has a new way to do path compression in a tree-based union/find partition data structure starting at a position p. She puts all the positions that are on the path from p to the root in a set S....
Suppose we are given a directed graph G with n vertices, and let M be the nÃn adjacency matrix corresponding to G. a. Let the product of M with itself (M 2 ) be defined, for 1¤i, j...
Describe the process of depth-first search (DFS) and provide a Python implementation to traverse a graph using DFS.
A number like 197 is called a **Fare prime** because when all of its digits are rotated (197, 971 and 719), each new number is also prime. Help me a code that can find all fare primes up to a...
Required: 1. Determine the inventory on March 31 and the cost of merchandise sold for the three-month period, using the first-in, first-out method and the periodic inventory system. Merchandise...

Prove that if we order the characters in an alphabet so that their frequencies are monotonically decreasing,

Question:

Step by Step Answer:

Little formalmathematical note here We are required to prove existence of an optimal code with some property Therefore we are required also to show th...View the full answer

Introduction to Algorithms

Students also viewed these Computer science questions