Efficient Maximum Length of Non-Decreasing Array with Operations
Intuition\nThe core idea is to maximize the length of a non-decreasing subarray. Since we can replace any subarray with its sum, we need to effectively manage a
# Intuition\nThe core idea is to maximize the length of a non-decreasing subarray. Since we can replace any subarray with its sum, we need to effectively manage and track subarrays to ensure the longest possible non-decreasing sequence. This can be achieved by leveraging prefix sums and a stack to maintain the state of the subarray sums.\n# Approach\nPrefix Sums:\n\nCalculate prefix sums of the array to efficiently compute the sum of any subarray.\npfx[i] will store the sum of the array from the start up to index i.\nUsing a Stack:\n\nUse a stack to keep track of tuples (prefix sum, suffix sum, length):\nprefix sum to track the cumulative sum up to a point.\nsuffix sum to track the sum of the elements considered so far.\nlength to track the length of the non-decreasing subarray.\nDynamic Programming Transition:\n\nAs we traverse through the array, we decide whether to extend the current subarray or start a new subarray.\nThe decision to extend or start anew is based on whether the current element can be appended to the last non-decreasing subarray tracked by the stack.\nBinary Search for Efficiency:\n\nUse binary search within the stack to efficiently find the correct position to merge subarrays. This ensures that we maintain a non-decreasing sequence.\n# Complexity\n- Time complexity:\n$$O(nlog(n))$$\n- Space complexity:\n$$O(n)$$\n# Code\n```\nint _ = [](){ std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); return 0; }();\n\nclass Solution {\npublic:\n    using longest = long long;\n    using element = std::tuple<longest, longest, int>;\n\n    int findMaximumLength(std::vector<int>& nums) {\n        int const n = nums.size();\n        std::vector<element> stack = {{0, 0, 0}}; // Initialize with prefix sum, suffix sum, and length\n        longest pfx = 0; // Prefix sum\n        for (int i = 0, j = 0; i < n; ++i) {\n            pfx += nums[i]; // Update prefix sum\n            while (j + 1 < stack.size() && std::get<0>(stack[j + 1]) <= pfx) {\n                ++j;\n            }\n            element const e = stack[j];\n            longest const s = std::get<1>(e), k = std::get<2>(e);\n            while (!stack.empty() && std::get<0>(stack.back()) >= pfx + pfx - s) {\n                stack.pop_back();\n            }\n            stack.push_back({pfx + pfx - s, pfx, static_cast<int>(k + 1)});\n        }\n        return std::get<2>(stack.back());\n    }\n};\n```\n\nI optimized the code the best i could, i dont get why it has a bad memory usage.
['Binary Search', 'Dynamic Programming', 'Monotonic Stack', 'Prefix Sum', 'C++']