Adding Parallel Binary Search module #3859
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bqi343
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envyaims
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bqi343
envyaims
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envyaims
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Aug 12, 2023
| ## Tutorial | ||
| This technique is usually used when we can solve a single query by doing linear or binary search on monotonic function. | ||
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| The trick is doing it offline, sort queries by their median (initially $l$, $r$ will be the binary search values), do linear search, |
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Suggested change
| The trick is doing it offline, sort queries by their median (initially $l$, $r$ will be the binary search values), do linear search, | |
| The trick is doing it offline, sorting queries by their median (initially $l$, $r$ will be the binary search values), linearly searching |
| This technique is usually used when we can solve a single query by doing linear or binary search on monotonic function. | ||
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| The trick is doing it offline, sort queries by their median (initially $l$, $r$ will be the binary search values), do linear search, | ||
| whenever you find a query its median in same as your position in linear search, check the monotonic function, and do same as binary search (edit either $l$ or $r$). |
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Suggested change
| whenever you find a query its median in same as your position in linear search, check the monotonic function, and do same as binary search (edit either $l$ or $r$). | |
| whenever you find a query its median in same as your position in linear search, checking the monotonic function, and binary searching (edit either $l$ or $r$). |
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| The trick is doing it offline, sort queries by their median (initially $l$, $r$ will be the binary search values), do linear search, | ||
| whenever you find a query its median in same as your position in linear search, check the monotonic function, and do same as binary search (edit either $l$ or $r$). |
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If that's what you meant, then resolve those changes. If not, then please rewrite that sentence since it doesn't really make sense right now.
| The trick is doing it offline, sort queries by their median (initially $l$, $r$ will be the binary search values), do linear search, | ||
| whenever you find a query its median in same as your position in linear search, check the monotonic function, and do same as binary search (edit either $l$ or $r$). | ||
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| You will need to do the linear search $O(\log_2{N})$ times, so $l = r$. |
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Rewrite this... It sounds weird
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| You will need to do the linear search $O(\log_2{N})$ times, so $l = r$. | ||
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| Usually the complexity would be: $O((N+Q) \cdot \log_2{(N+Q)}^2)$ |
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This is an incomplete thought. Usually it's that time complexity but you should also state the time complexity of the parallel binary search following a ", but"
| <FocusProblem problem="sam" /> | ||
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| ## Solution - New Roads Queries | ||
| We can see that connectivity of the nodes is a monotonic function. |
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| We can see that connectivity of the nodes is a monotonic function. | ||
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| Now let's use parallel binary search: |
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Combine these sentences in some way
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| When sweeping through the array of edges, union them in the DSU. | ||
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| Whenever there is a query with median = $i$, if the two nodes where connected in DSU, it means the answer is $\leq i$ ($r = i$), otherwise it means $\gt i$ ($l = i+1$). |
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Split this into two sentences since it's too wordy and grammatically incorrect
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| <FocusProblem problem="sam" /> | ||
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| ## Solution - New Roads Queries |
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Definitely expand on this solution
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This pull request has been automatically marked as stale because it has not had recent activity. Please address the requested changes and re-request reviews. Thank you for your contribution! |
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Changes requested have not been made. Free free to create a new PR. |
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I did this pull request because the previous one was closed by stale (#3777 )