Unique paths algorithm and tests added to dynamic programming section

algorithms/dp/unique_paths.py

@@ -0,0 +1,33 @@
+"""
+
+Context: we have an m*n grid (m,n are integers) and we are looking to find the amount of unique paths
+we can take in order to go from the top left square to the bottom right one. We can only move one cell down
+or one cell to the right each time.
+
+"""
+
+
+def unique_paths(m, n):
+    # the dynamic programming matrix we are going to use in order to get the final solution
+    # we initialize an m*n matrix of zeros
+    dp = [[0 for _ in range(n)] for __ in range(m)]
+
+    # dp[i][j] = the amount of unique paths we can take in order to reach the square of the grid
+    # which has coordinates i and j.
+
+    for i in range(m):
+        dp[i][0] = 1
+    for j in range(n):
+        dp[0][j] = 1
+
+    # Base case: each square in the first row and column has only 1 possible path to them
+
+    for i in range(1, m):
+        for j in range(1, n):
+            dp[i][j] = dp[i-1][j] + dp[i][j-1]
+
+    # for each square, the amount of ways to reach it is equal to the sum of:
+    #   the amount of paths we can take to the square directly above it
+    #   the amount of paths we can take to the square directly to its left
+
+    return dp[m-1][n-1]

tests/test_dp.py

@@ -13,8 +13,8 @@
     longest_increasing_subsequence,
     longest_increasing_subsequence_optimized,
     longest_increasing_subsequence_optimized2,
-    int_divide,find_k_factor,
-    planting_trees, regex_matching
+    int_divide, find_k_factor,
+    planting_trees, regex_matching, unique_paths
 )
 
 
@@ -259,5 +259,17 @@ def test_symbol_2(self):
         self.assertTrue(regex_matching.is_match(s, p))
 
 
+class TestUniquePaths(unittest.TestCase):
+    def test2d(self):
+        m = 3
+        n = 7
+        self.assertEqual(unique_paths.unique_paths(m, n), 28)
+
+    def test1d(self):
+        m = 5
+        self.assertEqual(unique_paths.unique_paths(m, 1), 1)
+        self.assertEqual(unique_paths.unique_paths(1, m), 1)
+
+
 if __name__ == '__main__':
     unittest.main()