# Code Analysis

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Not to be confused with Source Code.

Code Analysis is a Division B and Division C event that was first run as a trial event at the 2018 Virginia state tournament and at the 2019 Wisconsin state tournament. It was also run at the 2019 Massachusetts state tournament as Python Code Analysis, using Python as the target language rather than Java. At the 2020 Washington state tournament, it replaced Ping Pong Parachute. Competitors are asked to determine the output or error that a given piece of code outputs without running the code. Each team is allowed one 8.5"x11" double-sided reference sheet, or two single-sided reference sheets of the same size.

## The Event

Teams are not allowed to bring electronic devices into the testing room. All code given will be in Java, but problems focus on general programming concepts as opposed to specific qualities of Java. Problems may be written in a variety of ways, such as a series of statements, a method to be called with specific arguments, or a complete program with a main() method. All inputs and values will be specified, and no external inputs are allowed. All code given will also be properly indented.

While problems may be written in different ways, there are only two types of answers that will be requested. The competitor will determine the output of the code as created by System.out.print(), System.out.printIn(), and/or System.out.format() if a problem has an output. Space will be provided for the competitor to write their answer, and if the answer depends on spacing then a grid will be given so the answer is aligned properly. However, if the code has an error, then the competitor will be asked to describe the run-time error that occurs when the code is run. The error message or exception type does not need to be reproduced, but the competitor must describe what goes wrong and how to correct it.

## Subjectivity in Test Writing

Test writers are free to craft the test according to their own coding philosophies. Based on an informal survey of a half dozen 2018/2019 tests:

• some embrace obfuscation, while others stick to clean ("honest") code.
• nearly all tests have at least one problem with recursion, although this recursion often ends up being simple single-branch nesting of no more than 3 levels.
• some tests emphasize mastery of printf and precise output formatting -- \n, whitespace, ASCII, etc. Other tests simply calculate numbers and print them, one per line.
• non-descriptive variable names and method names are very common -- i, x, n, foo, etc.
• some tests use nonsensical junk code with zero practical value. Other tests are full of real, usable code -- sorting, towers of hanoi, prime number calculations, etc.

## Binary

Binary is the most basic form of data used by a computer. While most programs are not written in binary, it is important to have an understanding of how binary works. Binary is a base 2 system of counting, where decimal is known as base 10. As indicated by the base, binary only uses two digits used in binary code - 0 and 1. Each number is known as a bit, and there are eight bits in a byte. Half a byte (4 bits) is also known as a nibble. Individual bits can be manipulated by bitwise operations, such as AND (&), OR (|), or XOR (^). Binary numbers are also known as bit strings, and when translated into decimal or hexadecimal numbers encode for specific data.

### ASCII

ASCII is a form of character encoding, where each letter or character used corresponds to a code that is readable by the computer. ASCII encodes for 128 characters, with each character corresponding to either a printed or non-printed symbol. Printed symbols consist of the 26 letters in the English alphabet, numerals 0 through 9, and various punctuation marks like periods or exclamation points. As ASCII was originally designed for teleprinters, the other non-printing symbols (also known as control characters) were used to control the formatting of characters on a page like return or tab. Each of these characters corresponds to a decimal number, which in turn represents a hexadecimal number and a binary number. This binary number is what the computer reads in order to display the desired character. While ASCII characters were originally encoded using 7 bits, extended versions of ASCII implement additional characters using 8 bit codes. Below is a table of ASCII values:

Original Characters
Decimal Hex Oct HTML Char Type
0 0x0 08 NUL (null) Control
1 0x1 18 SOH (start of heading) Control
2 0x2 28 STX (start of text) Control
3 0x3 38 ETX (end of text) Control
4 0x4 48 EOT (end of transmission) Control
5 0x5 58 ENQ (enquiry) Control
6 0x6 68 ACK (acknowledge) Control
7 0x7 78 BEL (bell) Control
8 0x8 108 BS (backspace) Control
9 0x9 118 TAB (horizontal tab) Control
10 0xA 128 LF (NL line feed, new line) Control
11 0xB 138 VT (vertical tab) Control
12 0xC 148 FF (NP form feed, new page) Control
13 0xD 158 CR (carriage return) Control
14 0xE 168 SO (shift out) Control
15 0xF 178 SI (shift in) Control
16 0x10 208 DLE (data link escape) Control
17 0x11 218 DC1 (device control 1) Control
18 0x12 228 DC2 (device control 2) Control
19 0x13 238 DC3 (device control 3) Control
20 0x14 248 DC4 (device control 4) Control
21 0x15 258 NAK (negative acknowledge) Control
22 0x16 268 SYN (synchronous idle) Control
23 0x17 278 ETB (end of transmission block) Control
24 0x18 308 CAN (cancel) Control
25 0x19 318 EM (end of medium) Control
26 0x1A 328 SUB (substitute) Control
27 0x1B 338 ESC(escape) Control
28 0x1C 348 FS (file separator) Control
29 0x1D 358 GS (group separator) Control
30 0x1E 368 RS (record separator) Control
31 0x1F 378 US (unit separator) Control
32 0x20 408 &#32; (space) Printable
33 0x21 418 &#33; ! Printable
34 0x22 428 &#34; " Printable
35 0x23 438 &#35; # Printable
36 0x24 448 &#36; \$ Printable
37 0x25 458 &#37; % Printable
38 0x26 468 &#38; & Printable
39 0x27 478 &#39; ' Printable
40 0x28 508 &#40; ( Printable
41 0x29 518 &#41; ) Printable
42 0x2a 528 &#42; * Printable
43 0x2b 538 &#43; + Printable
44 0x2c 548 &#44; , Printable
45 0x2d 558 &#45; - Printable
46 0x2e 568 &#46; . Printable
47 0x2f 578 &#47; / Printable
48 0x30 608 &#48; 0 Printable
49 0x31 618 &#49; 1 Printable
50 0x32 628 &#50; 2 Printable
51 0x33 638 &#51; 3 Printable
52 0x34 648 &#52; 4 Printable
53 0x35 658 &#53; 5 Printable
54 0x36 668 &#54; 6 Printable
55 0x37 678 &#55; 7 Printable
56 0x38 708 &#56; 8 Printable
57 0x39 718 &#57; 9 Printable
58 0x3a 728 &#58; : Printable
59 0x3b 738 &#59; ; Printable
60 0x3c 748 &#60; < Printable
61 0x3d 758 &#61; = Printable
62 0x3e 768 &#62; > Printable
63 0x3f 778 &#63; ? Printable
64 0x40 1008 &#64; @ Printable
65 0x41 1018 &#65; A Printable
66 0x42 1028 &#66; B Printable
67 0x43 1038 &#67; C Printable
68 0x44 1048 &#68; D Printable
69 0x45 1058 &#69; E Printable
70 0x46 1068 &#70; F Printable
71 0x47 1078 &#71; G Printable
72 0x48 1108 &#72; H Printable
73 0x49 1118 &#73; I Printable
74 0x4a 1128 &#74; J Printable
75 0x4b 1138 &#75; K Printable
76 0x4c 1148 &#76; L Printable
77 0x4d 1158 &#77; M Printable
78 0x4e 1168 &#78; N Printable
79 0x4f 1178 &#79; O Printable
80 0x50 1208 &#80; P Printable
81 0x51 1218 &#81; Q Printable
82 0x52 1228 &#82; R Printable
83 0x53 1238 &#83; S Printable
84 0x54 1248 &#84; T Printable
85 0x55 1258 &#85; U Printable
86 0x56 1268 &#86; V Printable
87 0x57 1278 &#87; W Printable
88 0x58 1308 &#88; X Printable
89 0x59 1318 &#89; Y Printable
90 0x5a 1328 &#90; Z Printable
91 0x5b 1338 &#91; [ Printable
92 0x5c 1348 &#92; \ Printable
93 0x5d 1358 &#93; ] Printable
94 0x5e 1368 &#94; ^ Printable
95 0x5f 1378 &#95; _ Printable
96 0x60 1408 &#96;  Printable
97 0x61 1418 &#97; a Printable
98 0x62 1428 &#98; b Printable
99 0x63 1438 &#99; c Printable
100 0x64 1448 &#100; d Printable
101 0x65 1458 &#101; e Printable
102 0x66 1468 &#102; f Printable
103 0x67 1478 &#103; g Printable
104 0x68 1508 &#104; h Printable
105 0x69 1518 &#105; i Printable
106 0x6a 1528 &#106; j Printable
107 0x6b 1538 &#107; k Printable
108 0x6c 1548 &#108; l Printable
109 0x6d 1558 &#109; m Printable
110 0x6e 1568 &#110; n Printable
111 0x6f 1578 &#111; o Printable
112 0x70 1608 &#112; p Printable
113 0x71 1618 &#113; q Printable
114 0x72 1628 &#114; r Printable
115 0x73 1638 &#115; s Printable
116 0x74 1648 &#116; t Printable
117 0x75 1658 &#117; u Printable
118 0x76 1668 &#118; v Printable
119 0x77 1678 &#119; w Printable
120 0x78 1708 &#120; x Printable
121 0x79 1718 &#121; y Printable
122 0x7a 1728 &#122; z Printable
123 0x7b 1738 &#123; { Printable
124 0x7c 1748 &#124; | Printable
125 0x7d 1758 &#125; } Printable
126 0x7e 1768 &#126; ~ Printable
127 0x7f 1778 &#127; DEL (delete) Control
Extended Characters
Decimal Hex Oct HTML Char Type
128 0x80 2008 &#128; Ç Extended
129 0x81 2018 &#129; ü Extended
130 0x82 2028 &#130; é Extended
131 0x83 2038 &#131; â Extended
132 0x84 2048 &#132; ä Extended
133 0x85 2058 &#133; à Extended
134 0x86 2068 &#134; å Extended
135 0x87 2078 &#135; ç Extended
136 0x88 2108 &#136; ê Extended
137 0x89 2118 &#137; ë Extended
138 0x8a 2128 &#138; è Extended
139 0x8b 2138 &#139; ï Extended
140 0x8c 2148 &#140; î Extended
141 0x8d 2158 &#141; ì Extended
142 0x8e 2168 &#142; Ä Extended
143 0x8f 2178 &#143; Å Extended
144 0x90 2208 &#144; É Extended
145 0x91 2218 &#145; æ Extended
146 0x92 2228 &#146; Æ Extended
147 0x93 2238 &#147; ô Extended
148 0x94 2248 &#148; ö Extended
149 0x95 2258 &#149; ò Extended
150 0x96 2268 &#150; û Extended
151 0x97 2278 &#151; ù Extended
152 0x98 2308 &#152; ÿ Extended
153 0x99 2318 &#153; Ö Extended
154 0x9a 2328 &#154; Ü Extended
155 0x9b 2338 &#155; ¢ Extended
156 0x9c 2348 &#156; £ Extended
157 0x9d 2358 &#157; ¥ Extended
158 0x9e 2368 &#158; Extended
159 0x9f 2378 &#159; ƒ Extended
160 0xa0 2408 &#160; á Extended
161 0xa1 2418 &#161; í Extended
162 0xa2 2428 &#162; ó Extended
163 0xa3 2438 &#163; ú Extended
164 0xa4 2448 &#164; ñ Extended
165 0xa5 2458 &#165; Ñ Extended
166 0xa6 2468 &#166; ª Extended
167 0xa7 2478 &#167; º Extended
168 0xa8 2508 &#168; ¿ Extended
169 0xa9 2518 &#169; Extended
170 0xaa 2528 &#170; ¬ Extended
171 0xab 2538 &#171; ½ Extended
172 0xac 2548 &#172; ¼ Extended
173 0xad 2558 &#173; ¡ Extended
174 0xae 2568 &#174; « Extended
175 0xaf 2578 &#175; » Extended
176 0xb0 2608 &#176; Extended
177 0xb1 2618 &#177; Extended
178 0xb2 2628 &#178; Extended
179 0xb3 2638 &#179; Extended
180 0xb4 2648 &#180; Extended
181 0xb5 2658 &#181; Extended
182 0xb6 2668 &#182; Extended
183 0xb7 2678 &#183; Extended
184 0xb8 2708 &#184; Extended
185 0xb9 2718 &#185; Extended
186 0xba 2728 &#186; Extended
187 0xbb 2738 &#187; Extended
188 0xbc 2748 &#188; Extended
189 0xbd 2758 &#189; Extended
190 0xbe 2768 &#190; Extended
191 0xbf 2778 &#191; Extended
192 0xc0 3008 &#192; Extended
193 0xc1 3018 &#193; Extended
194 0xc2 3028 &#194; Extended
195 0xc3 3038 &#195; Extended
196 0xc4 3048 &#196; Extended
197 0xc5 3058 &#197; Extended
198 0xc6 3068 &#198; Extended
199 0xc7 3078 &#199; Extended
200 0xc8 3108 &#200; Extended
201 0xc9 3118 &#201; Extended
202 0xca 3128 &#202; Extended
203 0xcb 3138 &#203; Extended
204 0xcc 3148 &#204; Extended
205 0xcd 3158 &#205; Extended
206 0xce 3168 &#206; Extended
207 0xcf 3178 &#207; Extended
208 0xd0 3208 &#208; Extended
209 0xd1 3218 &#209; Extended
210 0xd2 3228 &#210; Extended
211 0xd3 3238 &#211; Extended
212 0xd4 3248 &#212; Extended
213 0xd5 3258 &#213; Extended
214 0xd6 3268 &#214; Extended
215 0xd7 3278 &#215; Extended
216 0xd8 3308 &#216; Extended
217 0xd9 3318 &#217; Extended
218 0xda 3328 &#218; Extended
219 0xdb 3338 &#219; Extended
220 0xdc 3348 &#220; Extended
221 0xdd 3358 &#221; Extended
222 0xde 3368 &#222; Extended
223 0xdf 3378 &#223; Extended
224 0xe0 3408 &#224; α Extended
225 0xe1 3418 &#225; ß Extended
226 0xe2 3428 &#226; Γ Extended
227 0xe3 3438 &#227; π Extended
228 0xe4 3448 &#228; Σ Extended
229 0xe5 3458 &#229; σ Extended
230 0xe6 3468 &#230; µ Extended
231 0xe7 3478 &#231; τ Extended
232 0xe8 3508 &#232; Φ Extended
233 0xe9 3518 &#233; Θ Extended
234 0xea 3528 &#234; Ω Extended
235 0xeb 3538 &#235; δ Extended
236 0xec 3548 &#236; Extended
237 0xed 3558 &#237; φ Extended
238 0xee 3568 &#238; ε Extended
239 0xef 3578 &#239; Extended
240 0xf0 3608 &#240; Extended
241 0xf1 3618 &#241; ± Extended
242 0xf2 3628 &#242; Extended
243 0xf3 3638 &#243; Extended
244 0xf4 3648 &#244; Extended
245 0xf5 3658 &#245; Extended
246 0xf6 3668 &#246; ÷ Extended
247 0xf7 3678 &#247; Extended
248 0xf8 3708 &#248; ° Extended
249 0xf9 3718 &#249; Extended
250 0xfa 3728 &#250; · Extended
251 0xfb 3738 &#251; Extended
252 0xfc 3748 &#252; Extended
253 0xfd 3758 &#253; ² Extended
254 0xfe 3768 &#254; Extended
255 0xff 3778 &#255; nbsp (Non-breaking space or no-break space) Extended

## Operators

Java can manipulate variables in a variety of ways using operators. An operator represents an action or a process, and return the result of that action being performed on one or more operands. The operand is the value which a given action is being performed on. Some operators appear much more frequently than others, but all have their own uses.

### Arithmetic Operators

In most cases, arithmetic operators are the same as they are in algebra. However, Java has a couple of additional operators not typically found in math.

Operator Description Example
+ (Addition) Adds values on either side of the operator. 2 + 5 returns 7.
− (Subtraction) Subtracts the value on the right of the operator from the value on the left. 2 - 5 returns -3.
* (Multiplication) Multiplies values on either side of the operator. 2 * 5 returns 10.
/ (Division) Divides the value on the left side of the operator by the value on the right and returns the quotient. 10 / 5 returns 2.
% (Modulus) Divides the value on the left side of the operator by the value on the right and returns the remainder. 10 % 3 returns 1.
++ (Increment) Pre increment increases the value of the operand by 1 and returns the new value of the operand. If i = 5, ++i returns 6. i is now equal to 6.
Post increment increases the value of the operand by 1 and returns the old value of the operand. If i = 5, i++ returns 5. i is now equal to 6.
−− (Decrement) Pre decrement decreases the value of the operand by 1 and returns the new value of the operand. If i = 5, --i returns 4. i is now equal to 4.
Post decrement decreases the value of the operand by 1 and returns the old value of the operand. If i = 5, i-- returns 5. i is now equal to 4.

### Relational Operators

Relational operators show the relationships between two primitives. All relational operators return a boolean, meaning that they are either true or false. The operator must compare the same data type otherwise the program will throw a compiler error. Some of these are also found in algebra, just like the arithmetic operators.

Operator Description Example
== (Equal To) Returns true if both primitives are of the same value. Otherwise, it returns false.
 int x = 2;
if (x == 5) { //if x is equal to 5...
System.out.println("This statement will not print since 2 == 5 is false");
} else { //otherwise
System.out.println("This statement will print instead");
}

!= (Not Equal To) Returns true if both primitives are of different values. Otherwise, it returns false.
 int x = 2;
if (x != 5) { //if x is not equal to 5...
System.out.println("This statement will print since 2 != 5 is true");
} else { //otherwise
System.out.println("This statement will not print");
}

> (Greater Than) Returns true if the primitive on the left side is larger than the primitive on the right side. Otherwise, it returns false.
 int x = 2;
boolean isXGreaterThanZero = x > 5; // You can use logical operators and assign the return value to a boolean!
if (isXGreaterThanZero) { // if x is greater than 5...
System.out.println("This statement will not print since 2 > 5 is false");
} else { // otherwise...
System.out.println("This statement will print instead");
}

< (Less Than) Returns true if the primitive on the left side is smaller than the primitive on the right side. Otherwise, it returns false.
 int x = 2;
boolean isXGreaterThanZero = x < 5; // You can use logical operators and assign the return value to a boolean!
if (isXGreaterThanZero) { // if x is less than 5...
System.out.println("This statement will print since 2 < 5 is true");
} else { // otherwise...
System.out.println("This statement will not print");
}

>= (Greater Than Or Equal To) Returns true if the primitive on the left side is larger than or equal to the primitive on the right side. Otherwise, it returns false.
 int x = 2;
if (x >= 2) { // if x is greater than or equal to 2...
System.out.println("This statement will print since 2 >= 2 is true");
} else { // otherwise...
System.out.println("This statement will not print");
}

<= (Less Than Or Equal To) Returns true if the primitive on the left side is smaller than or equal to the primitive on the right side. Otherwise, it returns false.
 int x = 2;
if (x <= 5) { // if x is less than or equal to 5...
System.out.println("This statement will print since 2 <= 5 is true");
} else { // otherwise...
System.out.println("This statement will not print");
}


### Bitwise Operators

NOTE: All bitwise evaluations are done in binary. They all return the primitive number type (int, long, byte, char) back.

Operator Description Example
| (OR) Compares each binary digit and if either digit is a 1, then it gives back a 1. Otherwise it gives back a 0. 710 | 1810 = 1112 | 100102 = 101112 = 2310
& (AND) Compares each binary digit and if both digits is a 1, then it gives back a 1. Otherwise it gives back a 0. 710 & 1810 = 1112 & 100102 = 102 = 210
^ (XOR) Compares each binary digit and if only one of the digits is a 1, then it gives back a 1. Otherwise it gives back a 0. 710 ^ 1810 = 1112 ^ 100102 = 101012 = 2110
~ (NOT/Complement) For each digit, it sets each 1 to 0 and each 0 to 1. ~1810 = ~100102 = 11012 = 1310
>> (Right Shift) Shifts all the bits to the right. Preserves the sign, meaning it keeps the same number of binary digits. 10>>1=5 since 10102 shifted to the right 1 is 01012 which is 510.
>>> (Unsigned Right Shift) Shifts all the bits to the right. This is the unsigned version of the signed right shift. It doesn't keep the same number of binary digits. 10>>1=5 since 10102 shifted to the right 1 is 1012 which is 510.
<< (Left Shift) Shifts all the bits to the left. 10<<1=20 since 10102 shifted to the left 1 is 101002 which is 2010.

### Logical Operators

Compares two boolean variables and returns a boolean.

Operator Short Circuit Description Example
| (OR) || Will return true if either boolean condition is true. Will return false if both conditions are false. If bool1 is true and bool2 is false, then bool1 | bool2 is true.
& (AND) && Will return true if both boolean conditions are true. Otherwise, it will return false. If bool1 is true and bool2 is false, then bool1 & bool2 is false.
^ (XOR) Will return true if one, but not both, of the boolean conditions is true. Will return false if both conditions are true or false. If bool1 is true and bool2 is true, then bool1 ^ bool2 is false.
! (NOT) Flips the boolean value. If bool1 is false, then !bool1 is true.

#### De Morgan’s Law

Given that A and B are both boolean variables, De Morgan’s Law states that

$\displaystyle{ !(A \& B) == !A \| !B }$

and

$\displaystyle{ !(A \| B) == !A \& !B }$

#### Short-Circuit Operators

Short circuit operators will not evaluate the second part of a boolean operation if it isn’t necessary. It is written in code as || for OR operations and && for AND operations.

An example, if the condition being evaluated is A || B and A is true, then regardless what B is, A || B will be true, so the computer doesn’t evaluate B. For the expression A && B and A was false, then the expression would return false regardless of what B is.

The reason why a short-circuit for XOR doesn’t exist is because if you evaluate A ^ B, if A is either true or false, the value B still needs to be evaluated to see whether the expression A ^ B returns true or false.

### Assignment Operators

Assignment operators allow data types to be assigned values.

Operator Description Example
= (Assignment) It is used to set the value to a data type. Both primitives and Objects can use this operator.
 int x; // By default, Java sets uninitialized primitives to 0
x = 10; // x is now set to 10

System.out.println(x); // This will print 10

+= (Increment) It is used to add some primitive value to itself. This is similar to doing x = x + y. This can only be used with PRIMITIVES excluding booleans.
 int x = 10;
x += 20;
System.out.println(x); // This will print 30

-= (Decrement) It is used to subtract some primitive value to itself. This is similar to doing x = x - y. This can only be used with PRIMITIVES excluding booleans.
 int x = 10;
x -= 20;
System.out.println(x); // This will print -10


### Miscellaneous Operators

#### Ternary Operator

The ternary operator is a way of assigning a variable a certain value based on a certain condition. It is almost identical to an if-else statement, but only assigns a value to a variable instead of running multiple lines of code.

Example:

 int x = (2 > 0) ? 5: 10;


Key

The condition

The ternary operator

The value assigned to x if the condition is true

The operator to define the start of the else block

The value assigned to x if the condition is false

## Control Flow Statements

### Conditional

#### If-Else

##### If

An if statement allows for a block of code to run if it meets a certain boolean condition. If the conditional it skips over the block of code and continues. The syntax for an if statement is as follows:

 if (/*conditional*/) {
// The block of code that runs if the conditional is true
}


If the brackets are not included with the if statement, then the statement immediately after if is the consequence.

 if (/*conditional*/)
// This line will run if the conditional is true
// This line is not part of the if statement


Here are some examples that can be run:

This is an example that shows when the conditional is true.

 // This code should print "Hello World!"

int x = 10;
if (x == 10) { // this statement is true, so it will run the code within the brackets
System.out.print("Hello ");
}
System.out.println("World!");


This is an example that shows when the conditional is false.

 // This code should print "World!"

int x = 10;
if (x > 20) { // this statement is false, so it will skip the code within the brackets
System.out.print("Hello ");
}
System.out.println("World!");


This is an example of using an if statement without the brackets.

 // This code should print "World!"

int x = 10;
if (x > 20) // this statement is false, so it will skip the immediate statement below
System.out.print("Hello "); // Since this line is considered as the "block" of code in the if statement, this will not run
System.out.println("World!");


## Data Types

### Primitive

Primitives are a data type that store their data in a certain amount of bytes. All these types can all be defined by assigning integers to them.

#### int

An int is one of the most fundamental types of primitives. Ints are allocated 4 bytes (32 bits) and can range from -2,147,483,648 to 2,147,483,647 in decimal. These numbers are easily accessible just by doing Integer.MIN_VALUE and Integer.MAX_VALUE respectfully.

The following code defines an int.

int x;


By default, Java sets the value of all primitives to 0. So, if x were to be printed, it would print out "0".

To initalize it, use the assignment operator. This can also be done while the int is defined.

int x = 10;  // x is 10
x = 20;      // x is now 20


Ints are one of a couple of primitives that can use Arithmetic Operators and Bitwise Operators along with Relational Operators and Assignment Operators which all primitives can use.

##### Overflow

Ints have the potential to overflow if they try to store a number larger than 2,147,483,647 (231-1). If a number does overflow, it will wrap back around and continue adding from -2,147,483,648 (-231).

So if x initially equals Integer.MAX_VALUE and 1 is added to it, it will experience overflow and wrap around to Integer.MIN_VALUE. x will then equal -231. If we instead added 2, the final result of x is -231+1 or Integer.MIN_VALUE + 1.

Overflow can also happen if the numbers that are less than -231 are then wrapped back up to 231-1.

So if x initially equals Integer.MIN_VALUE and 1 is subtracted from it, it will experience overflow and wrap around to Integer.MAX_VALUE. x will then equal 231-1. If we instead subtracted 2, the final result of x is 231-2 or Integer.MAX_VALUE - 1.

#### boolean

A boolean is a 1 bit primitive. Its purpose is to record whether something is true (1) or false (0). The following code defines a boolean.

boolean x;


By default, Java sets the value of x to false (0). So, if x were to be printed, it would print out "false".

To initalize it, use the assignment operator. This can also be done while the boolean is defined.

boolean x = true;  // x is true
x = false;         // x is now false


Booleans are the only primitive that can use Logical Operators along with Relational Operators and Assignment Operators which all primitives can use.

#### char

A char is a 2 byte (16 bits) primitive that stores a integer that maps bijectively to an ASCII character.

The following code defines a char.

char x;


By default, Java sets the value of all primitives to 0.

To initalize it, use the assignment operator. This can also be done while the char is defined.

char x = 65;  // x is 'A' (ASCII code 65)
x = 'g';     // x is now 'g' (ASCII code 103)


Only a certain range of chars can be printed out, on the ASCII table, it notes the printable ASCII codes.

Chars are one of a couple of primitives that can also use Arithmetic Operators and Bitwise Operators. However, the primitive type that they return is an int and will need to be cast into a char if needs to be kept as a char. It can also use the Relational Operators and Assignment Operators just like the other primitives.

## Variables

Variables, also known as instance fields, is the way data is stored. Variables can represent different data types like primitives and objects.

When defining variables, there are 3 parts: the access modifier, the data type, and the name.

### Access Modifiers

Access modifiers determine which classes are allowed to access a variable or function. It allows to maintain integrity in a program and prevents users from accessing certain properties and methods that are meant to be kept secret.

There are 3 main modifiers: public, private, and protected. Below is a table of what modifiers give to variables and functions if they are added to them.

Access Levels
Modifier Class Package Subclass World
public Yes Yes Yes Yes
protected Yes Yes Yes No
no modifier Yes Yes No No
private Yes No No No

### Miscellaneous Modifiers

The static modifier is a modifier that declares whether a variable can be accessed at the class level. In other words, an instance of the Object does not need to be created in order to access this variable. Functions can also have a static modifier.

The final modifier is a modifier that declares a variable as a constant value. Upon declaration, it needs to be instantiated and can not be written afterward. The name of a final variable typically follows uppercase snake case (e.g. UPPERCASE_SNAKE_CASE) compared to the typical camel case of normal variables.

### Name

Naming convention for variables mostly follows camel case (e.g. camelCase) as most of Java surrounds the use of camel case. However, if a variable is declared as a final variable, then the name must be in uppercase snake case (e.g. UPPERCASE_SNAKE_CASE) as it is the way to distinguish between manipulatable variables and constant variables.

## Functions

Functions are a block of code that when called will run the lines of code contained within it. Functions are often used to simplify code. One way it can simplify code is by reusing code. Instead of redundantly writing multiple lines of code, the code can be put into a function and called multiple times. Another way functions can simply code is by creating helper functions. In multiple cases when creating long and complex algorithms, helper functions are used to break the algorithm into manageable steps, allowing for easy debugging and clean code that is way to read.

### Defining a Function

Functions are defined in four parts: its access modifier, its return type, its name, and its parameters. In objects, all functions have a certain level of access that is defined in the function definition. Functions, similar to variables, can be public, private, or protected. The return type refers to the primitive or object type that will be returned once the function is done executing. The name is simply the name of the function. This is the name that will be used to call the function when it needs to be executed. Finally, there are the parameters which are the values that are required for the function to run properly. These can also be known as arguments. Parameters of a function are defined within the function definition, typically stating the type of object or primitive and the name it is will be referred under. When passed into a function, primitive values follow the pass by value protocol while object values follow pass by reference. A function can have multiple parameters, but all parameters need to be filled in order for a function to execute.

 public boolean isFirstGreaterThanSecond(int first, int second) {
if (first > second) {
return true;
}
return false;
}


Key

The access modifier

The return type

The name of the function

The parameters

### The Return statement

Functions can have a return value of void which doesn't return any value once the function completes execution. Once the function execution reaches a return statement, the function will exit out and return the value stated in the return statement. The type of value specified in the return statement must match the return value stated in the definition otherwise the code will not compile. Functions that define a return type, must return a value otherwise the function will not compile. Functions that are void can use return; to exit the function without returning any value.

### Overloading

Functions can also be overload other functions. For a function to be overloaded, the overloading function needs to be defined with the same name, but either a different amount of parameters or different types of parameters. This way the compiler knows which function to call on execution. Function overloading can mostly be seen by overloading default functions like toString()` as certain objects might want to return a more comprehendible string rather than a random string of characters.

## Scoring

Each problem specifies its own worth. No one problem can be worth more than 20% of the total score possible.