saima8 / DS-and-Algo

A playground for practicing Data structure and Algorithm.

DS-and-Algo

A playground for practicing Data structure and Algorithm.

Table of contents for Data Structure

• Complexity Analysis
  • Time Complexity
  • Space Complexity
• Memory
  • Bit
  • Byte
  • Fixed-width Integer
  • Memory

Complexity Analysis

The process of analysing how efficient an algorithm is. Complexity analysis usually involves finding both the Time Complexity and the Space Complexity of an algorithm. Complexity analysis is used to effectively determined how "good" an algorithm is and whether it's "better" than another one.

Time Complexity

A measure of how fast an algorithm runs, time complexity is a central concept in the field of algorithms and coding interviews. It's expressed using Big O notation

Space Complexity

A measure of how much auxiliary memory an algorithm takes up, space complexity is a central concept in the field of algorithms and coding interviews. It's expressed using Big O notation

Memory

The bedrock of all data structures, memory is the underlying concept that you absolutely need to know in oredr to understand why data structures work the way they do.

Bit

Short for binary digit, a bit is a fundamental unit of information in Computer Science that represents a state with one of two values, typically 0 and 1.

Strings

Any data stored in a computer is, at the most basic level, represented in bits.

Byte

A group of 8 bits. For example, 01101000 is a byte.

A single byte can represent up to 256 data values (2^8).

Since a binary number is a number expressed with only two symbols, like 0 and 1, a byte can represent all the numbers between 0 and 255, inclusive, in binary format. Example:

  1: 00000001
  2: 00000010

Fixed-width Integer

An integer represented by a fixed amount of bits. For example, a 32-bit integer is an integer represented by 32 bits (4 bytes), and a 64-bit integer is a integer represented by 64 bits (8 bytes).

Regardless of how large an integer is, its fixed-width-integer representation is, by definition, made up of a constant number of bits.

Memory

Broadly speaking, memory is the foundational layer of computing, where all data is stored.

Important points:

• Data stored in memory is stored in bytes and, by extension, bits.
• Bytes in memory can "point" to other bytes in memory, so as to store references to other data.
• The amount of memory that a machine has is bounded, making it valuable to limit how much an algorithm takes up.
• Accessing a byte or a fixed number of bytes (like 4 bytes or 8 bytes in the case of 32-bit and 64-bit integers) is an elementary operation, which can be loosely treated as a single unit of operational work.

Strings

string = "this is a string"
newString = ""

for char in string:
  newString += char

The operation above has a time complexity of O(n^2) where n is the length of the string. because each addition of a character to newString creates an entirely new string and is itself an O(n) operation. Therefore, n O(n) operations are performed, leading to an O(n^2) time-complexity operation overall.