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Time Complexity

What is time complexity ?
Ans: Time complexity not a run time of a code, its totally depends on system configuration, processor, server , input size will increase time complexity.


Time complexity ko likhne ke tarike jo hote hai use notation kehte hai.

Notation is basically symbol



NOTATION OF COMPLEXITY

Best Case: kam se kam time me chla gya code best case hota hai

Ω (Omega) Ω(1) se likhte hai

Average Case: Ek average time jisme code chle 

Θ(n+1)/2

Worst Case: Worst case ka mtlb kuch bhi ho jaye is time ko ye exceed nhi kregea

O(n)


Nested Loop me Time Complexity multiply hoti hai aur n^2 banti hai
Wahi Do different loops me N+M hoti hai jisme jiski sabse bdi value hai wo big of O me jati hai

  1. O(1) - Constant Time:

    • Operations that take a constant amount of time, regardless of the size of the input data.

  2. O(log n) - Logarithmic Time:

    • Algorithms that have a logarithmic time complexity, often seen in binary search or certain tree-based algorithms. This is best time Complexity this is near from constant time

  3. O(n) - Linear Time:

    • The running time of the algorithm grows linearly with the size of the input.

  4. O(n log n) - Linearithmic Time:

    • Common in efficient sorting algorithms like mergesort and heapsort. or already inbuild sorting method like Array.sort

  5. O(n^2) - Quadratic Time:

    • Algorithms where the running time is proportional to the square of the size of the input.

  6. O(2^n) - Exponential Time:

    • Algorithms where the running time doubles with each additional element in the input. this is on recursion , This is generally brute force approach and this is bad time Complexity, to improve this will use dynammic programming technique

  7. O(n!) - Factorial Time:

    • Algorithms where the running time grows factorially with the size of the input. this is worst of all, ye sabse bura hota hai







Sabse least logn hota hai


     >>>   time complexity of all searching and sorting algorithm


    1) Sabse chota hota hai logn

    2) uske bad n logn

    3) n

    4) n2




Time complexity wise algorithm -

1) O(log n)
>> 1- binary search will gives you big of O log n notation.
About Binary Search: Binary Search is used to efficiently find a target value within a sorted array or list by repeatedly dividing the search interval in half. It is a divide-and-conquer algorithm that compares the target value with the middle element of the array and determines whether the target lies in the first half or the second half of the array. By eliminating half of the remaining elements at each step, Binary Search achieves a time complexity of O(log n).
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