Basic Algorithms Fall 2012 Problem Set 4
Due: Wednesday, Oct. 10
Problems 13 assume the following. You have n coins they all look identical, and all have the
same weight except one, which is heavier than all the rest. You also have a balance scale, on whi
Basic Algorithms Fall 2012 Problem Set 3
Due: Wednesday, Oct. 3
NOTE: All students should complete exercises 15. Students in the honors section should additionally complete exercises 68, and hand in the solutions to these problems separately on Wednesday,
Basic Algorithms. For Thursday Oct. 22 @ 11:55 PM Please submit your selfevaluations of HW6
Homework 6 solutions
11.20 (stone-age DP: did they really teach it this way? Yes)
11.20 Computing ABCDE. The dimensions are (20100), (10010), (1020), (20100)(1005)
CSCI-UA.0310-001/002 Basic Algorithms
October 27, 2016
Problem Set 6
Lecturer: Yevgeniy Dodis
Due: Tuesday, November 1
Problem 6-1 (Walks on Augmented Trees)
8 (+4) Points
Consider a binary search tree. For any element x, define Successor(x) to be the suc
CSCI-UA.0310-001/002 Basic Algorithms
October 6, 2016
Problem Set 5
Lecturer: Yevgeniy Dodis
Due: Tuesday, October 11
Problem 5-1 (Running Median 2)
10 points
In homework 4, we designed a data structure supporting the following operations:
Build(A[1 . .
CSCI-UA.0310-001/002 Basic Algorithms
October 13, 2016
Problem Set 6
Lecturer: Yevgeniy Dodis
Due: Tuesday, October 18
Problem 6-1 (Preorder and Postorder Tree Walks)
8 Points
Consider a binary search tree. For a node p, denote by ppre and ppost the posit
CSCI-UA.0310-001/002 Basic Algorithms
November 6, 2016
Problem Set 8
Lecturer: Yevgeniy Dodis
Due: Tuesday, November 8
Problem 8-1 (I Am a Big Fan of Rats)
6 points
Using dynamic programming, find the optimum printing of the text I am a big fan of rats, i
Basic Algorithms Fall 2012 Problem Set 9
Due: Wednesday, Dec. 12
1. Let
SetPACK = cfw_ C, k : C is a collection of nite sets, at least k of which are pairwise disjoint.
Show that SetPACK is NP-complete.
Hint: reduction from Independent Set.
2. You are giv
Basic Algorithms Fall 2012 Problem Set 9
Due: Thursday, Dec. 6
1. Colorful paths (I). You are given a directed graph G = (V, E ), and nodes s, t. Nodes are
colored red, yellow, blue, or white. Let us say a path (not necessarily simple) is colorful if it
r
Basic Algorithms Fall 2012 Problem Set 8
Due: Thursday, Nov. 29
1. Suppose that you start with an arbitrary forest of up trees, containing n nodes altogether.
These trees are not necessarily balanced at all. You then perform m nd operations, using
path co
Basic Algorithms Fall 2012 Problem Set 7
Due: Wednesday, Nov. 21
1. Exercise 16.3-3 on p. 436 of CLRS.
2. Problem 16-1 on p. 446 of CLRS.
3. Consider a k -digit decimal counter, with initial value 0. Suppose that n additions to the
counter of numbers of t
Basic Algorithms Fall 2012 Problem Set 6
Due: Thursday, Nov. 15
1. Recall the following family H of hash functions dened in class: the universe of data items is
U := Zt+1 , and the set of hash keys is K := Zt ; for k = (k1 , . . . , kt ) K, a = (a0 , a1 ,
Basic Algorithms Fall 2012 Problem Set 5
Due: Wednesday, Oct. 17
1. Consider maintaining a collection of lists of items on which the following operations can be
performed:
(i) Given two lists L1 and L2 , form their concatenation L (destroying L1 and L2 in
Basic Algorithms Fall 2012 Problem Set 2
Due: Sept. 24
1. Suppose a die is rolled repeatedly until it comes up 1 or is rolled n times, whichever comes
rst. Let X be the random variable representing the number of rolls. Calculate E[X ].
Hint: use the fact
Basic Algorithms Fall 2012 Problem Set 1
Due: Sept. 17
1. Compare the following pairs of functions, and indicate whether f = o(g ), g = o(f ), f = (g ),
or NOTA (none of the above).
f (n)
a)
b)
c)
d)
e)
f)
g)
h)
g (n)
100n + log2 n
log2 n
2n
n2 / log2 n
n
Chapter 1 Algorithm Analysis
We are interested in designing good algorithms (a step-by-step procedure for
performing some task in a finite amount of time) and good data structures (a
systematic way of organizing and accessing data).
Unlike v22.102, howeve