Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 10 potx
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 10 potx
... focus on—bitonic sequences have the form
0
i
1
j
0
k
1
i
0
j
1
k
010 101
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 ... the input to a half-cleaner is a bitonic 0-1 sequence, then for the output:
•
both the top and bottom half are bitonic,
•
every element in the top half is ≤ every element in the bottom hal...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 5 potx
... O(h) time,
analogous to the changes we made for persistence in insertion. But to do so
without using parent pointers we need to walk down the tree to the node to be
deleted, to build up a stack ... keys are not distinct, because in order to Þnd the
path to the node to delete—a particular node with a given key—we have to
make some changes to how we store things in the tre...
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 ... append x’s list onto end of y’s list. Use y’s tail pointer to Þnd
the end.
22 -10 Lecture Notes for Chapter 22: Elementary Graph Algorithms
Idea: By considering vertices in second...
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
... 5.
•
MAX-HEAPIFY is applied to subtrees rooted at nodes (in order): 16, 2, 3, 1, 4.
1
23
4567
8 910
1
23
4567
8 910
4
13
2 910
14 8 7
16
41 23 16 9 10 14 8 7
16
14 10
893
241
7
A
i
2345678 9101
Correctness
Loop ... M
AX-HEAPIFY on the following heap example.
16
410
14 7 9
281
(a)
16
14 10
4793
281
(b)
16
14 10
8793
241
(c)
3
1
3
4567
910
2
8
1
3
4567
910
2
8
1
3
4567
910...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 3 docx
... overview
[The treatment in the second edition differs from that of the Þrst edition. We use
a different partitioning method—known as “Lomuto partitioning”—in the second
edition, rather than the “Hoare ... program may need to scale a set of (x, y) data to Þt
onto a rectangular display. To do so, the program must Þrst Þnd the minimum
and maximum of each coordinate.
A simple algori...
Introduction to Algorithms Second Edition Instructor’s Manual 2nd phần 4 pot
... c(7n /10 + 6) +an
≤ cn/5 + c + 7cn /10 + 6c + an
= 9cn /10 + 7c + an
= cn + (−cn /10 + 7c +an).
•
This last quantity is ≤ cn if
−cn /10 + 7c + an ≤ 0
cn /10 −7c ≥ an
cn −70c ≥ 10an
c(n − 70) ≥ 10an
c ... 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 usual.
To updat...
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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