# Câu 1
## a. Tìm ước chung lớn nhất
```mermaid
graph TD
A(Bắt đầu) --> B[/Nhập 2 số a, b/]
B --> C{a=b}
C -->|Đúng| D[/Hiển thị ước chung lớn nhất/]
E -->|Đúng| F[a=a-b]
C -->|Sai| E{a>b}
E -->|Sai| G[b=b-a]
F --> C
G --> C
D --> H(Kết thúc)
```
## b. Giải và biện luận phương trình bậc 2
```mermaid
graph TD
A(Bắt đầu) --> B[/Nhập 3 số a, b, c/]
B --> C{a=0}
C --> |Sai| D[delta = b^2 - 4*a*c]
D --> E{delta=0}
E --> |Đúng| F["x1=-b/(2*a)"]
F --> P[/Phương trình có nghiệm kép, x/]
E --> |Sai| H{delta > 0}
H --> |Đúng| K["x1=(delta^(1/2)-b)/(2*a*c), x2=(-delta^(1/2)-b)/(2*a*c)"]
K --> G[/Phương trình có 2 nghiệm phân biệt, x1,x2/]
H --> |Sai| L[/Phương trình vô nghiệm/]
G --> T(Kết thúc)
L --> T
P --> T
C --> |Đúng| U{b=0}
U --> |Đúng| V{c=0}
V --> |Sai| L
U --> |Sai| N[x=-c/b]
N --> M[/Phương trình có 1 nghiệm duy nhất, x/]
V --> |Đúng| I[/Phương trình có vô số nghiệm/]
M --> T
I --> T
```
# Câu 2
```mermaid
classDiagram
PremiumCustomer --|> Customer
RegularCustomer --|> Customer
PurchaseDetail -- Product
PurchaseDetail -- Customer
Bill ..|> PaymentCounter : Accepts
Bill ..> Discount
Bill ..> PurchaseDetail
Bill --o Customer : Belongs to
Discount ..> PurchaseDetail
Customer "1" -- "*" Product : Is Sold To, Purchases
Address "1" --* "1" Customer : Has
class Customer{
custName: String
custID: Int
custPhnum: Int
purchaseItem()
requestBill()
enterCustDetail()
}
class PremiumCustomer{
premiumDiscount: Int
enterCustDetail()
}
class RegularCustomer{
regularDiscount: Int
enterCustDetail()
}
class Address{
street: String
city: String
state: String
zipcode: Int
enterStreet()
enterCity()
enterState()
enterZipcode()
}
class Product{
productID: Int
productName: String
productPrice: Float
getPrice()
setPrice()
}
class PurchaseDetail{
custID: Int
quantity: Int
purchaseDate: Date
productID: Int
caculateTotalAmt()
generatePurchaseList()
}
class Discount{
discountType
discountValue
SelectDiscount()
}
class Bill{
payableAmt
caculatePayableAmt()
generateBill()
}
class PaymentCounter{
<<>>
caculatePayableAmt()
generateBill()
}
```
## Chú thích:
**Nguyên mẫu của class PaymentCounter**
```
class PaymentCounter{
<<interface>>
caculatePayableAmt()
generateBill()
}
```
`Em không hiểu tại sao khi em chèn thêm text vào trong cặp dấu "<<>>" thì nó không hiển thị được.`
[Class Diagram em vẽ trong Mermaid live editor](https://mermaid-js.github.io/mermaid-live-editor/#/edit/eyJjb2RlIjoiY2xhc3NEaWFncmFtXG4gICAgUHJlbWl1bUN1c3RvbWVyIC0tfD4gQ3VzdG9tZXJcbiAgICBSZWd1bGFyQ3VzdG9tZXIgLS18PiBDdXN0b21lclxuICAgIFxuICAgIFB1cmNoYXNlRGV0YWlsIC0tIFByb2R1Y3RcbiAgICBQdXJjaGFzZURldGFpbCAtLSBDdXN0b21lclxuICAgIFxuICAgIEJpbGwgLi58PiBQYXltZW50Q291bnRlciA6IEFjY2VwdHNcbiAgICBCaWxsIC4uPiBEaXNjb3VudFxuICAgIEJpbGwgLi4-IFB1cmNoYXNlRGV0YWlsXG4gICAgQmlsbCAtLW8gQ3VzdG9tZXIgOiBCZWxvbmdzIHRvXG4gICAgXG4gICAgRGlzY291bnQgLi4-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)
# Câu 3
```mermaid
sequenceDiagram
participant Customer
participant Search Page
participant Search Results Page
participant Catalog
participant Search Results
activate Customer
Note left of Customer: The Customer specifies an author <br/> on the Search Page and then <br/>presses the Search button.
Customer ->>+ Search Page: 1:onsearch(author)
Note left of Customer: The system validates the <br/> Customer's search criterial.
Search Page ->> Search Page: 1.1:validateSearchCriteria()
alt author entered
Note left of Customer: If author is entered, the System <br/>searches the Catalog for books <br/>assoicated with the specified author.
Search Page ->> Catalog: 1.2:searchByAuthor(author)
activate Catalog
Catalog ->> Search Results: 1.2.1:create()
activate Search Results
Note left of Customer: When the search is complete, the <br/>system displays the search results on <br/>the Search Results Page.
Search Results ->> Search Results Page: 1.2.1.1:display()
deactivate Search Results
activate Search Results Page
deactivate Search Results Page
else author not entered
deactivate Catalog
Note left of Customer: If the Customer did not enter the <br/>name of an author before pressing <br/>the Search button, the System displays <br/>an error message.
Search Page ->>- Search Page: 1.3:displayErrorMessage()
end
deactivate Customer
```
# Câu 4
**ATM State Machine Diagram**
```mermaid
stateDiagram
Idl: Idle
state VerifyAccount{
VerC: VerifyCard
CV: CardValid
VP: VerifyPin
PIC: PinIncorrect
PC: PinCorrect
CV --> VP
VerC --> CardValid
CardValid --> CV : [cardValid]
VP --> PinCorrect
PinCorrect --> PIC : [else]
PinCorrect --> PC: [PINValid]
PIC --> VP: [tries < maxTries]/tries++
VP: pinSubmitted /
VP: checkPin /
VP: returnCard /
VerC: cardSubmitted /
VerC: readCard /
VerC: returnCard /
}
PR: PrintReceipt
DM: DispenseMoney
AAc: AccountActions
DM --> PR
AAc --> DM
AAc --> PR
DM --> TransactionComplete
PR --> TransactionComplete
[*] --> Idl
Idl --> VerifyAccount
TransactionComplete --> Idl
```
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