13
Algorithms and Data Structures Solutions to Assignment 1 (only for the non-programming tasks) 1
Assignment1 Solutions
Embed Size (px)
DESCRIPTION
Algorithms and Data Structures
Citation preview
-
Algorithms and Data Structures
Solutions to Assignment 1 (only for the non-programming
tasks)
1
-
Task 1
0-2 0-2
1-4 1-4
2-5 2-5
3-6 3-6
0-4 0-4
6-0 6-0
1-3 is connected (throught 1-4-0-6-3)
input output
2
-
Task 2
We do not provide the code for the solution.
However, the key idea is this:
At the beginning, there are N sets remaining.
Every time we do a union, the number of remaining sets decreases
by 1.
3
-
Task 3
p q 0 1 2 3 4 5 6
Number of times
the id array is
accessed
0 2 2 1 2 3 4 5 6 10005
1 4 2 4 2 3 4 5 6 10005
2 5 5 4 5 3 4 5 6 10008
3 6 5 4 5 6 4 5 6 10005
0 4 4 4 4 6 4 4 6 10011
6 0 4 4 4 4 4 4 4 10008
1 3 4 4 4 4 4 4 4 2
4
-
Task 4 Figure 1.7
p q 0 1 2 3 4 5 6 7 8 9
3 4 0 1 2 3 3 5 6 7 8 9
4 9 0 1 2 3 3 5 6 7 8 3
8 0 8 1 2 3 3 5 6 7 8 3
2 3 8 1 3 3 3 5 6 7 8 3
5 6 8 1 3 3 3 5 5 7 8 3
5 9 8 1 3 3 3 3 5 7 8 3
7 3 8 1 3 3 3 3 5 3 8 3
4 8 8 1 3 3 3 3 5 3 3 3
6 1 8 3 3 3 3 3 5 3 3 3
5
-
Task 4 Figure 1.8
p q 0 1 2 3 4 5 6 7 8 9
0 1 0 0 2 3 4 5 6 7 8 9
2 3 0 0 2 2 4 5 6 7 8 9
4 5 0 0 2 2 4 4 6 7 8 9
6 7 0 0 2 2 4 4 6 6 8 9
8 9 0 0 2 2 4 4 6 6 8 8
0 2 0 0 0 2 4 4 6 6 8 8
4 6 0 0 0 2 4 4 4 6 8 8
0 4 0 0 0 2 0 4 4 6 8 8
0 8 0 0 0 2 0 4 4 6 0 8
6
-
Task 5
p q 0 1 2 3 4 5 6 # times
0 2 0 1 0 3 4 5 6 3
1 4 0 1 0 3 1 5 6 3
2 5 0 1 0 3 1 0 6 5
3 6 0 1 0 3 1 0 3 3
0 4 0 0 0 3 1 0 3 5
6 0 0 1 0 0 1 0 3 5
1 3 0 0 0 0 1 0 3 6
7
-
Task 6
M=106 input pairs
N=109 nodes
Assumption: each input pair leads to a union (otherwise, in the
extreme case, if no input pair leads to a union, the running time
is 0 days).
F = Minimum number of instructions to execute one iteration of a
for loop execution = 10 instructions
C = 109 instructions/sec
Formula = (M*N*F)/C = 1016 / 109 =107 sec
115.74 days (1 day = 86400 sec)
8
-
Task 7
M=106 input pairs
N=109 nodes
W = maximum number of instructions to execute each iteration of
a while loop = 100 instructions
C = 109 instructions/sec
Formula = (M * W) / C = 106 x 100 / 109 = 10-1 second
9
-
Task 8
Assume: length 4 4 nodes + 3 edges.
Input Sequence: 6-1, 2-3, 1-3, 5-8,4-0,7-9, 8-7,8-4,9-2
5
8 4 7 6
0 9 1 3
2 10
-
Task 10 Step 1
0
1
2
3
4
5
6
7
Connect:
1 to 0
3 to 2
5 to 4
7 to 6
11
-
Task 10 Step 2
0
1 2
3
4
5 6
7
Connect:
2 to 0
6 to 4
12
-
Task 10 Step 3
0
1 2
3
4
5 6
7
Connect 4 to 0
13
