Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 8 potx
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 8 potx
... edge it visits to the cycle C, which is then added to the Euler
tour T , when we return from a call to VISIT(u), all edges entering or leaving
vertex u have been added to the tour. When we advance ... B to the end of A, instead
splice B into A right after the Þrst element of A. We have to traverse B to update
representative pointers anyway, so we can just make the last element o...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 5 potx
... contains
max[x] = max endpoint value in subtree rooted at x .
int
max
M
8
[17,19]
23
M
8
[21,23]
23
M
8
[5,11]
18
M
8
[15, 18]
18
M
8
[4 ,8]
8
M
8
[7,10]
10
[leave on board]
max[x] = max
⎧
⎨
⎩
high[int[x]] ... nodes (ancestors of
14-2 Lecture Notes for Chapter 14: Augmenting Data Structures
M
8
B
B
B
B
R
R R
R
i=5
r=6
i=3
r=2
i=1
r=1
i=5
r=2
M
8
M
8
P
2
M
8
Q
1
M
8...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 10 potx
... 101
Half-cleaner:
0
0
1
1
1
0
0
0
0
0
0
1
0
1
01
bitonic
clean
bitonic
0
0
1
1
1
1
1
0
0
1
0
1
1
1
01
bitonic
clean
bitonic
Depth = 1.
Lemma
If the input to a half-cleaner is a bitonic 0-1 sequence, then for the output:
•
both the top and ... Networks
A bitonic sorting network
Constructing a sorting network
Step 1: Construct a “bitonic sorter.” It sorts any bitonic sequence.
A sequence is b...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 1 pptx
... Structures
Lecture Notes 14-1
Solutions 14-9
Preface
This document is an instructor’s manual to accompany Introduction to Algorithms,
Second Edition, by Thomas H. Cormen, Charles E. Leiserson, Ronald L. ... invariants is like mathematical induction:
Instructor’s Manual
by Thomas H. Cormen
Clara Lee
Erica Lin
to Accompany
Introduction to Algorithms
Second Edition...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 2 pps
... 4-13
nn
log
4
n
n
2
n
4
n
4
n
8
n
8
n
8
n
16
n
16
n
16
n
32
n
32
n
64
log
8
n
.
.
.
n(
4+2+1
8
) =
7
8
n
n(
1
4
+
2
8
+
3
16
+
2
32
+
1
64
)
= n
16+16+12+4+1
64
= n
49
64
=
7
8
2
n
log n
i=1
7
8
i
n = (n)
We ... 5.
•
MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4.
1
23
4567
89 10
1
23
4567
89 10
4
13
2910
14 8 7
16
41 23 16 9 10 14...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 3 docx
... Notes for Chapter 7: Quicksort 7-3
81 640395
p,j ri
81 640395
prj
186 40395
p,i rj
186 40395
p,i rj
186 4 0395
prji
186 40 395
prji
13640 89 5
prji
13640 89 5
pri
16540 89 3
pri
i
A[r]: pivot
A[j r–1]: not ... Chapter 8: Sorting in Linear Time 8- 11
Solution to Exercise 8. 3-2
Insertion sort is stable. When inserting A[ j] into the sorted sequence A[1 j −1],
we do it the followi...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 4 pot
... CLRS:
•
ASCII values: C = 67, L = 76, R = 82 , S = 83 .
•
There are 1 28 basic ASCII values.
•
So interpret CLRS as (67 ·1 28
3
) +(76 ·1 28
2
) + (82 ·1 28
1
) + (83 ·1 28
0
) =
141,764,947.
Division method
h(k) ... pointer) to the new slot, and updating the pointer in the slot
that pointed to j to point to the new slot. Then insert the new element in
the now-empty slot as usu...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 6 pps
... row-major order, i.e.,
row-by-row from top to bottom, and left to right within each row. Column-
major order (column-by-column from left to right, and top to bottom within
each column) would also ... long it takes to get through S
1,1
.
•
If j ≥ 2, have two choices of how to get to S
1, j
:
•
Through S
1, j −1
, then directly to S
1, j
.
•
Through S
2, j −1
, then transfer ove...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 7 ppsx
... to go to get to 1 or 1/4, starting from 1/2, rate
of increase of differs.
•
For α to go from 1/ 2to1 ,num increases from size /2tosize, for a total
increase of size /2. increases from 0 to size. ... sorting A and B into monotoni-
cally increasing order works as well.
Lecture Notes for Chapter 16: Greedy Algorithms 16-3
Solution to S
ij
is (solution to S
ik
) ∪
{
a
k
}
∪ (s...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 9 pdf
... + E) to compute G
.
•
O(VE) to run BELLMAN-FORD.
•
(E) to compute w.
•
O(V
2
lg V +VE) to run Dijkstra’s algorithm
|
V
|
times (using Fibonacci heap).
•
(V
2
) to compute D matrix.
Total: ... t
(k−1)
kj
.
T
RANSITIVE-CLOSURE(E, n)
for i ← 1 to n
do for j ← 1 to n
do if i = j or (i, j) ∈ E[G]
then t
(0)
ij
← 1
else t
(0)
ij
← 0
for k ← 1 to n
do for i ← 1 to n
do for j...
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