Maximum Subarray
Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
Constraints:
- 1 <= nums.length <= 10^5
- -10^4 <= nums[i] <= 10^4
Examples:
Input: [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The subarray [4,-1,2,1] has the largest sum 6.
Solutions
Kadane's Algorithm
Time: O(n)Space: O(1)
Kadane's algorithm scans the entire array and at each position finds the maximum sum of the subarray ending at that position.
public int maxSubArray(int[] nums) {
int maxSoFar = nums[0];
int maxEndingHere = nums[0];
for (int i = 1;
i < nums.length;
i++) {
maxEndingHere = Math.max(nums[i], maxEndingHere + nums[i]);
maxSoFar = Math.max(maxSoFar, maxEndingHere);
}
return maxSoFar;
}Follow-up:
What if the input array is empty?
