Add Unique Path III Solution

Author: harsitagarwalla187

Diff for: Unique-Path-III.md

@@ -0,0 +1,84 @@
+# Unique Paths III
+[Question](https://leetcode.com/problems/unique-paths-iii/description/)
+
+# Solution:
+```cpp
+class Solution {
+
+    int m, n, tWalk, ans;
+    
+    // m -> no. of rows
+    // n -> no. of columns
+    // tWalk -> total empty square to walk over i.e grid[i][j] == 0
+    // ans -> no. of ways to reach the ending square
+
+    void DFS(vector<vector<int>> &grid, int i, int j) {
+
+        // Condition to check the index are in range 
+        //                  &
+        // there is no obstacle in the square
+        if(i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == -1) 
+            return;
+
+        // Check Current Square is the ending Square 
+        if(grid[i][j] == 2) {
+            // If there is no square left to walk over then 
+            // we have find a way to reach the ending square 
+            // so increment the ans and return else
+            // return also because there are more square to 
+            // walk over before stepping in end square
+            if(tWalk == -1) ans++;
+            return; 
+        }
+
+        // Mark current square has been walked so that 
+        // we don't walk over again
+        grid[i][j] = -1;
+        // Since we have walked one more square so 
+        // decrement total swaures to walk
+        tWalk--;
+
+        // Recursive call for Left Square
+        DFS(grid, i, j-1);
+        // Recursive call for Right Square
+        DFS(grid, i, j+1);
+        // Recursive call for Upward Square
+        DFS(grid, i-1, j);
+        // Recursive call for Downward Square
+        DFS(grid, i+1, j);
+
+        // Restore Total Walk
+        tWalk++; 
+        // Restore current square identity
+        grid[i][j] = 0;
+    }
+
+public:
+
+    int uniquePathsIII(vector<vector<int>>& grid) {
+        
+        m = grid.size();
+        n = grid[0].size();
+        ans = 0;
+        tWalk = 0;
+
+        int sx, sy;
+        for(int i=0; i<m; i++) {
+            for(int j=0; j<n; j++) {
+                // Calaculating total square to walk over
+                if(grid[i][j] == 0) tWalk++;
+                // Storing the starting Square index 
+                if(grid[i][j] == 1) {
+                    sx = i;
+                    sy = j;
+                } 
+            }
+        }
+
+        DFS(grid, sx, sy);
+
+        return ans;
+    }   
+
+};
+```