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| 1 | +// Time: O(m * n * log(m * n) + m * n * α(m * n)) = O(m * n * log(m * n)) |
| 2 | +// Space: O(m * n) |
| 3 | + |
| 4 | +class Solution { |
| 5 | +public: |
| 6 | + vector<vector<int>> matrixRankTransform(vector<vector<int>>& matrix) { |
| 7 | + map<int, vector<pair<int, int>>> lookup; |
| 8 | + for (int i = 0; i < size(matrix); ++i) { |
| 9 | + for (int j = 0; j < size(matrix[0]); ++j) { |
| 10 | + lookup[matrix[i][j]].emplace_back(i, j); |
| 11 | + } |
| 12 | + } |
| 13 | + vector<int> rank(size(matrix) + size(matrix[0])); |
| 14 | + for (const auto& [x, pairs] : lookup) { |
| 15 | + vector<int> new_rank(rank); |
| 16 | + const auto& cb = [&new_rank](int x, int y, int z) { |
| 17 | + new_rank[x] = max(new_rank[y], new_rank[z]); |
| 18 | + }; |
| 19 | + UnionFind union_find(size(matrix) + size(matrix[0]), cb); |
| 20 | + for (const auto& [i, j] : pairs) { |
| 21 | + union_find.union_set(i, j + size(matrix)); |
| 22 | + } |
| 23 | + for (const auto& [i, j] : pairs) { |
| 24 | + matrix[i][j] = rank[i] = rank[j + size(matrix)] = new_rank[union_find.find_set(i)] + 1; |
| 25 | + } |
| 26 | + } |
| 27 | + return matrix; |
| 28 | + } |
| 29 | + |
| 30 | +private: |
| 31 | + class UnionFind { |
| 32 | + public: |
| 33 | + UnionFind(const int n, function<void(int, int, int)> cb) |
| 34 | + : set_(n) |
| 35 | + , rank_(n) |
| 36 | + , count_(n) |
| 37 | + , cb_(cb) { |
| 38 | + iota(set_.begin(), set_.end(), 0); |
| 39 | + } |
| 40 | + |
| 41 | + int find_set(const int x) { |
| 42 | + if (set_[x] != x) { |
| 43 | + set_[x] = find_set(set_[x]); // Path compression. |
| 44 | + } |
| 45 | + return set_[x]; |
| 46 | + } |
| 47 | + |
| 48 | + bool union_set(const int x, const int y) { |
| 49 | + int x_root = find_set(x), y_root = find_set(y); |
| 50 | + if (x_root == y_root) { |
| 51 | + return false; |
| 52 | + } |
| 53 | + if (rank_[x_root] < rank_[y_root]) { // Union by rank. |
| 54 | + set_[x_root] = y_root; |
| 55 | + cb_(y_root, x_root, y_root); |
| 56 | + } else if (rank_[x_root] > rank_[y_root]) { |
| 57 | + set_[y_root] = x_root; |
| 58 | + cb_(x_root, x_root, y_root); |
| 59 | + } else { |
| 60 | + set_[y_root] = x_root; |
| 61 | + ++rank_[x_root]; |
| 62 | + cb_(x_root, x_root, y_root); |
| 63 | + } |
| 64 | + --count_; |
| 65 | + return true; |
| 66 | + } |
| 67 | + |
| 68 | + int size() const { |
| 69 | + return count_; |
| 70 | + } |
| 71 | + |
| 72 | + private: |
| 73 | + vector<int> set_; |
| 74 | + vector<int> rank_; |
| 75 | + int count_; |
| 76 | + function<void(int, int, int)> cb_; |
| 77 | + }; |
| 78 | +}; |
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