Longest Increasing Path in a Matrix

Time: O(mn)
Space: O(mn)

Author: SteffiKeranJ

DFS/longestIncreasingPath.cpp

@@ -0,0 +1,50 @@
+class Solution {
+        int r;
+        int c;
+public:
+    int longestIncreasingPath(vector<vector<int>>& matrix) {
+        r = matrix.size();
+        if(r == 0) return 0;
+        c= matrix[0].size();
+        int maxlength = 0;
+        vector<vector<int>> dfs(r, vector<int>(c, 0));
+        for(int i = 0; i < r; ++i) {
+            for(int j = 0 ; j < c; ++j) {
+                int curr = recursive(i,j, dfs, matrix);
+                maxlength = max(maxlength, curr); 
+            }
+        }
+        return maxlength;
+    }
+    
+    int recursive(int i, int j, vector<vector<int>>& dfs, vector<vector<int>>& matrix) {
+        if(dfs[i][j] != 0) return dfs[i][j];
+        else {
+            int maxi = 1;
+            
+            // b.c 1
+            if (i-1 >= 0 && (matrix[i-1][j]>matrix[i][j])) {
+                maxi = max(maxi,1+ recursive(i-1, j, dfs, matrix));
+            }
+            
+            // b.c 2
+            if (j -1 >=0 && (matrix[i][j-1]>matrix[i][j])) {
+                maxi = max(maxi,1+ recursive(i, j-1, dfs, matrix));
+            }
+            
+            // b.c 3
+            
+            if (i+1 < r && (matrix[i+1][j]>matrix[i][j])) {
+                maxi = max(maxi,1+ recursive(i+1, j, dfs, matrix));
+            }
+            
+            // b.c. 4
+            if(j+1 < c && (matrix[i][j+1]>matrix[i][j])) {
+                    maxi = max(maxi,1+ recursive(i, j+1, dfs, matrix));
+            }            
+         dfs[i][j] = maxi;
+        return maxi;
+        }
+       
+    }
+};