Finding a range satisfying a property in faster than linear time

Question

Given an array A[] we need to find a range which has the maximum size and its minimum element is >= 1. We also need to update this range by decreasing all its elements by 1.

One idea I got is to keep a segment tree for efficient updates. But how do I get the range in <= logarithmic time?

Maybe we can use binary search here.

Thanks

Are you interested in repeatedly finding the largest positive range and decrementing? — David Eisenstat, Feb 10 '17 at 21:10

score 1 · Accepted Answer · answered Feb 10 '17 at 21:18

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It's very interesting problem and I think it can be solved using Segment Tree.

Here are my idea (I hope it works fast enough):

For each segment, we need to store 4 info:

leftmost index of number < 1
rightmost index of number < 1
max size for this segment (store as range a and b)
lazy flag (true/false)

When we want to query max size, we can do recursive call to calculate the final answer. Assume our method was calcAnswer(left,right).

resA = calcAnswer(left, mid);

resB = calcAnswer(mid+1,right);

Max size will be max(resA.max_size, resB.max_size, combine(resA.right_index,resB.left_index)).

If the number of elements in array A[] are small (N<=50000), we can use Mo's Algorithm.

answered Feb 10 '17 at 21:18

algojava

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N is <= 10^5 in the problem. – Ivankovich Feb 10 '17 at 21:19
if the problem comes from Online Judge, please kindly share to me. I want try to code my solution and submit it :). Thanks. – algojava Feb 10 '17 at 21:23
This problem might have a lot simpler solution per se, considering the fact that it is Div2 C – Ivankovich Feb 10 '17 at 21:26
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Yes, I just solved the problem using optimized BruteForce (156 ms). No need to coding Segment Tree. – algojava Feb 10 '17 at 22:00

Finding a range satisfying a property in faster than linear time

1 Answers1