1 The Foundations: Logic And Proofs 2 Basic Structures: Sets, Functions, Sequences, Sums, And Matrices 3 Algorithms 4 Number Theory And Cryptography 5 Induction And Recursion 6 Counting 7 Discrete Probability 8 Advanced Counting Techniques 9 Relations 10 Graphs 11 Trees 12 Boolean Algebra 13 Modeling Computation A Appendices expand_more
8.1 Applications Of Recurrence Relations 8.2 Solving Linear Recurrence Relations 8.3 Divide-and-conquer Algorithms And Recurrence Relations 8.4 Generating Functions 8.5 Inclusion-exclusion 8.6 Applications Of Inclusion-exclusion Chapter Questions expand_more
Problem 1E: Use mathematical induction to verify the formula derived in Example 2 for the number of moves... Problem 2E: a) Find a recurrence relation for the number of permutations of a set with n elements. b) Use this... Problem 3E: A vending machine dispensing books of stamps accepts only one-dollar coins, $1 bills, and $5 bills.... Problem 4E: A country uses as currency coins with values of 1 peso, 2 pesos, 5 pesos, and 10 pesos and bills... Problem 5E: How many was are there to pay a bill of 17 pesos using the currency described in Exercise 4, where... Problem 6E: a) Find a recurrence relation for the number of strictly increasing sequences of positive integers... Problem 7E: a) Find a recurrence relation for the number of bit strings of length n that contain a pair of... Problem 8E: a) Find a recurrence relation for the number of bit strings of length n that contain three... Problem 9E: a) Find a recurrence relation for the number of bit strings of length n that do not contain three... Problem 10E: a) Find a recurrence relation for the number of bit strings of length n that contain the string 01.... Problem 11E: a) Find a recurrence relation for the number of ways to climb n stairs if the person climbing the... Problem 12E: a) Find a recurrence relation for the number of ways to climb n stairs if the person climbing the... Problem 13E: a) Find a recurrence relation for the number of ternary strings of length n that do not contain two... Problem 14E: a) Find a recurrence relation for the number of ternary strings of length n that contain two... Problem 15E: a) Find a recurrence relation for the number of ternary strings of length n that do not contain two... Problem 16E: a) Find a recurrence relation for the number of ternary strings of length n that contain either two... Problem 17E: a) Find a recurrence relation for the number of ternary strings of length n that do not contain... Problem 18E: a) Find a recurrence relation for the number of ternary strings of length n that contain two... Problem 19E: Messages are transmitted over a communications channel using two signals. The transmittal of one... Problem 20E: A bus driver pays all tolls, using only nickels and dimes, by throwing one coin at a time into the... Problem 21E: a) Find the recurrence relation satisfied by Rn, where Rnis the number of regions that a plane is... Problem 22E: a) Find the recurrence relation satisfied by Rn, where Rnis the number of regions into which the... Problem 23E: a) Find the recurrence relation satisfied by Sn, where Snis the number of regions into which... Problem 24E: Find a recurrence relation for the number of bit sequences of length n with an even number of 0s. Problem 25E: How many bit sequences of length seven contain an even number of 0s? Problem 26E: a) Find a recurrence relation for the number of ways to completely cover a 2n checkerboard with 12... Problem 27E: a) Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the... Problem 28E: Show that the Fibonacci numbers satisfy the recurrence relation fn=5fn4+3fn+5 for n=5,6,7,... ,... Problem 29E Problem 30E Problem 31E: a) Use the recurrence relation developed in Example 5 to determine C5, the number of ways to... Problem 32E: In the Tower of Hanoi puzzle, suppose our goal is to transfer all n disks from peg 1 to peg 3, but... Problem 33E: Exercises 33-37 deal with a variation of the Josephus problem described by Graham, Knuth, and... Problem 34E: Exercises 33-37 deal with a variation of the Josephus problem described by Graham, Knuth, and... Problem 35E Problem 36E: Exercises 33-37 deal with a variation of the Josephus problem described by Graham, Knuth, and... Problem 37E Problem 38E Problem 39E: Show that the Reve’s puzzle with four disks can be solved using nine, and no fewer, moves. Problem 40E Problem 41E: Show that if R(n) is the number of moves used by the Frame-Stewart algorithm to solve the Reve’s... Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E: Show that an2=an2an+2an . Problem 50E Problem 51E Problem 52E Problem 53E: Construct the algorithm described in the text after Algorithm 1 for determining which talks should... Problem 54E: Use Algorithm 1 to determine the maximum number of total attendees in the talks in Example 6 if i,... Problem 55E: For each part of Exercise 54, use your algorithm from Exercise 53 to find the optimal schedule for... Problem 56E: In this exercise we will develop a dynamic programming algorithm for finding the maximum sum of... Problem 57E: Dynamic programming can be used to develop an algorithm for solving the matrix-chain multiplication... format_list_bulleted