Lecture 115: Largest Square area in Matrix

Lectures/Lecture_115/Lecture_Codes/README.md

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+# Lecture Codes
+
+|  **Problem**  |  **Solution**  |  **Level**  |
+|:--------------|:--------------:|:-----------:|
+|  [Largest square formed in a matrix](https://www.geeksforgeeks.org/problems/largest-square-formed-in-a-matrix0806/1)  |  [Solution1](), [Solution2](), [Solution3](), [Solution4]()  |  Medium  |

Lectures/Lecture_115/Lecture_Codes/largest_square_formed_in_a_matrix_1.cpp

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+// Gives TLE
+
+class Solution {
+  public:
+    int solve(vector<vector<int>> &mat, int i, int j, int &maxi, int &n, int &m) {
+        if (i >= n || j >= m) {
+            return 0;
+        } 
+
+        int right = solve(mat, i, j+1, maxi, n, m);
+        int diagonal = solve(mat, i+1, j+1, maxi, n, m);
+        int down = solve(mat, i+1, j, maxi, n, m);
+
+        if (mat[i][j] == 1) {
+            int ans = 1 + min(right, min(diagonal, down));
+
+            maxi = max(maxi, ans);
+
+            return ans;
+        }
+        else {
+            return 0;
+        }
+    }
+
+    int maxSquare(int n, int m, vector<vector<int>> mat) {
+        // code here
+        int maxi = 0;
+
+        solve(mat, 0, 0, maxi, n, m);
+
+        return maxi;
+    }
+};

Lectures/Lecture_115/Lecture_Codes/largest_square_formed_in_a_matrix_2.cpp

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+// Recursion + Memoization
+
+class Solution {
+  public:
+    int solve(vector<vector<int>> &mat, int i, int j, int &maxi, int &n, int &m, vector<vector<int>> &dp) {
+        if (i >= n || j >= m) {
+            return 0;
+        } 
+
+        if (dp[i][j] != -1) {
+            return dp[i][j];
+        }
+
+        int right = solve(mat, i, j+1, maxi, n, m, dp);
+        int diagonal = solve(mat, i+1, j+1, maxi, n, m, dp);
+        int down = solve(mat, i+1, j, maxi, n, m, dp);
+
+        if (mat[i][j] == 1) {
+            dp[i][j] = 1 + min(right, min(diagonal, down));
+
+            maxi = max(maxi, dp[i][j]);
+
+            return dp[i][j];
+        }
+        else {
+            return dp[i][j] = 0;
+        }
+    }
+
+    int maxSquare(int n, int m, vector<vector<int>> mat) {
+        // code here
+        vector<vector<int>> dp(n, vector<int>(m ,-1));
+        int maxi = 0;
+
+        solve(mat, 0, 0, maxi, n, m, dp);
+
+        return maxi;
+    }
+};

Lectures/Lecture_115/Lecture_Codes/largest_square_formed_in_a_matrix_3.cpp

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+// tabulation method
+
+class Solution {
+  public:
+    int solve(vector<vector<int>> &mat, int &maxi, int &n, int &m) {
+
+        vector<vector<int>> dp(n+1, vector<int>(m+1 ,0));
+
+        for (int i=n-1; i>=0; i--) {
+            for (int j=m-1; j>=0; j--) {
+                int right = dp[i][j+1];
+                int diagonal = dp[i+1][j+1];
+                int down = dp[i+1][j];
+
+                if (mat[i][j] == 1) {
+                    dp[i][j] = 1 + min(right, min(diagonal, down));
+                    maxi = max(maxi, dp[i][j]);
+                }
+                else {
+                    dp[i][j] = 0;
+                }
+            }
+        }
+        return dp[0][0];
+    }
+
+    int maxSquare(int n, int m, vector<vector<int>> mat) {
+        // code here
+        int maxi = 0;
+
+        solve(mat, maxi, n, m);
+
+        return maxi;
+    }
+};

Lectures/Lecture_115/Lecture_Codes/largest_square_formed_in_a_matrix_4.cpp

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+// space optimization
+
+class Solution {
+  public:
+    int solve(vector<vector<int>> &mat, int &maxi, int &n, int &m) {
+        vector<int> curr(m+1, 0);
+        vector<int> next(m+1, 0);
+
+        for (int i=n-1; i>=0; i--) {
+            for (int j=m-1; j>=0; j--) {
+                int right = curr[j+1];
+                int diagonal = next[j+1];
+                int down = next[j];
+
+                if (mat[i][j] == 1) {
+                    curr[j] = 1 + min(right, min(diagonal, down));
+                    maxi = max(maxi, curr[j]);
+                }
+                else {
+                    curr[j] = 0;
+                }
+            }
+            next = curr;
+        }
+        return next[0];
+    }
+
+    int maxSquare(int n, int m, vector<vector<int>> mat) {
+        // code here
+        int maxi = 0;
+
+        solve(mat, maxi, n, m);
+
+        return maxi;
+    }
+};