 7.4.1: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.2: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.3: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.4: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.5: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.6: For Exercises 16, write the nodes in a depthfirst search of the fo...
 7.4.7: For Exercises 710, write the nodes in a depthfirst search of the f...
 7.4.8: For Exercises 710, write the nodes in a depthfirst search of the f...
 7.4.9: For Exercises 710, write the nodes in a depthfirst search of the f...
 7.4.10: For Exercises 710, write the nodes in a depthfirst search of the f...
 7.4.11: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.12: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.13: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.14: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.15: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.16: For Exercises 1116, write the nodes in a breadthfirst search of th...
 7.4.17: For Exercises 1720, write the nodes in a breadthfirst search of th...
 7.4.18: For Exercises 1720, write the nodes in a breadthfirst search of th...
 7.4.19: For Exercises 1720, write the nodes in a breadthfirst search of th...
 7.4.20: For Exercises 1720, write the nodes in a breadthfirst search of th...
 7.4.21: For Exercises 2124, write the nodes in a depthfirst search of the ...
 7.4.22: For Exercises 2124, write the nodes in a depthfirst search of the ...
 7.4.23: For Exercises 2124, write the nodes in a depthfirst search of the ...
 7.4.24: For Exercises 2124, write the nodes in a depthfirst search of the ...
 7.4.25: For Exercises 2528, write the nodes in a breadthfirst search of th...
 7.4.26: For Exercises 2528, write the nodes in a breadthfirst search of th...
 7.4.27: For Exercises 2528, write the nodes in a breadthfirst search of th...
 7.4.28: For Exercises 2528, write the nodes in a breadthfirst search of th...
 7.4.29: In the computer network in the accompanying figure, the same messag...
 7.4.30: Using the graph for Exercise 29, use the breadthfirst search algor...
 7.4.31: Use the depthfirst search algorithm to do a topological sort on th...
 7.4.32: Use the depthfirst search algorithm to do a topological sort on th...
 7.4.33: The data structure used to implement a breadthfirst search is a qu...
 7.4.34: Find a way to traverse a tree in level order, that is, so that all ...
 7.4.35: Describe how the depthfirst search algorithm can be used in a conn...
 7.4.36: a. Describe the order in which nodes are visited in a breadthfirst...
Solutions for Chapter 7.4: Traversal Algorithms
Full solutions for Mathematical Structures for Computer Science  7th Edition
ISBN: 9781429215107
Solutions for Chapter 7.4: Traversal Algorithms
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Mathematical Structures for Computer Science was written by Patricia and is associated to the ISBN: 9781429215107. Since 36 problems in chapter 7.4: Traversal Algorithms have been answered, more than 4265 students have viewed full stepbystep solutions from this chapter. Chapter 7.4: Traversal Algorithms includes 36 full stepbystep solutions. This textbook survival guide was created for the textbook: Mathematical Structures for Computer Science, edition: 7.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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