Create sum-of-remoteness-of-all-cells.cpp

Author: kamyu104

C++/sum-of-remoteness-of-all-cells.cpp

@@ -0,0 +1,54 @@
+// Time:  O(n^2)
+// Space: O(n^2)
+
+// flood fill, bfs, math
+class Solution {
+public:
+    long long sumRemoteness(vector<vector<int>>& grid) {
+        static const vector<pair<int, int>> DIRECTIONS = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
+        const auto& bfs = [&](int i, int j) {
+            int64_t total = grid[i][j];
+            int cnt = 1;
+            grid[i][j] = -1;
+            vector<pair<int64_t, int>> q = {{i, j}};
+            while (!empty(q)) {
+                vector<pair<int64_t, int>> new_q;
+                for (const auto& [i, j] : q) {
+                    for (const auto& [di, dj] : DIRECTIONS) {
+                        int ni = i + di, nj = j + dj;
+                        if (!(0 <= ni && ni < size(grid) &&
+                              0 <= nj && nj < size(grid[0]) &&
+                              grid[ni][nj] != -1)) {
+                            continue;
+                        }
+                        total += grid[ni][nj];
+                        ++cnt;
+                        grid[ni][nj] = -1;
+                        new_q.emplace_back(ni, nj);
+                    }
+                }
+                q = move(new_q);
+            }
+            return pair(total, cnt);
+        };
+    
+        vector<pair<int64_t, int>> groups;
+        for (int i = 0; i < size(grid); ++i) {
+            for (int j = 0; j < size(grid[0]); ++j) {
+                if (grid[i][j] == -1) {
+                    continue;
+                }
+                groups.emplace_back(bfs(i, j));
+            }
+        }
+        int64_t total = 0;
+        for (const auto& [t, _] : groups) {
+            total += t;
+        }
+        int64_t result = 0;
+        for (const auto& [t, c] : groups) {
+            result += (total - t) * c;
+        }
+        return result;
+    }
+};