ta1_sol - COMP 271H Design and Analysis of Algorithms 2006...

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COMP 271H Design and Analysis of Algorithms 2006 Fall Semester Tutorial 1 Solution 1. Design a linear time algorithm to solve the maximum contiguous subarray problem. Idea: Our problem is to find the sum of the maximum contiguous subarray. We will solve this problem incrementally. We define two variables: LocalMaxSum and GlobalMaxSum. We first consider an empty array, each time we add one item to the array and update the LocalMaxSum. If the updated LocalMaxSum is greater than GlobalMaxSum. We set GlobalMaxSum as the value of LocalMaxSum. The algorithm terminates until all items are being processed. Observation: (Note: Observation is just used to guide you thinking, it won’t be included in the solution. But it may help in the correctness proof.) We first consider an array with only four items. We have processed the first two items and we are now going to process the third item (the underline item). Case 1: LocalMaxSum is non-negative. NextItem is non-negative.
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