|
| 1 | +// RMQ problem, very intuitive and efficient, but be careful with the coding. |
| 2 | +/** |
| 3 | + * Definition for a binary tree node. |
| 4 | + * struct TreeNode { |
| 5 | + * int val; |
| 6 | + * TreeNode *left; |
| 7 | + * TreeNode *right; |
| 8 | + * TreeNode(int x) : val(x), left(NULL), right(NULL) {} |
| 9 | + * }; |
| 10 | + */ |
| 11 | +#include <cmath> |
| 12 | +#include <vector> |
| 13 | +using std::log; |
| 14 | +using std::vector; |
| 15 | + |
| 16 | +class Solution { |
| 17 | +public: |
| 18 | + TreeNode* constructMaximumBinaryTree(vector<int>& nums) { |
| 19 | + auto &v = nums; |
| 20 | + int n = v.size(); |
| 21 | + int dep = (int)(log(n) / log(2.0)) + 1; |
| 22 | + |
| 23 | + int i; |
| 24 | + max_idx.resize(dep, vector<int>(n)); |
| 25 | + for (i = 0; i < n; ++i) { |
| 26 | + max_idx[0][i] = i; |
| 27 | + } |
| 28 | + |
| 29 | + int j; |
| 30 | + int b2 = 1; |
| 31 | + int i1, i2; |
| 32 | + for (i = 1; i < dep; ++i) { |
| 33 | + for (j = 0; j < n; ++j) { |
| 34 | + i1 = max_idx[i - 1][j]; |
| 35 | + if (j + b2 < n) { |
| 36 | + i2 = max_idx[i - 1][j + b2]; |
| 37 | + max_idx[i][j] = (v[i1] > v[i2]) ? i1 : i2; |
| 38 | + } else { |
| 39 | + max_idx[i][j] = i1; |
| 40 | + } |
| 41 | + } |
| 42 | + b2 <<= 1; |
| 43 | + } |
| 44 | + |
| 45 | + TreeNode *root; |
| 46 | + traverse(root, nums, 0, n); |
| 47 | + max_idx.clear(); |
| 48 | + |
| 49 | + return root; |
| 50 | + } |
| 51 | +private: |
| 52 | + vector<vector<int>> max_idx; |
| 53 | + |
| 54 | + int rmq(vector<int> &v, int ll, int rr) { |
| 55 | + int d = 0; |
| 56 | + int b2 = 1; |
| 57 | + int lr, rl; |
| 58 | + while (true) { |
| 59 | + lr = ll + b2; |
| 60 | + rl = rr - b2; |
| 61 | + if (lr >= rl) { |
| 62 | + // two intervals overlap |
| 63 | + break; |
| 64 | + } else { |
| 65 | + // double the interval length |
| 66 | + d += 1; |
| 67 | + b2 <<= 1; |
| 68 | + } |
| 69 | + } |
| 70 | + int i1 = max_idx[d][ll]; |
| 71 | + int i2 = max_idx[d][rl]; |
| 72 | + return (v[i1] > v[i2]) ? i1 : i2; |
| 73 | + } |
| 74 | + |
| 75 | + void traverse(TreeNode *&root, vector<int> &v, int ll, int rr) { |
| 76 | + if (ll >= rr) { |
| 77 | + root = NULL; |
| 78 | + return; |
| 79 | + } |
| 80 | + int mm = rmq(v, ll, rr); |
| 81 | + root = new TreeNode(v[mm]); |
| 82 | + traverse(root->left, v, ll, mm); |
| 83 | + traverse(root->right, v, mm + 1, rr); |
| 84 | + } |
| 85 | +}; |
0 commit comments