From 3b1119f66e7794eab701fe2b6c4081b943c97c1c Mon Sep 17 00:00:00 2001
From: Hiro Funatsuka <hiro.funatsuka@gmail.com>
Date: Sun, 10 May 2026 11:58:57 +0900
Subject: [PATCH 1/2] Solve unique paths

---
 62_unique_paths/problem.md |  1 +
 62_unique_paths/step1.md   | 17 +++++++++++++++++
 62_unique_paths/step2.md   | 20 ++++++++++++++++++++
 62_unique_paths/step3.md   | 19 +++++++++++++++++++
 4 files changed, 57 insertions(+)
 create mode 100644 62_unique_paths/problem.md
 create mode 100644 62_unique_paths/step1.md
 create mode 100644 62_unique_paths/step2.md
 create mode 100644 62_unique_paths/step3.md

diff --git a/62_unique_paths/problem.md b/62_unique_paths/problem.md
new file mode 100644
index 0000000..3119501
--- /dev/null
+++ b/62_unique_paths/problem.md
@@ -0,0 +1 @@
+## 問題: [62. Unique Paths](https://leetcode.com/problems/unique-paths/description/)
diff --git a/62_unique_paths/step1.md b/62_unique_paths/step1.md
new file mode 100644
index 0000000..3847198
--- /dev/null
+++ b/62_unique_paths/step1.md
@@ -0,0 +1,17 @@
+# Step 1
+
+- ある地点$grid[i][j]$に辿り着けるルートの数は$grid[i - 1][j]$に辿り着くルートの数と$grid[i][j - 1]$に辿り着くルートの数の和である
+
+```python
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        grid = [[1] * n] + [[1] + [0] * (n - 1)] * (m - 1)
+        for i in range(1, m):
+            for j in range(1, n):
+                grid[i][j] = grid[i - 1][j] + grid[i][j - 1]
+        return grid[m - 1][n - 1]
+```
+
+時間計算量: $O(m \times n)$
+
+空間計算量: $O(m \times n)$
diff --git a/62_unique_paths/step2.md b/62_unique_paths/step2.md
new file mode 100644
index 0000000..fb131f8
--- /dev/null
+++ b/62_unique_paths/step2.md
@@ -0,0 +1,20 @@
+# Step 2
+
+- 空間計算量を改善する
+
+```python
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        prev_row = [1] * n
+        for i in range(1, m):
+            new_row = [1] + [0] * (n - 1)
+            for j in range(1, n):
+                new_row[j] = new_row[j - 1] + prev_row[j]
+            prev_row = new_row
+        return prev_row[n - 1]
+
+```
+
+時間計算量: $O(m \times n)$
+
+空間計算量: $O(n)$
diff --git a/62_unique_paths/step3.md b/62_unique_paths/step3.md
new file mode 100644
index 0000000..de1f188
--- /dev/null
+++ b/62_unique_paths/step3.md
@@ -0,0 +1,19 @@
+# Step 3
+
+```python
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        prev_row = [1] * n
+        for i in range(1, m):
+            new_row = [1] + [0] * (n - 1)
+            for j in range(1, n):
+                new_row[j] = new_row[j - 1] + prev_row[j]
+            prev_row = new_row
+        return prev_row[n - 1]
+```
+
+1回目: 1分　20秒
+
+2回目: 1分　6秒
+
+3回目: 1分　6秒

From 0ecd0f3eab61902956969abf9443dfa2ba9b63c1 Mon Sep 17 00:00:00 2001
From: Hiro Funatsuka <hiro.funatsuka@gmail.com>
Date: Sun, 10 May 2026 13:37:55 +0900
Subject: [PATCH 2/2] Refactor code

---
 62_unique_paths/step2.md | 8 +++-----
 62_unique_paths/step3.md | 8 +++-----
 2 files changed, 6 insertions(+), 10 deletions(-)

diff --git a/62_unique_paths/step2.md b/62_unique_paths/step2.md
index fb131f8..c8177ee 100644
--- a/62_unique_paths/step2.md
+++ b/62_unique_paths/step2.md
@@ -5,13 +5,11 @@
 ```python
 class Solution:
     def uniquePaths(self, m: int, n: int) -> int:
-        prev_row = [1] * n
+        row = [1] * n
         for i in range(1, m):
-            new_row = [1] + [0] * (n - 1)
             for j in range(1, n):
-                new_row[j] = new_row[j - 1] + prev_row[j]
-            prev_row = new_row
-        return prev_row[n - 1]
+                row[j] += row[j - 1]
+        return row[n - 1]
 
 ```
 
diff --git a/62_unique_paths/step3.md b/62_unique_paths/step3.md
index de1f188..9a64dfa 100644
--- a/62_unique_paths/step3.md
+++ b/62_unique_paths/step3.md
@@ -3,13 +3,11 @@
 ```python
 class Solution:
     def uniquePaths(self, m: int, n: int) -> int:
-        prev_row = [1] * n
+        row = [1] * n
         for i in range(1, m):
-            new_row = [1] + [0] * (n - 1)
             for j in range(1, n):
-                new_row[j] = new_row[j - 1] + prev_row[j]
-            prev_row = new_row
-        return prev_row[n - 1]
+                row[j] += row[j - 1]
+        return row[n - 1]
 ```
 
 1回目: 1分　20秒