daihan's blog

Kadane's Algorithm + Update
By daihan, 7 years ago, In English

You are given an array of size N , then you are given N integers A[i] = i'th element .

You will have to process some query , Q . Two types of query :

1 — that means print the maximum sub array sum in this array .

2 p V — Update the value of index p to V ;

Constraints:

1<=N<=9*10^4

1 ≤ Q ≤ 100000

How to solve it efficiently ? I got TLE in test 4 .

Problem link: https://toph.co/p/problem---smsms

My code : https://ideone.com/GC3o8V

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7 years ago, # |
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simple segment tree with merging nodes

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7 years ago, # |
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This problem can be solved using a segment tree.

To understand the solution, you can try to find the Maximum Sub Array Sum in a recursive divide & conquer approach. Once you have a d&c solution (that should have linear time), we can use that to mantain a segmentree containing all the needed information for each interval.

Hint : you might also need to save information about prefix/suffix of the interval you are recurring on :)

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7 years ago, # |
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There is the same problem on SPOJ

There is my solution

1) Use Segment Tree (if you don't know it, solve some easy problems on segment tree previously)

2) Each node of the Segment Tree will contain 4 numbers:

sum — sum of all numbers of this segment

maxprefix — maximum sum of the prefix on this segment

maxsuffix — maximum sum of the suffix on this segment

maxsum — maximum sibarray sum on this segment

Combine function will be easy:

1) sum = left.sum + right.sum

2) maxprefix = max(left.maxprefix, left.sum+right.maxprefix)

3) maxsuffix = max(left.maxsuffix + right.sum, right.maxsuffix)

4) maxsum = max(left.maxsum, right.maxsum, left.suffix+right.prefix)

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