Editorial for DMOPC '18 Contest 2 P4 - Damage Output

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Author: r3mark

For the first subtask, brute-force all subarrays and their sums.

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

For the second subtask, check all subarrays and use a prefix sum to calculate their sums.

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

For the third subtask, we do a two-pointer walk. Keep a left and right pointer, initially both set to the starting index. If the subarray currently described by the two pointers has a sum less than $M$ ~M~, move the right pointer. Otherwise, move the left pointer. Since all the elements are non-negative, this will find the smallest subarray with sum at least $M$ ~M~.

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

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