Algorithm 1 Linear Time Maximum Subarray

Input: An array $A[1..n]$ .

Output: A tuple $(p, q, s)$ representing the maximun subarray of $A$ and its summation.

1: $p = 1, q = 1, s = A[1]$

2: // $A[p..q]$ is the maximum subarray and s is its summation

3: $i = 1, tmp = A[1]$

4: // tmp is the summation of $A[i..j-1]$

5:for $j = 2$ to $n$ do

6:if $tmp < 0$ then

7: $i = j$

8: $tmp = A[j]$

9:else

10: $tmp = tmp + A[j]$

11:end if

12:if $tmp > s$ then

13: $p = i, q = j, s = tmp$

14:end if

15:end for

16:return $(p, q, r)$