Kadane's algorithm

Kadane's Algorithm is an $$O(n)$$ algorithm for finding the maximum contiguous subsequence in a one-dimensional sequence.

Pseudocode
The algorithm keeps track of the tentative maximum subsequence in (maxSum, maxStartIndex, maxEndIndex). It accumulates a partial sum in currentMaxSum and updates the optimal range when this partial sum becomes larger than maxSum.

Kadane's Algorithm(array[1..n]) begin (maxSum, maxStartIndex, maxEndIndex) := (-INFINITY, 0, 0) currentMaxSum := 0 currentStartIndex := 1 for currentEndIndex := 1 to n do       currentMaxSum := currentMaxSum + array[currentEndIndex] if currentMaxSum > maxSum then (maxSum, maxStartIndex, maxEndIndex) := (currentMaxSum, currentStartIndex, currentEndIndex) endif

if currentMaxSum < 0 then currentMaxSum := 0 currentStartIndex := currentEndIndex + 1 endif endfor

return (maxSum, maxStartIndex, maxEndIndex) end