This video explains common Big O runtime complexities relevant to coding interviews. The speaker covers various complexities (O(1), O(n), O(n^2), etc.), providing examples and clarifying misconceptions. The video also promotes the speaker's website, neetcode.io, offering free and paid coding interview preparation resources.
To explain each complexity with an example, I'll use array-based examples for consistency, though some complexities apply more broadly. Remember, Big O focuses on how runtime scales with input size (n), ignoring constant factors.
O(1) - Constant Time: Accessing an element by its index in an array. No matter how large the array, accessing the element at index 5 always takes the same amount of time.
O(n) - Linear Time: Iterating through an array to find a specific value. The time it takes to search increases proportionally to the number of elements in the array.
O(n²) - Quadratic Time: Nested loops iterating over an array. For each element in the outer loop, the inner loop iterates over all elements. Runtime grows proportionally to the square of the input size. Example: Bubble sort.
O(n*m) - Linear Time (with two variables): Iterating through a matrix (two-dimensional array). n represents rows, and m represents columns. Runtime grows proportionally to the product of the number of rows and columns.
O(n³)- Cubic Time: Three nested loops iterating over an array. Runtime grows proportionally to the cube of the input size. Example: Finding all possible triplets in an array.
O(log n) - Logarithmic Time: Binary search on a sorted array. Each comparison eliminates half the remaining search space. The runtime grows very slowly with input size.
O(n log n) - Linearithmic Time: Merge sort. This combines logarithmic behavior (from dividing the array recursively) with linear behavior (from merging the sorted subarrays). Efficient for sorting large datasets.
O(2ⁿ) - Exponential Time: Finding all subsets of a set (power set). The number of subsets doubles with each additional element. Runtime grows extremely quickly with input size. Example: Recursive Fibonacci calculation (inefficient version).
O(√n) - Square Root Time: Finding all factors of a number. You only need to check up to the square root of the number to find all its factors because factors come in pairs.
O(n!) - Factorial Time: Finding all permutations of a set. The number of permutations grows incredibly fast with the number of elements. Example: The Traveling Salesperson Problem (solved inefficiently).
It's crucial to note that these are simplified examples. Real-world scenarios might involve more complex interactions, but the core idea of Big O remains the same: describing how runtime scales with input size.
