Editorial for DMOPC '18 Contest 5 P3 - A Familiar Problem - Olympiads Online Judge

Editorial for DMOPC '18 Contest 5 P3 - A Familiar Problem

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Author: Kirito

For the first subtask, we can iterate over all subarrays $\mathcal O(N^2)$ ~\mathcal O(N^2)~ subarrays, and find their sum in $\mathcal O(N)$ ~\mathcal O(N)~ time, keeping track of the longest one where the sum does not exceed $M$ ~M~.

Time Complexity: $\mathcal O(N^3)$ ~\mathcal O(N^3)~

For the second subtask, we can find the sum in $\mathcal O(1)$ ~\mathcal O(1)~ time by using a prefix sum array.

Time Complexity: $\mathcal O(N^2)$ ~\mathcal O(N^2)~

For the third subtask, we can use a 2-pointer approach. As the right pointer advances, the left pointer should point to the left-most index where the sum is less than $M$ ~M~. Since both pointers will only move from left to right, the time complexity is $\mathcal O(N)$ ~\mathcal O(N)~.

Time Complexity: $\mathcal O(N)$ ~\mathcal O(N)~

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