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How can I improve time complexity?

Revision en1, by subject17, 2022-10-31 21:47:33

Hi, can anyone please help me with this problem: https://leetcode.com/problems/maximum-number-of-books-you-can-take/ I've come up with a working brute force approach (TLE): // Time O(N^2) long long maximumBooks(vector& books) { long long res = 0; for (int i = 0; i < (int)books.size(); i++) {

long long currentSum = 0;
        int lastVal = INT_MAX;

        for (int j = i; j >= 0; j--) {

            if (books[j] >= lastVal) {
                lastVal--;
                currentSum = (lastVal > 0) ? currentSum + lastVal : currentSum;
            }
            else {
                currentSum += books[j];
                lastVal = books[j];
            }

        }

        res = max(res, currentSum);
    }

    return res;
}

However, this problem can be solved in linear time according to this post: https://leetcode.com/problems/maximum-number-of-books-you-can-take/discuss/2508360/Java-O(n)-DP-%2B-Monotonic-Stack-oror-Beats-73-time-and-space-oror-Explanation-with-comments But I'm unable to understand how to calculate the summation as mentioned in the article Could someone please clarify/explain the linear time solution in plain English?

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en2 English subject17 2022-10-31 21:48:40 12
en1 English subject17 2022-10-31 21:47:33 1320 Initial revision (published)