GATE CS 2019 Set 1 — Question 35
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Question
Consider a sequence of 14 elements: .
The subsequence sum . Determine the maximum of , where . (Divide and conquer approach may be used.)
The subsequence sum . Determine the maximum of , where . (Divide and conquer approach may be used.)
Correct answer
29 to 29
Solution
To find the maximum subsequence sum (Maximum Subarray Problem), we can use Kadane's Algorithm.Given array .Let's trace the current sum () and maximum sum ():
Let's use the variation where we reset to 0 if it becomes negative, but update max before resetting if we want at least one element, or just track max.
: . , set . Max = 0 (or -5 if at least one element required, let's assume max initialized to first element).
: . , set .
: . Max = 6.
: . Max = 9.
: .
: .
: . Max = 19.
: . Max = 23.
: .
: .
: .
: . Max = 29.
: .
: .The maximum subsequence sum is 29. The subarray corresponds to indices 2 to 11: .
Sum: .
- Initialize , .
Let's use the variation where we reset to 0 if it becomes negative, but update max before resetting if we want at least one element, or just track max.
: . , set . Max = 0 (or -5 if at least one element required, let's assume max initialized to first element).
: . , set .
: . Max = 6.
: . Max = 9.
: .
: .
: . Max = 19.
: . Max = 23.
: .
: .
: .
: . Max = 29.
: .
: .The maximum subsequence sum is 29. The subarray corresponds to indices 2 to 11: .
Sum: .
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