62. Unique Paths

Author: Partho Biswas

README.md

@@ -588,6 +588,7 @@ BFS, DFS, Dijkstra, Floyd–Warshall, Bellman-Ford, Kruskal, Prim's, Minimum Spa
 |38| **[801. Minimum Swaps To Make Sequences Increasing](https://tinyurl.com/rvtcyvb)** | [Python](https://tinyurl.com/wu6rdaw/801_Minimum_Swaps_To_Make_Sequences_Increasing.py)| [Art 1](https://tinyurl.com/tzx7wpv), [Art 2](https://tinyurl.com/ugybcmz) | Medium | TODO: Check again. Very analytical and tricky to come up with |
 |39| **[279. Perfect Squares](https://tinyurl.com/jcjc6kf)** | [Python](https://tinyurl.com/wu6rdaw/279_Perfect_Squares.py)| **[Must](https://tinyurl.com/raomm4y)**, [Vid 1](https://tinyurl.com/rxpaqe8), [Vis 2](https://tinyurl.com/uevqohx) | Medium | TODO: Check again. Very Important. Very analytical and tricky to come up with |
 |40| **[139. Word Break](https://tinyurl.com/yyyy9dqz)** | [Python](https://tinyurl.com/wu6rdaw/139_Word_Break.py)| **[Must](https://tinyurl.com/sdzmo32)**, [Vid 1](https://tinyurl.com/s4hvakw), [Vis 2](https://tinyurl.com/rjwjanc), [Vid 3](https://tinyurl.com/rdxmwwg) | Medium | TODO: Check again. Very Important. |
+|41| **[62. Unique Paths](https://tinyurl.com/j8xmh7u)** | [Python](https://tinyurl.com/wu6rdaw/62_Unique_Paths.py)| **[Vid 1](https://tinyurl.com/wp6vsqq)**, [Art 1](https://tinyurl.com/roammlg), [Art 2](https://tinyurl.com/tt5fpjk) | Medium | TODO: Check again |
 
 
 </p>

leetcode.com/python/62_Unique_Paths.py

@@ -0,0 +1,60 @@
+# Approach 1: Recursion.
+class Solution(object):
+    def uniquePaths(self, m, n):
+        """
+        :type m: int
+        :type n: int
+        :rtype: int
+        """
+        return self.uniquePathsHelper(m, 0, n, 0, 0)
+
+
+    def uniquePathsHelper(self, m, currentM, n, currentN, paths):
+        if (currentN, currentM) == (n - 1, m - 1):
+            return paths + 1
+        if currentM >= m or currentN >= n:
+            return paths
+        down = self.uniquePathsHelper(m, currentM, n, currentN + 1, paths)
+        right = self.uniquePathsHelper(m, currentM + 1, n, currentN, paths)
+        return down + right
+
+
+# Approach 2: Recursion with memoization. Source: https://tinyurl.com/tvolzor
+class Solution(object):
+    def uniquePaths(self, m, n):
+        """
+        :type m: int
+        :type n: int
+        :rtype: int
+        """
+        memo = {}
+        return self.uniquePathsHelper(m, n, memo)
+
+    def uniquePathsHelper(self, m, n, memo):
+        if (m, n) in memo:
+            return memo[(m, n)]
+        elif m == 1 or n == 1:
+            return 1
+        up = self.uniquePathsHelper(m, n - 1, memo)
+        left = self.uniquePathsHelper(m - 1, n, memo)
+        memo[(m, n)] = up + left
+        return memo[(m, n)]
+
+
+
+
+# Approach 3: DP. Source: https://tinyurl.com/tvolzor
+class Solution(object):
+    def uniquePaths(self, m, n):
+        """
+        :type m: int
+        :type n: int
+        :rtype: int
+        """
+        if not m or not n:
+            return 0
+        dp = [[1 for _ in range(m)] for _ in range(n)]
+        for i in range(1, n):
+            for j in range(1, m):
+                dp[i][j] = dp[i][j - 1] +  dp[i - 1][j]
+        return dp[-1][-1]