Start with a maximum sum of 0. Compute the sum of each 1-element subarray, then compute the sum of each 2-element subarray, then compute the sum of each 3-element subarray, etc. For each sum you compute, if it is larger than the maximum sum you've seen, then it becomes the maximum sum. ALGORITHM 2 Same as algorithm 1 but now once you compute the sum of the subarray from A[i] to A[j], the sum of the subarray from A[i] to A[j+1] is just the previous sum you computed plus A[j+1]. Don't add up all of the previous values all over again. ALGORITHM 3 (Optional) Same as algorithm 1 but store the temporary steps in an array.