Merge pull request keon#60 from ankit167/count_paths_in_a_matrix

Added code to find the number of unique paths in a matrix

Author: ankit167

README.md

@@ -112,6 +112,7 @@ Minimal and clean example implementations of data structures and algorithms in P
     - [sparse_dot_vector](matrix/sparse_dot_vector.py)
     - [sparse_mul](matrix/sparse_mul.py)
     - [spiral_traversal](matrix/spiral_traversal.py)
+    - [count_paths](matrix/count_paths.py)
 - [queue](queue)
     - [max_sliding_window](queue/max_sliding_window.py)
     - [moving_average](queue/moving_average.py)

matrix/count_paths.py

@@ -0,0 +1,38 @@
+
+
+#
+# Count the number of unique paths from a[0][0] to a[m-1][n-1]
+# We are allowed to move either right or down from a cell in the matrix.
+# Approaches-
+# (i) Recursion- Recurse starting from a[m-1][n-1], upwards and leftwards,
+#                add the path count of both recursions and return count.
+# (ii) Dynamic Programming- Start from a[0][0].Store the count in a count
+#                           matrix. Return count[m-1][n-1]
+# T(n)- O(mn), S(n)- O(mn)
+#
+def count_paths(m, n):
+    if m < 1 or n < 1:
+        return -1
+    count = [[None for j in range(n)] for i in range(m)]
+
+    # Taking care of the edge cases- matrix of size 1xn or mx1
+    for i in range(n):
+        count[0][i] = 1
+    for j in range(m):
+        count[j][0] = 1
+
+    for i in range(1, m):
+        for j in range(1, n):
+            # Number of ways to reach a[i][j] = number of ways to reach
+            #                                   a[i-1][j] + a[i][j-1]
+            count[i][j] = count[i-1][j] + count[i][j-1]
+
+    print count[m-1][n-1]
+
+
+def main():
+    m, n = map(int, raw_input().split())
+    count_paths(m, n)
+
+if __name__ == '__main__':
+    main()