Create 04 - Space Optimized - 1 | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/15 - Largest Square Formed in a Matrix/04 - Space Optimized - 1 | DP | Approach.cpp

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+// User function Template for C++
+class Solution {
+  public:
+    // Function to compute the largest square submatrix with all 1s using space optimization
+    int solve(vector<vector<int>>& mat, int& maxi) {
+        // Edge case: If the matrix is empty, return 0
+        if (mat.empty()) return 0;
+        
+        // Dimensions of the matrix
+        int n = mat.size();
+        int m = mat[0].size();
+        
+        // Two 1D vectors to store the current and next rows of the DP table
+        vector<int> curr(m + 1, 0); // Current row
+        vector<int> next(m + 1, 0); // Next row
+        
+        // Iterate through the matrix in reverse (bottom to top, right to left)
+        for (int i = n - 1; i >= 0; i--) {
+            for (int j = m - 1; j >= 0; j--) {
+                // Fetch values from the next row and the current row (for right, diagonal, and down)
+                int right = curr[j + 1];       // Cell to the right
+                int diagnol = next[j + 1];    // Diagonal cell
+                int down = next[j];           // Cell below
+                
+                // If the current cell contains 1, calculate the size of the square ending here
+                if (mat[i][j] == 1) {
+                    curr[j] = 1 + min({right, diagnol, down}); // Add 1 to the smallest adjacent square
+                    maxi = max(maxi, curr[j]);                // Update the maximum square size
+                } else {
+                    curr[j] = 0; // If the cell contains 0, it cannot form a square
+                }
+            }
+            
+            // Update the `next` row to the current row for the next iteration
+            next = curr;
+        }
+        
+        return next[0]; // This value is not used but returned for compatibility
+    }
+
+    // Main function to find the size of the largest square submatrix with all 1s
+    int maxSquare(vector<vector<int>>& mat) {
+        int maxi = 0; // Variable to store the maximum square size
+        solve(mat, maxi); // Compute the largest square using the solve function
+        return maxi; // Return the maximum square size
+    }
+};