1.4 KiB
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:
Resources:
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, 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.