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The main idea is to use Kadane's Algorithm to find the maximum subarray sum for two scenarios: one, where the subarray wraps around the end and beginning of the array, and two, where it does not.
Calculate the maximum subarray sum using Kadane's algorithm in the normal way. Then calculate the minimum subarray sum using a similar technique but by negating the result. The maximum possible circular subarray sum will be the maximum value between the normal subarray sum and the total array sum minus the minimum subarray sum.
Time Complexity: O(n) — as both the applications of Kadane's algorithm are linear.
Space Complexity: O(1) — no additional space is used except for a few variables.
1#include <stdio.h>
2#include <limits.h>
3
4int kadane(int *arr, int n) {
5 int current_max
This C solution performs a similar task as the Python example but executes in a structured imperative approach. It first computes the maximum and minimum subarray sums using a modified Kadane's algorithm and calculates the potential circular maximum.
Instead of using basic Kadane's approach, we can consider computing the maximum subarray sum with additional memory for storing maximum and minimum values up to each index. This allows precise tracing of subarrays—as contiguous and potential wrap-around cases.
Time Complexity: O(n)
Space Complexity: O(1)
1public
This Java version remains clear and direct with similar logic to other implementations, keeping track of maximum and minimum subarray values while ensuring efficient operations inline with dynamic programming techniques.