feat: add solutions to lc problem: No.2209

solution/2200-2299/2209.Minimum White Tiles After Covering With Carpets/README.md

@@ -73,18 +73,19 @@ tags:
 
 ### 方法一：记忆化搜索
 
-我们设计一个函数 $dfs(i, j)$ 表示从下标 $i$ 开始，使用 $j$ 条地毯，最少有多少个白色砖块没有被覆盖。答案即为 $dfs(0, numCarpets)$。
+我们设计一个函数 $\textit{dfs}(i, j)$ 表示从下标 $i$ 开始，使用 $j$ 条地毯，最少有多少个白色砖块没有被覆盖。答案即为 $\textit{dfs}(0, \textit{numCarpets})$。
 
 对于下标 $i$，我们分情况讨论：
 
 -   如果 $i \ge n$，说明已经覆盖完所有砖块，返回 $0$；
--   如果 $floor[i] = 0$，则不需要使用地毯，直接跳过即可，即 $dfs(i, j) = dfs(i + 1, j)$；
--   如果 $j = 0$，那么我们可以直接利用前缀和数组 $s$ 计算出剩余未被覆盖的白色砖块的数目，即 $dfs(i, j) = s[n] - s[i]$；
--   如果 $floor[i] = 1$，那么我们可以选择使用地毯覆盖，也可以选择不使用地毯覆盖，取两者的最小值即可，即 $dfs(i, j) = min(dfs(i + 1, j), dfs(i + carpetLen, j - 1))$。
+-   如果 $\textit{floor}[i] = 0$，则不需要使用地毯，直接跳过即可，即 $\textit{dfs}(i, j) = \textit{dfs}(i + 1, j)$；
+-   如果 $j = 0$，那么我们可以直接利用前缀和数组 $s$ 计算出剩余未被覆盖的白色砖块的数目，即 $\textit{dfs}(i, j) = s[n] - s[i]$；
+-   如果 $\textit{floor}[i] = 1$，那么我们可以选择使用地毯覆盖，也可以选择不使用地毯覆盖，取两者的最小值即可，即 $\textit{dfs}(i, j) = \min(\textit{dfs}(i + 1,
+    j), \textit{dfs}(i + \textit{carpetLen}, j - 1))$。
 
 记忆化搜索即可。
 
-时间复杂度 $O(n\times m)$，空间复杂度 $O(n\times m)$。其中 $n$ 和 $m$ 分别为字符串 $floor$ 的长度和 $numCarpets$ 的值。
+时间复杂度 $O(n\times m)$，空间复杂度 $O(n\times m)$。其中 $n$ 和 $m$ 分别为字符串 $\textit{floor}$ 的长度和 $\textit{numCarpets}$ 的值。
 
 <!-- tabs:start -->
 
@@ -94,10 +95,10 @@ tags:
 class Solution:
     def minimumWhiteTiles(self, floor: str, numCarpets: int, carpetLen: int) -> int:
         @cache
-        def dfs(i, j):
+        def dfs(i: int, j: int) -> int:
             if i >= n:
                 return 0
-            if floor[i] == '0':
+            if floor[i] == "0":
                 return dfs(i + 1, j)
             if j == 0:
                 return s[-1] - s[i]
@@ -106,7 +107,7 @@ class Solution:
         n = len(floor)
         s = [0] * (n + 1)
         for i, c in enumerate(floor):
-            s[i + 1] = s[i] + int(c == '1')
+            s[i + 1] = s[i] + int(c == "1")
         ans = dfs(0, numCarpets)
         dfs.cache_clear()
         return ans
@@ -116,17 +117,14 @@ class Solution:
 
 ```java
 class Solution {
-    private int[][] f;
+    private Integer[][] f;
     private int[] s;
     private int n;
     private int k;
 
     public int minimumWhiteTiles(String floor, int numCarpets, int carpetLen) {
         n = floor.length();
-        f = new int[n][numCarpets + 1];
-        for (var e : f) {
-            Arrays.fill(e, -1);
-        }
+        f = new Integer[n][numCarpets + 1];
         s = new int[n + 1];
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor.charAt(i) == '1' ? 1 : 0);
@@ -142,7 +140,7 @@ class Solution {
         if (j == 0) {
             return s[n] - s[i];
         }
-        if (f[i][j] != -1) {
+        if (f[i][j] != null) {
             return f[i][j];
         }
         if (s[i + 1] == s[i]) {
@@ -167,12 +165,19 @@ public:
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor[i] == '1');
         }
-        function<int(int, int)> dfs;
-        dfs = [&](int i, int j) {
-            if (i >= n) return 0;
-            if (j == 0) return s[n] - s[i];
-            if (f[i][j] != -1) return f[i][j];
-            if (s[i + 1] == s[i]) return dfs(i + 1, j);
+        auto dfs = [&](this auto&& dfs, int i, int j) -> int {
+            if (i >= n) {
+                return 0;
+            }
+            if (j == 0) {
+                return s[n] - s[i];
+            }
+            if (f[i][j] != -1) {
+                return f[i][j];
+            }
+            if (s[i + 1] == s[i]) {
+                return dfs(i + 1, j);
+            }
             int ans = min(1 + dfs(i + 1, j), dfs(i + carpetLen, j - 1));
             f[i][j] = ans;
             return ans;
@@ -220,6 +225,37 @@ func minimumWhiteTiles(floor string, numCarpets int, carpetLen int) int {
 }
 ```
 
+#### TypeScript
+
+```ts
+function minimumWhiteTiles(floor: string, numCarpets: number, carpetLen: number): number {
+    const n = floor.length;
+    const f: number[][] = Array.from({ length: n }, () => Array(numCarpets + 1).fill(-1));
+    const s: number[] = Array(n + 1).fill(0);
+    for (let i = 0; i < n; ++i) {
+        s[i + 1] = s[i] + (floor[i] === '1' ? 1 : 0);
+    }
+    const dfs = (i: number, j: number): number => {
+        if (i >= n) {
+            return 0;
+        }
+        if (j === 0) {
+            return s[n] - s[i];
+        }
+        if (f[i][j] !== -1) {
+            return f[i][j];
+        }
+        if (s[i + 1] === s[i]) {
+            return dfs(i + 1, j);
+        }
+        const ans = Math.min(1 + dfs(i + 1, j), dfs(i + carpetLen, j - 1));
+        f[i][j] = ans;
+        return ans;
+    };
+    return dfs(0, numCarpets);
+}
+```
+
 <!-- tabs:end -->
 
 <!-- solution:end -->

solution/2200-2299/2209.Minimum White Tiles After Covering With Carpets/README_EN.md

@@ -37,7 +37,7 @@ tags:
 <pre>
 <strong>Input:</strong> floor = &quot;10110101&quot;, numCarpets = 2, carpetLen = 2
 <strong>Output:</strong> 2
-<strong>Explanation:</strong> 
+<strong>Explanation:</strong>
 The figure above shows one way of covering the tiles with the carpets such that only 2 white tiles are visible.
 No other way of covering the tiles with the carpets can leave less than 2 white tiles visible.
 </pre>
@@ -47,7 +47,7 @@ No other way of covering the tiles with the carpets can leave less than 2 white
 <pre>
 <strong>Input:</strong> floor = &quot;11111&quot;, numCarpets = 2, carpetLen = 3
 <strong>Output:</strong> 0
-<strong>Explanation:</strong> 
+<strong>Explanation:</strong>
 The figure above shows one way of covering the tiles with the carpets such that no white tiles are visible.
 Note that the carpets are able to overlap one another.
 </pre>
@@ -69,18 +69,18 @@ Note that the carpets are able to overlap one another.
 
 ### Solution 1: Memoization Search
 
-Design a function $dfs(i, j)$ to represent the minimum number of white bricks that are not covered starting from index $i$ using $j$ carpets. The answer is $dfs(0, numCarpets)$.
+We design a function $\textit{dfs}(i, j)$ to represent the minimum number of white tiles that are not covered starting from index $i$ using $j$ carpets. The answer is $\textit{dfs}(0, \textit{numCarpets})$.
 
-For index $i$, we discuss different cases:
+For index $i$, we discuss the following cases:
 
--   If $i \ge n$, it means that all bricks have been covered, return $0$;
--   If $floor[i] = 0$, there is no need to use a carpet, just skip it, that is, $dfs(i, j) = dfs(i + 1, j)$;
--   If $j = 0$, we can directly calculate the number of remaining white bricks that have not been covered using the prefix sum array $s$, that is, $dfs(i, j) = s[n] - s[i]$;
--   If $floor[i] = 1$, we can choose to use a carpet to cover it, or choose not to use a carpet to cover it, and take the minimum of the two, that is, $dfs(i, j) = min(dfs(i + 1, j), dfs(i + carpetLen, j - 1))$.
+-   If $i \ge n$, it means all tiles have been covered, return $0$;
+-   If $\textit{floor}[i] = 0$, then we do not need to use a carpet, just skip it, i.e., $\textit{dfs}(i, j) = \textit{dfs}(i + 1, j)$;
+-   If $j = 0$, then we can directly use the prefix sum array $s$ to calculate the number of remaining uncovered white tiles, i.e., $\textit{dfs}(i, j) = s[n] - s[i]$;
+-   If $\textit{floor}[i] = 1$, then we can choose to use a carpet or not, and take the minimum of the two, i.e., $\textit{dfs}(i, j) = \min(\textit{dfs}(i + 1, j), \textit{dfs}(i + \textit{carpetLen}, j - 1))$.
 
-Use memoization search.
+We use memoization search to solve this problem.
 
-The time complexity is $O(n\times m)$, and the space complexity is $O(n\times m)$. Where $n$ and $m$ are the lengths of the string $floor$ and the value of $numCarpets$ respectively.
+The time complexity is $O(n \times m)$, and the space complexity is $O(n \times m)$. Here, $n$ and $m$ are the length of the string $\textit{floor}$ and the value of $\textit{numCarpets}$, respectively.
 
 <!-- tabs:start -->
 
@@ -90,10 +90,10 @@ The time complexity is $O(n\times m)$, and the space complexity is $O(n\times m)
 class Solution:
     def minimumWhiteTiles(self, floor: str, numCarpets: int, carpetLen: int) -> int:
         @cache
-        def dfs(i, j):
+        def dfs(i: int, j: int) -> int:
             if i >= n:
                 return 0
-            if floor[i] == '0':
+            if floor[i] == "0":
                 return dfs(i + 1, j)
             if j == 0:
                 return s[-1] - s[i]
@@ -102,7 +102,7 @@ class Solution:
         n = len(floor)
         s = [0] * (n + 1)
         for i, c in enumerate(floor):
-            s[i + 1] = s[i] + int(c == '1')
+            s[i + 1] = s[i] + int(c == "1")
         ans = dfs(0, numCarpets)
         dfs.cache_clear()
         return ans
@@ -112,17 +112,14 @@ class Solution:
 
 ```java
 class Solution {
-    private int[][] f;
+    private Integer[][] f;
     private int[] s;
     private int n;
     private int k;
 
     public int minimumWhiteTiles(String floor, int numCarpets, int carpetLen) {
         n = floor.length();
-        f = new int[n][numCarpets + 1];
-        for (var e : f) {
-            Arrays.fill(e, -1);
-        }
+        f = new Integer[n][numCarpets + 1];
         s = new int[n + 1];
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor.charAt(i) == '1' ? 1 : 0);
@@ -138,7 +135,7 @@ class Solution {
         if (j == 0) {
             return s[n] - s[i];
         }
-        if (f[i][j] != -1) {
+        if (f[i][j] != null) {
             return f[i][j];
         }
         if (s[i + 1] == s[i]) {
@@ -163,12 +160,19 @@ public:
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor[i] == '1');
         }
-        function<int(int, int)> dfs;
-        dfs = [&](int i, int j) {
-            if (i >= n) return 0;
-            if (j == 0) return s[n] - s[i];
-            if (f[i][j] != -1) return f[i][j];
-            if (s[i + 1] == s[i]) return dfs(i + 1, j);
+        auto dfs = [&](this auto&& dfs, int i, int j) -> int {
+            if (i >= n) {
+                return 0;
+            }
+            if (j == 0) {
+                return s[n] - s[i];
+            }
+            if (f[i][j] != -1) {
+                return f[i][j];
+            }
+            if (s[i + 1] == s[i]) {
+                return dfs(i + 1, j);
+            }
             int ans = min(1 + dfs(i + 1, j), dfs(i + carpetLen, j - 1));
             f[i][j] = ans;
             return ans;
@@ -216,6 +220,37 @@ func minimumWhiteTiles(floor string, numCarpets int, carpetLen int) int {
 }
 ```
 
+#### TypeScript
+
+```ts
+function minimumWhiteTiles(floor: string, numCarpets: number, carpetLen: number): number {
+    const n = floor.length;
+    const f: number[][] = Array.from({ length: n }, () => Array(numCarpets + 1).fill(-1));
+    const s: number[] = Array(n + 1).fill(0);
+    for (let i = 0; i < n; ++i) {
+        s[i + 1] = s[i] + (floor[i] === '1' ? 1 : 0);
+    }
+    const dfs = (i: number, j: number): number => {
+        if (i >= n) {
+            return 0;
+        }
+        if (j === 0) {
+            return s[n] - s[i];
+        }
+        if (f[i][j] !== -1) {
+            return f[i][j];
+        }
+        if (s[i + 1] === s[i]) {
+            return dfs(i + 1, j);
+        }
+        const ans = Math.min(1 + dfs(i + 1, j), dfs(i + carpetLen, j - 1));
+        f[i][j] = ans;
+        return ans;
+    };
+    return dfs(0, numCarpets);
+}
+```
+
 <!-- tabs:end -->
 
 <!-- solution:end -->

solution/2200-2299/2209.Minimum White Tiles After Covering With Carpets/Solution.cpp

@@ -7,16 +7,23 @@ class Solution {
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor[i] == '1');
         }
-        function<int(int, int)> dfs;
-        dfs = [&](int i, int j) {
-            if (i >= n) return 0;
-            if (j == 0) return s[n] - s[i];
-            if (f[i][j] != -1) return f[i][j];
-            if (s[i + 1] == s[i]) return dfs(i + 1, j);
+        auto dfs = [&](this auto&& dfs, int i, int j) -> int {
+            if (i >= n) {
+                return 0;
+            }
+            if (j == 0) {
+                return s[n] - s[i];
+            }
+            if (f[i][j] != -1) {
+                return f[i][j];
+            }
+            if (s[i + 1] == s[i]) {
+                return dfs(i + 1, j);
+            }
             int ans = min(1 + dfs(i + 1, j), dfs(i + carpetLen, j - 1));
             f[i][j] = ans;
             return ans;
         };
         return dfs(0, numCarpets);
     }
-};
+};

solution/2200-2299/2209.Minimum White Tiles After Covering With Carpets/Solution.java

@@ -1,15 +1,12 @@
 class Solution {
-    private int[][] f;
+    private Integer[][] f;
     private int[] s;
     private int n;
     private int k;
 
     public int minimumWhiteTiles(String floor, int numCarpets, int carpetLen) {
         n = floor.length();
-        f = new int[n][numCarpets + 1];
-        for (var e : f) {
-            Arrays.fill(e, -1);
-        }
+        f = new Integer[n][numCarpets + 1];
         s = new int[n + 1];
         for (int i = 0; i < n; ++i) {
             s[i + 1] = s[i] + (floor.charAt(i) == '1' ? 1 : 0);
@@ -25,7 +22,7 @@ private int dfs(int i, int j) {
         if (j == 0) {
             return s[n] - s[i];
         }
-        if (f[i][j] != -1) {
+        if (f[i][j] != null) {
             return f[i][j];
         }
         if (s[i + 1] == s[i]) {
@@ -35,4 +32,4 @@ private int dfs(int i, int j) {
         f[i][j] = ans;
         return ans;
     }
-}
+}

solution/2200-2299/2209.Minimum White Tiles After Covering With Carpets/Solution.py

@@ -1,10 +1,10 @@
 class Solution:
     def minimumWhiteTiles(self, floor: str, numCarpets: int, carpetLen: int) -> int:
         @cache
-        def dfs(i, j):
+        def dfs(i: int, j: int) -> int:
             if i >= n:
                 return 0
-            if floor[i] == '0':
+            if floor[i] == "0":
                 return dfs(i + 1, j)
             if j == 0:
                 return s[-1] - s[i]
@@ -13,7 +13,7 @@ def dfs(i, j):
         n = len(floor)
         s = [0] * (n + 1)
         for i, c in enumerate(floor):
-            s[i + 1] = s[i] + int(c == '1')
+            s[i + 1] = s[i] + int(c == "1")
         ans = dfs(0, numCarpets)
         dfs.cache_clear()
         return ans