700542. Play with an array
Here is the detailed Markdown blog post for the GeeksforGeeks problem "Play with an array":
Play with an Array
Summary
Given an array of integers, you need to find the maximum sum of a contiguous subarray within it. This problem involves arrays and data structures.
Detailed Explanation
The problem can be solved by using the concept of Kadane's algorithm. The idea is to maintain two variables: the current maximum sum (CMS) and the maximum sum so far (MSF). Initialize MSF with the first element of the array, and CMS with the same value. Iterate through the array starting from the second element.
Step-by-step breakdown:
- For each element
arr[i], calculate the current maximum sum (CMS) as the maximum ofarr[i-1] + arr[i]andarr[i]. This is because a subarray ending atican either be extended by addingarr[i]to the previous subarray or start anew witharr[i]. - Update MSF if CMS becomes greater than it.
- Repeat steps 1-2 until you have processed all elements in the array.
Time complexity: O(n), where n is the number of elements in the array, since we only need to iterate through the array once.
Space complexity: O(1), as we are only using a constant amount of space to store CMS and MSF.
Optimized Solutions
Here are some optimized solutions for this problem:
Java
public int maxSubArraySum(int[] arr) {
int msf = arr[0];
int cms = arr[0];
for (int i = 1; i < arr.length; i++) {
cms = Math.max(arr[i], cms + arr[i]);
msf = Math.max(msf, cms);
}
return msf;
}