276. Paint Fence

276_paint_fence/problem.md

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+## 問題: [276. Paint Fence](https://www.lintcode.com/problem/514/)

276_paint_fence/step1.md

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+# Step 1
+
+- 3連続同じ色にはできない
+- $post_{k}$に塗れる色は、$post_{k - 1}$、$post_{k - 2}$による
+- 解けなかったので[解説](https://www.geeksforgeeks.org/dsa/painting-fence-algorithm/)を見た
+  - 塗り方の選択肢は2つ
+    1. $post_{n}$を$post_{n-1}$と違う色にする
+       - 色の選択肢は$k-1$
+    2. $post_{n}$と$post_{n-1}$を同じにする
+       - 色の選択肢は$k-1$
+  - $numWays(n) = numWays(n - 2) * (k - 1) + numWays(n-1)*(k-1)$
+
+```python
+class Solution:
+    """
+    @param n: non-negative integer, n posts
+    @param k: non-negative integer, k colors
+    @return: an integer, the total number of ways
+    """
+    def num_ways(self, n: int, k: int) -> int:
+        # write your code here
+        if n == 0:
+            return 0
+        if n == 1:
+            return k
+        if n == 2:
+            return k * k
+        return num_ways(n - 1) * (k - 1) + num_ways(n - 2) * (k - 1)
+```
+
+時間計算量: $O(2^n)$
+
+空間計算量:$O(n)$

276_paint_fence/step2.md

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+# Step 2
+
+- 再帰をなくして計算量を改善する
+
+```python
+class Solution:
+    """
+    @param n: non-negative integer, n posts
+    @param k: non-negative integer, k colors
+    @return: an integer, the total number of ways
+    """
+    def num_ways(self, n: int, k: int) -> int:
+        # write your code here
+        if n == 0:
+            return 0
+        if n == 1:
+            return k
+        if n == 2:
+            return k * k
+        num_ways_prev_2 = k
+        num_ways_prev_1 = k * k
+
+        for i in range(2, n):
+            tmp = num_ways_prev_1
+            num_ways_prev_1 = (k - 1) * (num_ways_prev_1 + num_ways_prev_2)
+            num_ways_prev_2 = tmp
+        return num_ways_prev_1
+
+```
+
+時間計算量: $O(n)$
+
+空間計算量: $O(1)$

276_paint_fence/step3.md

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+# Step 3
+
+```python
+class Solution:
+    """
+    @param n: non-negative integer, n posts
+    @param k: non-negative integer, k colors
+    @return: an integer, the total number of ways
+    """
+    def num_ways(self, n: int, k: int) -> int:
+        # write your code here
+        if n == 0:
+            return 0
+        if n == 1:
+            return k
+        if n == 2:
+            return k * k
+        num_ways_prev_2 = k
+        num_ways_prev_1 = k * k
+
+        for i in range(2, n):
+            tmp = num_ways_prev_1
+            num_ways_prev_1 = (k - 1) * (num_ways_prev_1 + num_ways_prev_2)
+            num_ways_prev_2 = tmp
+        return num_ways_prev_1
+```
+
+1回目: 1分　17秒
+
+2回目: 1分　20秒
+
+3回目: 1分　16秒