42 lines
1.6 KiB
Markdown
42 lines
1.6 KiB
Markdown
# Kadane's Algorithm
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#### 2022-06-09
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---
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##### Data structures:
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#array
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##### Algorithms:
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#algorithm #Kadane_s_algorithm
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##### Difficulty:
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#CS_analysis #difficulty-easy
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##### Time complexity:
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O(n)
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##### Related problems:
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```expander
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tag:#coding_problem tag:#Kadane_s_algorithm -tag:#template_remove_me
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```
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- [[Leetcode Best-Time-To-Buy-And-Sell-Stock]]
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- [[Leetcode Maximum-Difference-Between-Increasing-Elements]]
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- [[Leetcode Maxinum-subarray]]
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##### Resources:
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- [Explainer article](https://medium.com/@rsinghal757/kadanes-algorithm-dynamic-programming-how-and-why-does-it-work-3fd8849ed73d)
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---
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### What is Kadane's Algorithm?
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It's a kind of dynamic programming. You calculate A[n] by calculating A[n - 1], which makes it O(n)
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==local_maximum at index i is the maximum of (A[i] and the sum of A[i] and local_maximum at index i-1).==
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> 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)_**.
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### When to use it?
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According my analyze [[Leetcode Best-Time-To-Buy-And-Sell-Stock#Thoughts| here]], we should use it when these conditions are met:
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- You want to find the value of the highest peak or lowest valley
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- The direction you search is mono-directional
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- The current value can be obtained from or, is related to the value before this one. |