Problem Difficulty Level: Medium

Author: Naganathan05

Graphs/Multi Source BFS/2812. Find the Safest Path in a Grid.cpp

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+/*---------------------------------------
+  Time Complexity: O(m * n * log(m * n))
+  Space Complexity: O(m * n)
+------------------------------------------*/
+
+class Solution {
+public:
+    int maximumSafenessFactor(vector<vector<int>>& grid) {
+        int n = grid.size();
+        int m = grid[0].size();
+        vector<vector<int>> safenessFactor(n, vector<int> (m, 1e9));
+        queue<pair<int, int>> fifo;
+
+        for(int i = 0; i <= n - 1; i++){
+            for(int j = 0; j <= m - 1; j++){
+                if(grid[i][j] == 1){
+                    safenessFactor[i][j] = 0;
+                    fifo.push({i, j});
+                }
+            }
+        }
+
+        while(!fifo.empty()){
+            auto [i, j] = fifo.front();
+            fifo.pop();
+
+            vector<pair<int, int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
+            for(auto dir : directions){
+                int newX = i + dir.first;
+                int newY = j + dir.second;
+
+                if(newX >= 0 && newY >= 0 && newX < n && newY < m && safenessFactor[newX][newY] > 1 + safenessFactor[i][j]){
+                    safenessFactor[newX][newY] = 1 + safenessFactor[i][j];
+                    fifo.push({newX, newY});
+                }
+            }
+        }
+
+        priority_queue<pair<int, pair<int, int>>> maxHeap;
+        vector<vector<bool>> visited(n, vector<bool>(m, false));
+        maxHeap.push({safenessFactor[0][0], {0, 0}});
+        visited[0][0] = true;
+        while(!maxHeap.empty()){
+            auto [safeness, temp] = maxHeap.top();
+            auto [i, j] = temp;
+            maxHeap.pop();
+
+            if(i == n - 1 && j == m - 1) return safeness;
+
+            vector<pair<int, int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
+            for(auto dir : directions){
+                int newX = i + dir.first;
+                int newY = j + dir.second;
+
+                if(newX >= 0 && newY >= 0 && newX < n && newY < m && !visited[newX][newY]){
+                    int currSafe = min(safeness, safenessFactor[newX][newY]);
+                    maxHeap.push({currSafe, {newX, newY}});
+                    visited[newX][newY] = true;
+                }
+            }
+        }
+        return 0;
+    }
+};
+
+/*
+Question Link: https://leetcode.com/problems/find-the-safest-path-in-a-grid/
+Author: M.R.Naganathan
+*/