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EC 504 functions
Creation date：2024-05-21 17:15:14
Belonging category：数学mathematics
Tag EC 504
functions

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EC 504 Midterm Pratice

Instructions: Put your name and BU ID on the first page. This exam is closed book
and no notes – except for 2 pages of personal notes to be passed in the end. No use
of laptops or internet. You have one hour and fifty minutes. Do the easy ones first.
1. (20 pts) Answer True or False to each of the questions below. Each question is worth 2 points.
Answer true only if it is true as stated, with no additional assumptions. No explanation is
needed, but any explanation is likely to earn partial credit, and no explanation will not earn
any credit if the answer is wrong.
(a) N2e−1/ ln(N) ∈ Θ(Neln(N)).
Solution: False: N2e−1/ ln(N) ∈ Θ(N2), since 1/ln(N) → 0 it does not change the
Θ(N2) factor.
(b) If fi(n) ∈ O(n2), then
∑n
i=1 fi(n) ∈ O(n3)
Solution: True. There are n terms, each of which is O(n2), so you can bound this by
a constant times n3, making it O(n3).
(c) The following tree is an AVL binary search tree – explain.
11
/ \
9 23
/ \ / \
8 12 16 50
/ \ / \
1 10 10 80
Solution: False. The key 12 must be the right of 11 and the second 10 to the left of
11.
(d) The second smallest element in a binary min-heap with all elements with distinct values
will always be a child of the root.
Solution: True. The children of the root must be smaller than any of their children.
(e) The set Θ(f(n)) is identical to the set O(f(n))∩Ω(f(n)) (Note: ∩ means intersection
of two sets.)
Solution: False. It is identical to Θ((f(n)) ∩ Ω(f(n)) but not the larger set O(f(n))
that include slower functions. (e.g. like the relation ≤).
(f) It is possible to formulate Quick Sort to be worst case O(N logN) including the cost
of picking a suitable pivot.
Solution: True. You pick the pivot to be them medium using the ()(N) algorirthm
that sorts N/5 columns recursive find the medium for N/5 in the middle row.
1
(g) Consider the array [2, 20, 3, 21, 90, 4,23, 22]. This array has elements in order of a
min-heap.
Solution: True. All path for the root are in decreasing order.
2
/ \
20 3
/ \ / \
21 90 4 23
/
22
(h) A min-Heap (or priority queue) is a null tree or a root node with a minimum value
plus a left and a right min-Heap subtrees.
Solution: True. This is the correct recursive defintion of a min-Heap.
(i) The maximum subsequence sum algorithm finds i and j that maximize
∑j
k=i a[k] for
an array a[N ] of positive and negative integers. The fastest one is a recursive algorithm
with complexity Θ(N logN).
Solution: False. As I demonstrated in class, qx the fastest one, which is a sort of
investors scan, is Θ(N) – suprising!
(j) NN ∈ O( eln(N !) )
Solution: True. The Sterling’s approxmation of the factorial: N ! =
√
2piNNNe−M(1+
O(1/N)) shows that is goes slower than N ! so N ! = O(NN) but not the reverse.
2. (10 pts) Consider the binary tree illustrated below.
*
/ \
+ -
/ \ / \
* 8 - 10
/ \ / \
+ 2 8 *
/ \ / \
6 7 2 3
(a) List the node values in the order in which they would be found in an in-order traversal.
2
(b) List nodes in pre-order.
(c) List the nodes in post=order.
(d) Which order is uses on stack to do the arithmetic? . (HINT the stack order is like
depth first search on this tree!) Evaluate the arithmetic using stack
Solution:
In-order
6 + 7 ∗ 2 + 8 ∗ 8 − 2 ∗ 3 − 10 (1)
pre-order
∗ + ∗ + 6 7 2 8 − − 8 ∗ 2 3 10 (2)
post-order
6 7 + 2 ∗ 8 + 8 2 3 ∗ − − 10 − ∗ (3)
Evaluation of arithmatic. Easiest way is bottom up on the tree (e.g. in-order) to get Result
is −272. The stack has two solutions.
You get −272 if you remeber that we pushed left and then right so for a minus sign is
pop y pop x =⇒ x− y.
You could assume pop x pop y - =⇒ y − x which gives 408. I accept this rule altough
it is inconsistent with the definition of post-order. This could be corrected by exchangeing
left and righ in post order. Hard becuase Minus sign hard because ther are not symmetric.
3
3. (20 pts) Consider the following min-heap.
1
/ \
10 2
/ \ / \
11 12 17 3
/ \ / \ / \ / \
15 18 201 13 155 20 4 5
/ \ /
17 16 21
(a) Show the min-heap which results after inserting the element 7 in the heap. (Indicate
the sequence of steps with arrows.) Then in this new heap show the steps required to
delete element 1 and then delete 11. Draw the final min-heap.
(b) Re-arrange the original min-heap (repeated below) into a max-heap by a “bottom up”
O(N) algorithm. Describe the steps level by level.
1
/ \
10 2
/ \ / \
11 12 17 3
/ \ / \ / \ / \
15 18 201 13 155 20 4 5
/ \ /
17 16 21
Solution:
Start with next to bottom row of 8
1
/ \
10 2
/ \ / \
11 12 17 3
/ \ / \ / \ / \
17 21 201 13 155 20 4 5 <---- Start with row of 8
/ \ /
15 16 18
4
1/ \
10 2
/ \ / \
21 201 155 5 <---- Next row of 4
/ \ / \ / \ / \
17 18 12 13 17 20 4 3
/ \ /
15 16 11
1
/ \
201 155 <---- Next row of 2
/ \ / \
21 13 20 5
/ \ / \ / \ / \
17 18 12 10 17 2 4 3
/ \ /
15 16 11
201 <---- Final Root node
/ \
21 155
/ \ / \
18 13 20 5
/ \ / \ / \ / \
17 11 12 10 17 2 4 3
/ \ /
15 16 1
(c) Using this example for a min-heap with the size N = 18 and a[0] = N. Describe
in a few word an an Θ(N logN) algorithm to sort in place the array elements
a[1], a[2], · · · , a[N ] in descending order (i.e. a[1] > a[2] > · · · > a[N ] )
Solution: a[0] store the size of heap starting with a[0] = N The algorithm is iterative.
You delete the min in a[1] restoring the heap and copying a[a[0]]] = a[1] reducing
the size by by 1 (a[0] = a[0] − 1) until the heap is empty (a[0] = 0) Now the array
a[1], a[2], ..a[N ] is sorted array in descending order. Restorig the heap each time is
(log(N) so the alogritym is O(NlogN)
(d) Solve the recursion relation for the Heap, T (H) = 2T (H − 1) + c0H to show that
“bottom up” scales like T (H) = Ω(N) (HINT: Use N ' 2H)
Solution:
5
Substitute the guess in the equation that is suggested: T (H) = c 2H
c 2H ' c 2 2H−1 + c0H = c 2H + c0H ' c 2H (4)
So the leading behavior is T [H] = c 2H ∈ Ω(H).
6
4. (20 pts) This problem is to construct step by step BST and AVL trees given the following
list of N = 12 elements.
1 2 12 7 3 6 30 36 37 2 40 51
(a) Insert them sequentially into a BST (Binary Search Tree).
Solution: The BST (depth of a node is the numbe of hop form the root. height is the
maximun number of hops to the deapest node.
1 h=7, d = 0
\
2 h=6, d = 1
/ \
h=0, d = 2 2 12 h=5, d = 2
/ \
h=2, d = 3 7 30 h=4, d = 3
/ \
h= 1,d = 4 3 36 h=3, d = 4
\ \
h=0, d = 5 6 37 h=2, d = 5
\
40 h=1, d = 6
\
51 h=0, d = 7
(b) Insert them sequentially into an empty AVL tree, restoring the AVL property after
each insertion. Show the AVL tree which results after each insertion and name the
type of rotation (RR or LL zig-zig or versus RL or LR zig-zag).
Solution: Final AVL form; See next page for sequence of steps!
30 h = 3 d = 0
/ \
3 36 h = 2 d = 1
/ \ / \
2 7 3 48 h = 1 d = 2 (excep 3 is h =0)
/ \ \ / \
1 2 6 37 54 h = 0 d = 3 (excep 3 is h =0)
(c) Give the total height TH(N) and the total depth TD(N) for both the resulting BST
and AVL.
(d) Compare the sum TH(N)+TD(N) for the BST and AVL. For each compare these values
with HN where H is the height of each tree.
7
Solution: BST:
TH(N) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 1 + 2 = 31
and
TD(N) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 2 + 3 + 4 + 5 = 42
So TH(N) + TD(N) = 73 < HN = 7 ∗ 12 = 84
AVL:
TH(N = 3 + 2 ∗ 2 + 3 ∗ 1 = 10
and
TD(N) = 2 ∗ 1 + 4 ∗ 2 + 5 ∗ 3 = 25
So‘ TH(N) + TD(N) = 35 < HN = 3 ∗ 12 = 36
Note a perfect tree of N = 15 and height H = 3 has
TH(N) = 3 + 2 ∗ 2 + 4 ∗ 1 = 11
and
TD(N) = 2 ∗ 1 + 4 ∗ 2 + 8 ∗ 3 = 34
so TH(N) + TD(N) = 45 = HN = 3 ∗ 15 = 45
I thought this is the only one that saturates the upper bound but a counter
example is to remove one leaf NH → NH −H and that leaf remove d = H
form the sum of TD(N)!
8
5. (10 POINTS) Consider the following recursion relation.
T (N) = 3T (N/2) +Nk
(a) Substitute T (N) = c0N
γ into the homogeneous equation (i.e. dropping Nk) and de-
termine γ and for what values of k does the exact solution satisfy T (N) = Θ(Nγ).
Solution: The homogeneous equation (i.e. drop the last term has solution by substi-
tution
c0 N
γ = c0 3 (N/2)
γ =⇒ 1 = 3/2γ or γ = log(3)/ log(2) (5)
Base 2 is nice since log2(2) = 1 or γ = log2(3)
This is gives a leading solution T (N) = Θ(Nγ) if k < γ
(b) Now assume that k = γ and find the exact solution in the form: T (N) = c0N
γ +
c1N
γ log2(N). (HINT: First show that c1 = 1. Then Determine c0 in terms of T (1) by
setting N = 1. )
Solution: Note a homogeneous solution never determines the multiplicative const c0.
For this we must find a fulls solution. The substution gives
c0 N
γ + c1N
γ log2(N) = c0 3 (N/2)
γ + c13(N/2)
γ log2(N/2) +N
γ
= c0 3 (N/2)
γ + c1(N)
γ[log2(N)− log2(2)] +Nγ (6)
Obviously the first (homegeneous term) still cancels. We could have ignore this piece
for now.
But to cancel the additive term we need to use both 3/2γ = 1 and again log2(2) = 1,
to get c1 = 1. The setting N = 1 we finally fix c0 by T (1) = c0 1
γ + c11
γ log2(1) = c0.
Actually you can do this step first if you prefer.
9
6. (20 pts) You are interested in compression. Given a file with characters, you want to find
the binary code which satisfies the prefix property (no conflicts) and which minimizes the
number of bits required. As an example, consider an alphabet with 8 symbols, with relative
weights (frequency) of appearance in an average text file 1 give below:
alphabet:| V | A | M | P | I | R | E | S |
weights:| 4 | 40 | 16 | 7 | 30 | 18 | 75 | 8 |
(a) Determine the Huffman code by constructing a tree with minimum external path
length:
∑8
i=1widi. (Arrange tree with smaller weights to the left.) Solution:
V P S M R I A E
4 7 8 16 18 30 40 75
27
40
11
1
Minimize ext length = ∑i wi di
4 V
34
74
16 M
198
49
19
18 R
75 E
7 P
8 S
30A
1
1
1
1
1
1
0
0
0
0
0
Sort Wi =
0
123
I
0
(b) Identity the code for each letter and list the number of bits for each letter and compute
the average number of bits per symbol in this code. Is it less than 3? (You can leave the
answer as a fraction since getting the decimal value is difficult without a calculator.)
Solution:
(c) Give an example of weights for these 8 symbols that would saturate 3 bits per letter.
What would the Huffman tree look like? Is a Huffman code tree always a full tree?
Solution:
1vampire: Origin mid 18th cent: from French, from Hungarian vampir, perhaps form Turkish uber “witch”.
In European folklore, a monster with long pointed canine teeth!
10
RESULTING CODE: AVERAGE BITS/CHAR =508/198 = 2.565
Letter Weight Code Bits Count
! E 75 0 1 75
! A 40 101 3 120
! I 30 111 3 90
! M 16 1000 4 64
! R 18 1001 4 72
! S 8 1100 4 32
! V 4 11010 5 20
! P 67 11011 5 35
Total: 198 508
28
External length = ∑i wi di
It is perfect binary tree. One can have each have weight 10 for example
( 80 )
/ \
(40) (40)
/ \ / \
(20) (20) (20) (20)
/ \ / \ / \ / \
V A M P I R E S
Actually the weight don’t have to exactly equal. Try it with weights:
100, 101, 102, 103, 104, 105, 106, 107
It is still perfect tree1
11
7. (10 POINTS EXTRA CREDIT) Given an array of N-distinct positive integers a[N ] and a
second array of N-distinct positive integers b[N ] to construct the sum:
N−1∑
i=0
a[i] ∗ b[i] (7)
(a) Assume that a[k] is sorted in ascending order. Give an O(N logN) algorithm that
maximizing the sum S by permuting the values of b[k]. Solution: To maximize the
sum you sort the array b[k] into ascending order by any Θ(NlogN) algorithm such
as merg sort. This is an example of every pair {i, j} maximizing the scalar product
a[i]b[i] + a[j]b[j] since a[i] < a[j] and b[i] < b[j]. Any exchang of i, j reduces this
contribution the sum.
(b) Given the result of part (a) give an algorithm that minimizes S in O(N).
Solution: To minimize the result of part (a) one just reverse the order of b[k] with
N/2 swaps of b[i] and b[N − 1− i] for i = 0, 1, · · ·N/2
(c) If you are allowed to permute independently both a[k] and b[k] how many different
solutions will maximize S? Solution: There are N ! solution because give maximun
Smax =
N−1∑
k=0
a[k] ∗ b[k] (8)
as describe in part (a) is unchange by any simultaineous permutation of k (pi(k)
Smax =
N−1∑
k=0
a[pi(k)] ∗ b[pi(k)] (9)
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CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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CSCI262 SCC.311 COMP8101 IAB320 CHC5028 TSP ICC565 CS512 320SC COMP2396 COMP207 SVM BSCH EECS 2101 COMP3230 CEG3136 INFO 3440 EE3009 MGT7174 COMP 3334 ECON20120 Econ 702 CFRM 505 CS4001 CSE 328 AMATH 482 ENG2008 MATH39522 DTS101TC CSC318 EDUC 124 NBA 5110 ECON0125 ELEC7310 EEP101 ECE 777AE MDS 6112 Bioc0036 ACCFIN5246 STA 404 CFRM505 Chinese 2241G MATH 376 AUENV 218 ELEC0006 ACCT 3230 FIN3020 ENVM3115 CMPSC 464 EE 4233 CST 8284 ENGI 2211 EEB240 COMP52715 PHYS1120 ECON0019 MAT187 FINN1037 CSci 5421 7SSMM803 STAT 400 LUBS5996M ELC5216 STATS 4A03 ENGG1003 BADM 3661 DATA423 ST332 ECO2121 6406ELE IB3K20 CSE 465 CSE115 CMPUT 206 ecs150 INU1111 QM222 DTS204TC MATH2319 CPT108 SENG6110 MATH3041 INFS3604 MA 4704 CIVIL 750 EEEE4123 CS 3800 comp3511 MEC206 CSCI-UA.202 IOM 302 NBS8295 BMS 201 ECON 3018 ESE 605 ADM3225 STAT7038 Economics 409 ECON 503 MSE800 4SSMN902 IEOR E4106 FRE6831 ISE 563 MATH 451 ECON0001 COMPSCI369 CITS4402 MA1608 MQBS1030 MUSC1982 CITS4012 ACC202 BAFI1026 MA117 ECON5074 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270M CIS 3207 Programs CSCI 2132 CS270 CSE-381 COMP3230A CIS 212 CSI 333 FINM 326 FINM-36702 Introduction to Software Analysis EEE102 GNG1106 ECS 60 CS 161 CSCI851 CSE1222 EDPS0249 TCHR5003 ANTA02 BBUS1SBY SOSC 1140 MDIA2091 FINS3641 INSY 661 ITEC3040 CPSC 481 computer DEE3519 COMP304 CSE536 Microtheory OFFICE 280 CIVE50003 COSC2673 ECS784U CMPSC/MATH 455 AMA 505 CSE 158 BUS1040 FIT3179 FIT5202 Math 104A Math 111A MBUS107 COMPSCI 761 COMP3710 COMPSCI 316 COMP559 COMP557 CP1 1902 COMP 310 ECED 3403 COMPX523 AGCM 3103 EMET 7001 ENGR3821 CISC 124 IPC comp20005 CS 323 CS105 STAT 326 MATH4007 CS4551 COMP1000 ACIT 4640 ENVX3002 CS2034 FC712 algorithms CSCI 4155 CSI4142 POL 850 MATH20811 2B03 CSCI803 Economies COMP 2016 Architect TRADE INFO1110 FIT1043 networks Robotics ICS 31 ECEC-301 FIT2099 CS 3640 CSE1010 Computational COMP1001 CSE 231 CS10 FIT5166 CSE 400 CSCI561 Math 350 CO-496 ENGG6400 CSCI 1133 COMP3055 MATH 819 CSE 6363 CIS 555 CS4420 COMP0037 ECS 140A Spanning Tree Protocol network 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4061 ECON 8820 INT104 ITE3713 CS551J ECM1410 CSMBD21 COMP 2012 CISC221 Code SCC312 COMP639 CMPSC 221 system COMP3217 COMP1721 ENG5056 Math 466 COMP0039 MFIN 5400F FINN40915 EENG31400 MODL5007M ​EEET 3050 EEET 3050 Quantitative Methods mathematics COMP1921 FIN3309 VE311 ESCI 1908 FIT5057 COSC2446 COMPUTING Math 110A EE 567 MATH10098 CISC642 EE10134 ECE 321 MTH2051 SIT 281 EEE3314 ELEC273 COMP5930M CE322 ELEC270 EE5101 MCEN90008 MTSC 887 Probability ENGN4528 MAE 424 MA2552 EBU5303 CHEM10600 EBU6018 ELEC2103 ELEE 5200 CSE 535 COMP6528 IS6153 IS3S664 BUSANA 7003 QTS0109 ECO3152B ENGR 227 LCSCI4208 MATH32051 ECS776P MGMT3004 N1551 JAVA ROB-6213 TNS3113 BEEM062 COMP47670 4SSMN903 BST 833 COEN 146 BASC0003 CAS EC501 Networks CSIT940 ELEC372 ACCFIN5034 Math 3527 DATA4000 INT102 FND109 MMM071 ROB6213 ETF5650 ECON 445 QMSS 301 Econ 320 PHY 4390 FIN 111 FINN41615 ECS 116 MTH6158 IOE 552 STA 141B Math 413 ECON3016 Physics 4303 Numerical BFF5270 EECS 111 FINANCE 251 COMP814 MGSC 410 ECON0051 EBU5376 STAT6118 ECON 20110 COMU7000 average acceleration BUSI4412 BFF3121 BIT233 ECMM462 ETC3430 DESN2348 INTE2584 ENME502 MA3XJ INTE2627 MA2815 MA3AM L0101 Math 3MB3 CPCCBC4004 EEEM061 0502E220 APPLIED 6SSMN310 ENV 3310 PM2PCOL3 CONS6201 MATH502 FIT5003 EEEN313 MATH3001 MECH3460 ECON30009 COSC1252 Assembler COMP 3023 ENGG7601 COMP20005 COMP SCI 1103 ICSI 402 INF2C CS320 COMPSCI7064 ECE 3220 PROGRAMMAMING MIPS Computer Science 2413 AM3611 MSOA TE2101 FFT CMPSC-121 CSE 109 COMP SCI 7064 HCI CMP-5013A CCN2042 COMP3400 EEEN30052 CO4215 EE101 KIT107 CSE 421 CSE521 MCD4720 EECS 280 MIT 403 GRPC VG101 APiE EECE 1080C FIT3143 CSE 325 ISOM 3029 CS3307 State SIT255 Engineering MQF Modelling ACX3150 SIA322 ACCT90004 COMU7201 MGMT90018 WRIT1000 COMP3702 BISM1201 COMP7505 IDEA9106 CSE3SMT BFC5926 BFC5280 BFC5935 QBUS3330 ECON3700 IFN521 ECON2121 COSC2626 MA413 DDES9903 ENGG1300 COMP9337 CO2201 ACCT2002 ICM289 MMM054 MSBA-204 DIGM707 CSC2250 Econ312 EVAT python CAN404 LUBS2840 CSCI-GA.2250 COMSM0093 COMP281 AFM 333 IBUS1001 CP2501 Math 105A VE320 TEC101 SOCY2166 COM240 EFIM20033 ENGI4467 EFIM20034 EC 979 BE432 7EJ502 CSSE6400 COMP90025 Econ 312 ENG2031 ECO0006 EXERSCI 207 CAN209 ECO 137W FT312 ECO 2199 MATH32052 BDW4213 APS 360 SAS 6 CHME0017 PO92Q Economics 01AV MATH39512 MATH 5486 COMP8620 ISE102 ECON235 ECON 206 FI 345 PHAY0020 MATH0099 MATH0085 EFB106 PHY 134 MAE115 circuits Chemistry CSE12 MATH-UA 233 PHAS0038 COMP2140 CONMGNT 7049 COMP151101 ECON 485 ACX5903 ENGN6536 ARCH1162 Law PHAS0042 CCF1C03 MATH 351 Phys 139 AG942 MGT001371 APH106 ECON1051 MA4AM MA3Z7 NUMBER THEORY REST0006 SESS0026 STAT0023 TABL 2741 CMP4008Y EFIM10015 Acct 560 PSYC735 GEOG 5 ACCT3104 CSEC5616 PHIL1012 ITLS6111 ECON8022 5CCM226A compX123 MA4XJ R001 EWB LLP120 COMP643 ENG 103 ECON 23950 ACCT 207 FINC 616 Bio99 Math 137A Psychology BCPM0054 MATH20212 EC3450 CENV6141 PSY 205 CE335 CS365 Calculus ACSD INFT6800 MCIT INFO6030 PHYS 111LV H63EEJ ECON2151 ENGI 2181 MTRX1701 PLIT08009 CS240 Math 270 CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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