# Kadane's Algorithm

#### 2022-06-09

---
##### Data structures:
#array
##### Algorithms:
#algorithm #Kadane_s_algorithm 
##### Difficulty:
#CS_analysis #difficulty-easy
##### Time complexity:
O(n)
##### Related problems:
```expander
tag:#coding_problem tag:#Kadane_s_algorithm  -tag:#template_remove_me 
```
 
- [[Leetcode Best-Time-To-Buy-And-Sell-Stock]]
- [[Leetcode Maximum-Difference-Between-Increasing-Elements]]
- [[Leetcode Maxinum-subarray]]
 


##### Resources:
- [Explainer article](https://medium.com/@rsinghal757/kadanes-algorithm-dynamic-programming-how-and-why-does-it-work-3fd8849ed73d)

---
### What is Kadane's Algorithm?

It's a kind of dynamic programming. You calculate A[n] by calculating A[n - 1], which makes it O(n)

==local_maximum at index i is the maximum of (A[i] and the sum of A[i] and local_maximum at index i-1).==

> Because of the way this algorithm uses optimal substructures (the maximum subarray ending at each position is calculated in a simple way from a related but smaller and overlapping subproblem: the maximum subarray ending at the previous position) this algorithm can be viewed as a simple example of dynamic programming. Kadane’s algorithm is able to find the maximum sum of a contiguous subarray in an array with a runtime of **_O(n)_**.

### When to use it?

According my analyze [[Leetcode Best-Time-To-Buy-And-Sell-Stock#Thoughts| here]], we should use it when these conditions are met:
- You want to find the value of the highest peak or lowest valley
- The direction you search is mono-directional
- The current value can be obtained from or, is related to the value before this one.