Prob 164: Number of unique paths in a grid

Author: mandliya

README.md

@@ -6,7 +6,7 @@
 
 | Current Status|     Stats     |
 | :------------: | :----------: |
-| Total Problems | 163 |
+| Total Problems | 164 |
 
 </center>
 
@@ -103,6 +103,8 @@ Include contains single header implementation of data structures and some algori
 | Longest Common Subsequence Problem | [lcs.cpp](dynamic_programming_problems/lcs.cpp) |
 | Maximum Value Contigous Subsequence Problem [wiki](https://en.wikipedia.org/wiki/Maximum_subarray_problem)| [max_subsequence.cpp](dynamic_programming_problems/max_subsequence.cpp)|
 | Catalan number - Count the number of possible Binary Search Trees with n keys | [catalan_number.cpp](dynamic_programming_problems/catalan_number.cpp)|
+| Calculate the number of unique paths from source origin (0, 0) to  destination (m-1, n-1) in a m x n grid. You can only move either in down or right direction.|
+[unique_paths.cpp](dynamic_programming_problems/unique_paths.cpp)|
 
 ### Tree Problems
 | Problem | Solution |

dynamic_programming_problems/unique_paths.cpp

@@ -0,0 +1,46 @@
+/*
+ * Level : Easy
+ * Given a grid, calculate the maximum number of unique paths
+ * from source (0,0) to destination (m, n). You can only move
+ * either in down or in right direction.
+ * 
+ *  S . . . . . . . .
+ *  . . . . . . . . .
+ *  . . . . . . . . .
+ *  . . . . . . . . .
+ *  . . . . . . . . .
+ *  . . . . . . . . D
+ * 
+ * In this 6 x 9 grid, 
+ * unique paths from source origin to destination are 1287.
+ * 
+ */
+
+#include <iostream>
+#include <vector>
+
+int unique_paths(int m, int n)
+{
+    std::vector<std::vector<int>> paths(m, std::vector<int>(n));
+    for (int i = 0; i < m; ++i) {
+        paths[i][0] = 1;
+    }
+
+    for (int j = 0; j < n; ++j) {
+        paths[0][j] = 1;
+    }
+
+    for (int i = 1; i < m; ++i) {
+        for (int j = 1; j < n; ++j) {
+            paths[i][j] = paths[i-1][j] + paths[i][j-1];
+        }
+    }
+    return paths[m-1][n-1];
+}
+
+int main()
+{
+    std::cout << "Number of unique paths for 6 x 9 grid: " <<
+        unique_paths(6, 9) << std::endl;
+    return 0;
+}