Algorithm Algorithms Professor John Reif
Breadth First Search input undirected graph G = (V,E) with root r e V
false true
initialize:
L 0
ALG 5.2 Breadth-First Search of Graphs:
(a) Single Source Shortest Path (b) Graph Matching
e for each v V do visit(v

Problem P
Algorithms Professor John Reif
size n
1
fi divide into
ALG 1.3
Deterministic Selection and Sorting:
(a) Selection Algorithms and Lower Bounds (b) Sorting Algorithms and Lower Bounds
subproblems size n solve these and "glue" together solutions k

Algorithms Professor John Reif
Assume Commutative Ring (R,+, , 0,1)
w is principal nth root of unity w i 1 for i=1,.,n-1
ALG 3.2
The Fast Fourier Transform and Applications to Multiplication
if w 1, w n = 1, a n d
n-1 j=0
wj p = 0
f o r 1 p<n
Examples: R

1
2
Taylor Expansion
(x - x 0) f (x ) = f (x 0) + (x - x 0 )f (x 0) + f (x 0) +. . . 2 f( x )
(x - x )f (x 2
Algorithms Professor John Reif
ALG 3.3
Newton Iteration and Polynomial Computation:
(a) (b) Newton Iteration: application division Polynomial Eval

Algorithms Professor John Reif
Hash Function f:A
keys
B
indices
ALG 4.2
Universal Hash Functions:
CLR - Chapter 34 Auxillary Reading Selections: AHU-Data Section 4.7 BB Section 8.4.4 Handout: Carter & Wegman, "Universal Classes of Hash Functions", JCSS, V

Fall 2011 - CPS 130 Assignment I: Asymptotes and Recurrences
Department of Computer Science - Duke University Due on Tuesday 20th Sep in Class
1 Explain why the statement, `The running time of algorithm A is at least O(n2 ) is meaningless. (5 points) 2 Pr

CPS 130 Assignment II: Sorting and Search Trees
Department of Computer Science - Duke University Due on Thursday 20th Oct in Class
1 Give an O(n log k) time algorithm to merge k sorted lists into one sorted list, where n is the total number of elements in

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