Kadane's Algorithm

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

[edit]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