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| 1 | +/// Source : https://leetcode.com/problems/subarray-with-elements-greater-than-varying-threshold/ |
| 2 | +/// Author : liuyubobobo |
| 3 | +/// Time : 2022-07-09 |
| 4 | + |
| 5 | +#include <iostream> |
| 6 | +#include <vector> |
| 7 | + |
| 8 | +using namespace std; |
| 9 | + |
| 10 | + |
| 11 | +/// Divide and Conquer |
| 12 | +/// Time Complexity: O(nlogn) |
| 13 | +/// Space Complexity: O(n) |
| 14 | +template<typename T> |
| 15 | +class MinIndexSegmentTree{ |
| 16 | + |
| 17 | +private: |
| 18 | + int n; |
| 19 | + vector<T> data, tree; |
| 20 | + |
| 21 | +public: |
| 22 | + MinIndexSegmentTree(const vector<T>& data): n(data.size()), data(data), tree(4 * n, 0){ |
| 23 | + buildSegTree(0, 0, n - 1); |
| 24 | + } |
| 25 | + |
| 26 | + T query(int index){ |
| 27 | + assert(0 <= index && index < n); |
| 28 | + return data[index]; |
| 29 | + } |
| 30 | + |
| 31 | + T query(int l, int r){ |
| 32 | + assert(l <= r); |
| 33 | + assert(0 <= l && l < n); |
| 34 | + assert(0 <= r && r < n); |
| 35 | + return query(0, 0, n - 1, l, r); |
| 36 | + } |
| 37 | + |
| 38 | +private: |
| 39 | + void buildSegTree(int treeID, int l, int r){ |
| 40 | + |
| 41 | + if(l == r){ |
| 42 | + tree[treeID] = l; |
| 43 | + return; |
| 44 | + } |
| 45 | + |
| 46 | + int mid = (l + r) / 2; |
| 47 | + buildSegTree(treeID * 2 + 1, l, mid); |
| 48 | + buildSegTree(treeID * 2 + 2, mid + 1, r); |
| 49 | + tree[treeID] = data[tree[treeID * 2 + 1]] < data[tree[treeID * 2 + 2]] ? tree[treeID * 2 + 1] : tree[treeID * 2 + 2]; |
| 50 | + return; |
| 51 | + } |
| 52 | + |
| 53 | + T query(int treeID, int l, int r, int ql, int qr){ |
| 54 | + |
| 55 | + if(ql == l && qr == r) |
| 56 | + return tree[treeID]; |
| 57 | + |
| 58 | + int mid = (l + r) / 2; |
| 59 | + if(qr <= mid) return query(treeID * 2 + 1, l, mid, ql, qr); |
| 60 | + else if(ql > mid) return query(treeID * 2 + 2, mid + 1, r, ql, qr); |
| 61 | + |
| 62 | + T resl = query(treeID * 2 + 1, l, mid, ql, mid); |
| 63 | + T resr = query(treeID * 2 + 2, mid + 1, r, mid + 1, qr); |
| 64 | + return data[resl] < data[resr] ? resl : resr; |
| 65 | + } |
| 66 | +}; |
| 67 | + |
| 68 | +class Solution { |
| 69 | + |
| 70 | +private: |
| 71 | + MinIndexSegmentTree<int> *seg_tree; |
| 72 | + |
| 73 | +public: |
| 74 | + int validSubarraySize(vector<int>& nums, int threshold) { |
| 75 | + |
| 76 | + seg_tree = new MinIndexSegmentTree<int>(nums); |
| 77 | + |
| 78 | + int res = solve(nums, 0, nums.size() - 1, threshold); |
| 79 | + return res ? res : -1; |
| 80 | + } |
| 81 | + |
| 82 | + int solve(const vector<int>& nums, int l, int r, int threshold){ |
| 83 | + |
| 84 | + if(l > r) return 0; |
| 85 | + if(l == r){ |
| 86 | + return nums[l] > threshold ? 1: 0; |
| 87 | + } |
| 88 | + |
| 89 | + int min_index = seg_tree->query(l, r); |
| 90 | + int min_value = nums[min_index]; |
| 91 | + |
| 92 | + if(min_value > threshold / (r - l + 1)) return r - l + 1; |
| 93 | + |
| 94 | + int resl = solve(nums, l, min_index - 1, threshold); |
| 95 | + if(resl) return resl; |
| 96 | + return solve(nums, min_index + 1, r, threshold); |
| 97 | + } |
| 98 | +}; |
| 99 | + |
| 100 | + |
| 101 | +int main() { |
| 102 | + |
| 103 | + vector<int> nums1 = {1, 3, 4, 3, 1}; |
| 104 | + cout << Solution().validSubarraySize(nums1, 6) << '\n'; |
| 105 | + // 3 |
| 106 | + |
| 107 | + vector<int> nums2 = {6,5,6,5,8}; |
| 108 | + cout << Solution().validSubarraySize(nums2, 7) << '\n'; |
| 109 | + // 1 |
| 110 | + |
| 111 | + return 0; |
| 112 | +} |
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