C
D `Gd q cu U f aF u G`f `GV u up` E
ccD Y W q u e F | u Gw I F e G`F GR Y U f aF u Gw p IF f p`Gw F cs R paw R `Vv p R u Gw u p`r uVa E GVS U T QC
D V Vu R a G e pu u ` IuH R G R b F cF
GF u R w d R
B
Q S @ H I GH D I a8
ySP yP w @ 9 H 9 ` @ G9 9 yP HEH W X yb GA @ 8 w @ 9 yb S 9 SW H V E8 U SPT D C RB Q
ED 9 ig [email protected] F 9 b 8 ySA GH D I 8 a H SyI H SW yP S 9 W Q yST w [email protected] W H F
PA S9 @ b9 H SW w @
Algorithms - 91.503 - Spring 2001
Final Exam
May 22, 2001
Do any 7 of the rst 9.
1. (10 pts) Prove by induction, that for all integers k 0,
k
Fk+2 = 1 +
Fi ,
i=0
where Fk is the k th Fibonacci number.
C
D `Gd q cu U f aF u G`f `GV u up` E
ccD Y W q u e F | u Gw I F e G`F GR Y U f aF u Gw p IF f p`Gw F cs R paw R `Vv p R u Gw u p`r uVa E GVS U T QC
D V Vu R a G e pu u ` IuH R G R b F cF
GF u R w d R
6
m7 C 8 WB C 8 BB RF U S F A G H G AE A S AE G b RF X C 8a
m
7 F G AE I F G YV S b G AE mT m G H Gj c C 8U
7 G H Gj c C 8q
7 cfw_ G H Gj c C 8S
7 HF
F S G q A G 7 BWH a H S RUG V BF WAE R F GA H F S
Fall 2009 - 91.503 - Algorithms
Computer Science Department
University of Massachusetts Lowell
Lowell, MA 01854
Oct. 6, 2009.
Name:
1.
2.
Total:
3.
4.
5.
6.
7.
/50
Exam Time: 1h & 15m. Each problem is
Fall 2010 - 91.503 - Algorithms
Computer Science Department
University of Massachusetts Lowell
Lowell, MA 01854
Oct. 5, 2010.
Name:
1.
2.
Total:
3.
4.
5.
6.
/50
Exam Time: 1h & 15m. Each problem is wo
Algorithms - 91.503 - Spring 2001
First Exam
March 9, 2001 - make-up class
1. (10 pts) A sequence of n operations is performed on a data structure. The ith operation
costs i if i is an exact power of
UML CS
Algorithms 91.503 (section 201) Homework #5
Spring, 2011
Assigned: Tuesday, 3/22
Due: Tuesday, 4/5 at 5:30 p.m.
This assignment covers textbook material in Chapter 34 (NP-Completeness) and the
UML CS
Analysis of Algorithms 91.503
Fall, 2004
Minimum Spanning Trees
In class we discussed a greedy algorithm to construct a Minimum Spanning Tree (MST) of an undirected graph G=(V,E).
Greedy_MST(G)
B
Q S @ H I GH D I a8
ySP yP w @ 9 H 9 ` @ G9 9 yP HEH W X yb GA @ 8 w @ 9 yb S 9 SW H V E8 U SPT D C RB Q
ED 9 ig [email protected] F 9 b 8 ySA GH D I 8 a H SyI H SW yP S 9 W Q yST w [email protected] W H F
PA S9 @ b9 H SW w @
Fall 2010 - 91.503 - Algorithms
Computer Science Department
University of Massachusetts Lowell
Lowell, MA 01854
Oct. 5, 2010.
Name:
1.
2.
Total:
3.
4.
5.
6.
/50
Exam Time: 1h & 15m. Each problem is wo
6
m7 C 8 WB C 8 BB RF U S F A G H G AE A S AE G b RF X C 8a
m
7 F G AE I F G YV S b G AE mT m G H Gj c C 8U
7 G H Gj c C 8q
7 cfw_ G H Gj c C 8S
7 HF
F S G q A G 7 BWH a H S RUG V BF WAE R F GA H F S
Algorithms - 91.503 - Spring 2001
First Exam
March 9, 2001 - make-up class
1. (10 pts) A sequence of n operations is performed on a data structure. The ith operation
costs i if i is an exact power of
Algorithms - 91.503 - Spring 2001
Final Exam
May 22, 2001
Do any 7 of the rst 9.
1. (10 pts) Prove by induction, that for all integers k 0,
k
Fk+2 = 1 +
Fi ,
i=0
where Fk is the k th Fibonacci number.
Start from vertex a. At each choice point, if you have more than one vertex satisfying
the minimality condition, pick the vertex lexicographically smaller.
a
d
e
b
f
c
h
g
Fall 2009 - 91.503 - Algorithms
Computer Science Department
University of Massachusetts Lowell
Lowell, MA 01854
Oct. 6, 2009.
Name:
1.
2.
Total:
3.
4.
5.
6.
7.
/50
Exam Time: 1h & 15m. Each problem is
Start from vertex a. At each choice point, if you have more than one vertex satisfying
the minimality condition, pick the vertex lexicographically smaller.
a
d
e
b
f
c
h
g
UMass Lowell CS
91.503
Fall, 2001
Name: _ MIDTERM EXAM + SOLUTIONS This exam is open: - books - notes and closed: - neighbors - calculators The upper bound on exam time is 3 hours. Please write your n