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 31.5, Problem 2E
Program Plan Intro
To discover all integers
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3: The function f(x)= max x, searches for the maximum value between a number. Prove formally that the
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3. Let A = {1, 2, 3} and B = {4,5}.
a) Find A x B
b) Find B x A
If A = {1, 2, 6} and B = {2, 3, 5}, then the union of A and B is
Chapter 31 Solutions
Introduction to Algorithms
Ch. 31.1 - Prob. 1ECh. 31.1 - Prob. 2ECh. 31.1 - Prob. 3ECh. 31.1 - Prob. 4ECh. 31.1 - Prob. 5ECh. 31.1 - Prob. 6ECh. 31.1 - Prob. 7ECh. 31.1 - Prob. 8ECh. 31.1 - Prob. 9ECh. 31.1 - Prob. 10E
Ch. 31.1 - Prob. 11ECh. 31.1 - Prob. 12ECh. 31.1 - Prob. 13ECh. 31.2 - Prob. 1ECh. 31.2 - Prob. 2ECh. 31.2 - Prob. 3ECh. 31.2 - Prob. 4ECh. 31.2 - Prob. 5ECh. 31.2 - Prob. 6ECh. 31.2 - Prob. 7ECh. 31.2 - Prob. 8ECh. 31.2 - Prob. 9ECh. 31.3 - Prob. 1ECh. 31.3 - Prob. 2ECh. 31.3 - Prob. 3ECh. 31.3 - Prob. 4ECh. 31.3 - Prob. 5ECh. 31.4 - Prob. 1ECh. 31.4 - Prob. 2ECh. 31.4 - Prob. 3ECh. 31.4 - Prob. 4ECh. 31.5 - Prob. 1ECh. 31.5 - Prob. 2ECh. 31.5 - Prob. 3ECh. 31.5 - Prob. 4ECh. 31.6 - Prob. 1ECh. 31.6 - Prob. 2ECh. 31.6 - Prob. 3ECh. 31.7 - Prob. 1ECh. 31.7 - Prob. 2ECh. 31.7 - Prob. 3ECh. 31.8 - Prob. 1ECh. 31.8 - Prob. 2ECh. 31.8 - Prob. 3ECh. 31.9 - Prob. 1ECh. 31.9 - Prob. 2ECh. 31.9 - Prob. 3ECh. 31.9 - Prob. 4ECh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4P
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- You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 3 69 10 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 5 999 2 999 999 0 6 999 1 999 6 17 999 999 2 6 0 999 7 999 7 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 9 999 999 999 999 999 999 4 80 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial 1 2 3 4 5 6 7 8 9 nearest 1 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.arrow_forwardThis problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".arrow_forwardTrue or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).arrow_forward
- 1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 16arrow_forwardLet N be the positive integers f: N->N, f(x)=5x, this function is O a. not injective O b. injective O c. surjective O d. No answer is correctarrow_forwardO. The maximal value of num = 16..arrow_forward
- let X = {0, 1}arrow_forwardCompute the following sums. n-2 narrow_forwardAssume there are n = 2x players in a single elimination tournament with x rounds. How many single elimination tournaments should there be in order for the total number of matches to equal the number of matches in a round robin tournament?arrow_forward
- Correct answer will be upvoted else downvoted. Computer science. Positive integer x is called divisor of positive integer y, in case y is distinguishable by x without remaining portion. For instance, 1 is a divisor of 7 and 3 isn't divisor of 8. We gave you an integer d and requested that you track down the littlest positive integer a, to such an extent that a has no less than 4 divisors; contrast between any two divisors of an is essentially d. Input The primary line contains a solitary integer t (1≤t≤3000) — the number of experiments. The primary line of each experiment contains a solitary integer d (1≤d≤10000). Output For each experiment print one integer a — the response for this experiment.arrow_forward4. if q= [1 5 6 8 3 2 459 10 11,x={ 3 57 8 3 12 4 11 5 91, then: a) find elements of (q) that are greater than 4. b) find elements of (9) that are equal to those in (x). c) find elements of (x) that are less than or equal to 7.arrow_forwardI am what you call a perfectionist. I always strive for perfection, and I appreciate everyone and everything that is perfect. That is why I have recently acquired an appreciation for perfect numbers! I absolutely need to know which numbers from 1 to 1000 are considered perfect. From what I recall, a perfect number is a positive integer that is equal to the sum of all its divisors other than itself. Example: 6 is a perfect number because the divisors of 6 other than itself are 1, 2, and 3, and 1 + 2 + 3 = 6. c++ codearrow_forward
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