Kadane's Algorithm & Dutch National Flag

Two Fundamental Array Algorithms

Kadane's Algorithm: Finds maximum contiguous subarray sum in $O(N)$ time and $O(1)$ space.

Dutch National Flag Algorithm: Sorts an array of 0s, 1s, and 2s in 1 single pass using 3 pointers (`low`, `mid`, `high`).

Production Code Example:

public class KadaneAndDNF {
    public int maxSubArray(int[] nums) {
        int maxSoFar = nums[0], currMax = nums[0];
        for (int i = 1; i < nums.length; i++) {
            currMax = Math.max(nums[i], currMax + nums[i]);
            maxSoFar = Math.max(maxSoFar, currMax);
        }
        return maxSoFar;
    }
}

Key Complexity & Algorithmic Takeaways:

When implementing Kadane's Algorithm & Dutch National Flag in coding interviews and production applications, keep these core guidelines in mind:

• Time Complexity Analysis: Always evaluate best-case, average-case, and worst-case time complexities ($O(1)$, $O(\log n)$, $O(n)$, $O(n \log n)$, $O(n^2)$).
• Space Complexity & Memory Bounds: Account for auxiliary memory usage, call stack frame recursion overhead, and heap allocations.
• Edge Cases & Validation: Test empty inputs, null pointers, single-element collections, duplicate values, and integer overflow bounds.
• Optimal vs Naive Solutions: Start with a clear brute-force solution, then optimize using techniques like Hashing, Two Pointers, Windowing, or Dynamic Programming.

Summary Takeaway:

Mastering Kadane's Algorithm & Dutch National Flag provides the foundational problem-solving skills needed to pass technical coding interviews at top tech companies and write ultra-performant software systems.