Important Formulas & Key Concepts

title: Important Formulas and Concepts description: Java ke important formulas aur key concepts

Data Type Ranges

byte	-128 to 127 (2^7)
short	-32,768 to 32,767 (2^15)
int	-2,147,483,648 to 2,147,483,647 (2^31)
long	-9,223,372,036... to 9,223,372,036... (2^63)
float	~1.4e-45 to ~3.4e38 (32-bit IEEE 754)
double	~4.9e-324 to ~1.8e308 (64-bit IEEE 754)
char	0 to 65,535 (Unicode)

String Pool Formula

String s1 = "hello"	Pool mein store
String s2 = "hello"	Same pool object (s1 == s2 → true)
String s3 = new String("hello")	Heap mein naya object (s1 == s3 → false)
s1.equals(s3)	true (content same)

Array Size Formula

Total elements = rows × columns (2D array) Index range = 0 to (length - 1) Last index = array.length - 1 Middle index = (lo + hi) / 2 OR lo + (hi - lo) / 2 (overflow safe)

Time Complexity Formulas

O(1)	Constant → Array index access, HashMap get
O(log n)	Binary search → Each step half karta hai: log₂(n) steps
O(n)	Linear → One loop
O(n log n)	Merge sort → n levels × log n splits
O(n²)	Quadratic → Nested loops
O(2ⁿ)	Exponential → Fibonacci recursive

Sorting Formulas

Bubble Sort comparisons = n(n-1)/2 Sum of 1 to n = n(n+1)/2 Binary Search steps = log₂(n) (max comparisons)

Thread Priority Range

MIN_PRIORITY = 1 NORM_PRIORITY = 5 (default) MAX_PRIORITY = 10

HashMap Internal Formula

Default capacity = 16 Default load factor = 0.75 Resize threshold = capacity × load factor = 16 × 0.75 = 12 After resize = capacity × 2 = 32 Hash index = hashCode % capacity

StringBuilder Capacity Formula

Default capacity = 16 After append = if (length > capacity) → new capacity = (old × 2) + 2

Collection Initial Capacities

ArrayList default capacity = 10 (grows 50%: newSize = oldSize + oldSize/2) HashMap default capacity = 16 (grows 2x when load factor exceeded) HashSet default capacity = 16

Exception Hierarchy

Throwable ├── Error (unrecoverable) │ └── OutOfMemoryError, StackOverflowError └── Exception ├── IOException (checked) ├── SQLException (checked) └── RuntimeException (unchecked) ├── NullPointerException ├── ArrayIndexOutOfBoundsException └── ClassCastException

JVM Memory Areas

Heap	Objects store hote hain (GC yahan kaam karta hai)
Stack	Method frames, local variables
Method Area	Class definitions, static variables
PC Register	Current instruction address
Native Stack	Native method calls

Integer Cache Range

Integer -128 to 127 → Cached (same object milta hai) Integer 128+ → New object banta hai Always use .equals() for Integer comparison

title: Important Formulas and Concepts description: Java ke important formulas aur key concepts

Data Type Ranges

byte	-128 to 127 (2^7)
short	-32,768 to 32,767 (2^15)
int	-2,147,483,648 to 2,147,483,647 (2^31)
long	-9,223,372,036... to 9,223,372,036... (2^63)
float	~1.4e-45 to ~3.4e38 (32-bit IEEE 754)
double	~4.9e-324 to ~1.8e308 (64-bit IEEE 754)
char	0 to 65,535 (Unicode)

String Pool Formula

String s1 = "hello"	Pool mein store
String s2 = "hello"	Same pool object (s1 == s2 → true)
String s3 = new String("hello")	Heap mein naya object (s1 == s3 → false)
s1.equals(s3)	true (content same)

Array Size Formula

Total elements = rows × columns (2D array) Index range = 0 to (length - 1) Last index = array.length - 1 Middle index = (lo + hi) / 2 OR lo + (hi - lo) / 2 (overflow safe)

Time Complexity Formulas

O(1)	Constant → Array index access, HashMap get
O(log n)	Binary search → Each step half karta hai: log₂(n) steps
O(n)	Linear → One loop
O(n log n)	Merge sort → n levels × log n splits
O(n²)	Quadratic → Nested loops
O(2ⁿ)	Exponential → Fibonacci recursive

Sorting Formulas

Bubble Sort comparisons = n(n-1)/2 Sum of 1 to n = n(n+1)/2 Binary Search steps = log₂(n) (max comparisons)

Thread Priority Range

MIN_PRIORITY = 1 NORM_PRIORITY = 5 (default) MAX_PRIORITY = 10

HashMap Internal Formula

Default capacity = 16 Default load factor = 0.75 Resize threshold = capacity × load factor = 16 × 0.75 = 12 After resize = capacity × 2 = 32 Hash index = hashCode % capacity

StringBuilder Capacity Formula

Default capacity = 16 After append = if (length > capacity) → new capacity = (old × 2) + 2

Collection Initial Capacities

ArrayList default capacity = 10 (grows 50%: newSize = oldSize + oldSize/2) HashMap default capacity = 16 (grows 2x when load factor exceeded) HashSet default capacity = 16

Exception Hierarchy

JVM Memory Areas

Heap	Objects store hote hain (GC yahan kaam karta hai)
Stack	Method frames, local variables
Method Area	Class definitions, static variables
PC Register	Current instruction address
Native Stack	Native method calls

Integer Cache Range

Integer -128 to 127 → Cached (same object milta hai) Integer 128+ → New object banta hai Always use .equals() for Integer comparison

Important Formulas & Key Concepts

Data Type Ranges

String Pool Formula

Array Size Formula

Time Complexity Formulas

Sorting Formulas

Thread Priority Range

HashMap Internal Formula

StringBuilder Capacity Formula

Collection Initial Capacities

Exception Hierarchy

JVM Memory Areas

Integer Cache Range

Continue learning this concept

Important Formulas & Key Concepts

Data Type Ranges

String Pool Formula

Array Size Formula

Time Complexity Formulas

Sorting Formulas

Thread Priority Range

HashMap Internal Formula

StringBuilder Capacity Formula

Collection Initial Capacities

Exception Hierarchy

JVM Memory Areas

Integer Cache Range

Continue learning this concept