maximum subarray kadane s algorithm leetcode 53

maximum subarray problem (leetcode 53) - kadane's algorithm

the maximum subarray problem is a classic problem in computer science, which can be efficiently solved using kadane's algorithm. the problem can be stated as follows:

**problem statement:**
given an integer array `nums`, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

**example:**

understanding kadane's algorithm

kadane's algorithm works on the principle of dynamic programming. the idea is to iterate through the array while keeping track of two values:

1. `current_sum`: the maximum sum of the subarray ending at the current position.
2. `max_sum`: the maximum sum encountered so far.

steps:
1. initialize `current_sum` to the first element of the array and `max_sum` to the same value.
2. iterate through the array starting from the second element.
3. for each element:
- update `current_sum` to be the maximum of the current element itself and the sum of `current_sum` and the current element.
- update `max_sum` to be the maximum of `max_sum` and `current_sum`.
4. at the end of the iteration, `max_sum` will contain the largest sum of the contiguous subarray.

time complexity
- the time complexity of kadane's algorithm is \(o(n)\), where \(n\) is the number of elements in the array.
- the space complexity is \(o(1)\) since we are using only a constant amount of space.

python implementation

here's a python implementation of kadane's algorithm for the maximum subarray problem:

explanation of code:
1. we start by initializing `current_sum` and `max_sum` with the first element of the array.
2. we loop through each number in the array starting from the second element.
3. for each number, we decide whether to add it to the existing `current_sum` or start a new subarray with the current number. this is done using `max(num, current_sum + num)`.
4. we continuously update `max_sum` to ensure it holds the maximum value found so far.
5. finall ...

#KadaneAlgorithm #MaximumSubarray #LeetCode53

maximum subarray
Kadane's algorithm
LeetCode 53
dynamic programming
array problem
contiguous subarray
maximum sum
algorithm optimization
time complexity
space complexity
prefix sum
sliding window
greedy approach
input constraints
interview question