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Commit 0b00ea9

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Deploying to main from @ 9a7155e 🚀
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‎book/binary_search.md

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<!-- prettier-ignore -->
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| 题号 | 标题 | 题解 | 标签 | 难度 | 力扣 |
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| :------: | :------ | :------: | :------ | :------: | :------: |
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| 875 | 爱吃香蕉的珂珂 | | [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) | 🟠 | [🀄️](https://leetcode.cn/problems/koko-eating-bananas) [🔗](https://leetcode.com/problems/koko-eating-bananas) |
249+
| 875 | 爱吃香蕉的珂珂 | [[✓]](/problem/0875.md) | [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) | 🟠 | [🀄️](https://leetcode.cn/problems/koko-eating-bananas) [🔗](https://leetcode.com/problems/koko-eating-bananas) |
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| 410 | 分割数组的最大值 | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) `2+` | 🔴 | [🀄️](https://leetcode.cn/problems/split-array-largest-sum) [🔗](https://leetcode.com/problems/split-array-largest-sum) |
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| 209 | 长度最小的子数组 | [[✓]](/problem/0209.md) | [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) [`前缀和`](/tag/prefix-sum.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/minimum-size-subarray-sum) [🔗](https://leetcode.com/problems/minimum-size-subarray-sum) |
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| 658 | 找到 K 个最接近的元素 | | [`数组`](/tag/array.md) [`双指针`](/tag/two-pointers.md) [`二分查找`](/tag/binary-search.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/find-k-closest-elements) [🔗](https://leetcode.com/problems/find-k-closest-elements) |

‎image/790.png

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‎plan/company_list.md

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| 133 | 克隆图 | [[✓]](/problem/0133.md) | [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/clone-graph) [🔗](https://leetcode.com/problems/clone-graph) | 20 |
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| 138 | 随机链表的复制 | [[✓]](/problem/0138.md) | [`哈希表`](/tag/hash-table.md) [`链表`](/tag/linked-list.md) | 🟠 | [🀄️](https://leetcode.cn/problems/copy-list-with-random-pointer) [🔗](https://leetcode.com/problems/copy-list-with-random-pointer) | 19 |
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| 124 | 二叉树中的最大路径和 | [[✓]](/problem/0124.md) | [`树`](/tag/tree.md) [`深度优先搜索`](/tag/depth-first-search.md) [`动态规划`](/tag/dynamic-programming.md) `1+` | 🔴 | [🀄️](https://leetcode.cn/problems/binary-tree-maximum-path-sum) [🔗](https://leetcode.com/problems/binary-tree-maximum-path-sum) | 19 |
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| 1268 | 搜索推荐系统 | | [`字典树`](/tag/trie.md) [`数组`](/tag/array.md) [`字符串`](/tag/string.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/search-suggestions-system) [🔗](https://leetcode.com/problems/search-suggestions-system) | 18 |
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| 1268 | 搜索推荐系统 | [[✓]](/problem/1268.md) | [`字典树`](/tag/trie.md) [`数组`](/tag/array.md) [`字符串`](/tag/string.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/search-suggestions-system) [🔗](https://leetcode.com/problems/search-suggestions-system) | 18 |
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| 953 | 验证外星语词典 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`字符串`](/tag/string.md) | 🟢 | [🀄️](https://leetcode.cn/problems/verifying-an-alien-dictionary) [🔗](https://leetcode.com/problems/verifying-an-alien-dictionary) | 18 |
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| 973 | 最接近原点的 K 个点 | [[✓]](/problem/0973.md) | [`几何`](/tag/geometry.md) [`数组`](/tag/array.md) [`数学`](/tag/math.md) `4+` | 🟠 | [🀄️](https://leetcode.cn/problems/k-closest-points-to-origin) [🔗](https://leetcode.com/problems/k-closest-points-to-origin) | 18 |
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| 29 | 两数相除 | [[✓]](/problem/0029.md) | [`位运算`](/tag/bit-manipulation.md) [`数学`](/tag/math.md) | 🟠 | [🀄️](https://leetcode.cn/problems/divide-two-integers) [🔗](https://leetcode.com/problems/divide-two-integers) | 18 |

‎plan/contest_list.md

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‎plan/rabbit_list.md

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| 74 | 搜索二维矩阵 | [[✓]](/problem/0074.md) | [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) [`矩阵`](/tag/matrix.md) | 🟠 | [🀄️](https://leetcode.cn/problems/search-a-2d-matrix) [🔗](https://leetcode.com/problems/search-a-2d-matrix) | 18 |
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| 1448 | 统计二叉树中好节点的数目 | [[✓]](/problem/1448.md) | [`树`](/tag/tree.md) [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/count-good-nodes-in-binary-tree) [🔗](https://leetcode.com/problems/count-good-nodes-in-binary-tree) | 18 |
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| 100 | 相同的树 | [[✓]](/problem/0100.md) | [`树`](/tag/tree.md) [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) `1+` | 🟢 | [🀄️](https://leetcode.cn/problems/same-tree) [🔗](https://leetcode.com/problems/same-tree) | 18 |
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| 1268 | 搜索推荐系统 | | [`字典树`](/tag/trie.md) [`数组`](/tag/array.md) [`字符串`](/tag/string.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/search-suggestions-system) [🔗](https://leetcode.com/problems/search-suggestions-system) | 18 |
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| 1268 | 搜索推荐系统 | [[✓]](/problem/1268.md) | [`字典树`](/tag/trie.md) [`数组`](/tag/array.md) [`字符串`](/tag/string.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/search-suggestions-system) [🔗](https://leetcode.com/problems/search-suggestions-system) | 18 |
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| 953 | 验证外星语词典 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`字符串`](/tag/string.md) | 🟢 | [🀄️](https://leetcode.cn/problems/verifying-an-alien-dictionary) [🔗](https://leetcode.com/problems/verifying-an-alien-dictionary) | 18 |
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| 973 | 最接近原点的 K 个点 | [[✓]](/problem/0973.md) | [`几何`](/tag/geometry.md) [`数组`](/tag/array.md) [`数学`](/tag/math.md) `4+` | 🟠 | [🀄️](https://leetcode.cn/problems/k-closest-points-to-origin) [🔗](https://leetcode.com/problems/k-closest-points-to-origin) | 18 |
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| 348 | 设计井字棋 🔒 | | [`设计`](/tag/design.md) [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) `2+` | 🟠 | [🀄️](https://leetcode.cn/problems/design-tic-tac-toe) [🔗](https://leetcode.com/problems/design-tic-tac-toe) | 18 |

‎problem/0020.md

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| 301 | 删除无效的括号 | | [`广度优先搜索`](/tag/breadth-first-search.md) [`字符串`](/tag/string.md) [`回溯`](/tag/backtracking.md) | 🔴 | [🀄️](https://leetcode.cn/problems/remove-invalid-parentheses) [🔗](https://leetcode.com/problems/remove-invalid-parentheses) |
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| 1003 | 检查替换后的词是否有效 | | [`栈`](/tag/stack.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/check-if-word-is-valid-after-substitutions) [🔗](https://leetcode.com/problems/check-if-word-is-valid-after-substitutions) |
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| 2116 | 判断一个括号字符串是否有效 | | [`栈`](/tag/stack.md) [`贪心`](/tag/greedy.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/check-if-a-parentheses-string-can-be-valid) [🔗](https://leetcode.com/problems/check-if-a-parentheses-string-can-be-valid) |
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| 2337 | 移动片段得到字符串 | | [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/move-pieces-to-obtain-a-string) [🔗](https://leetcode.com/problems/move-pieces-to-obtain-a-string) |
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| 2337 | 移动片段得到字符串 | [[✓]](/problem/2337.md) | [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/move-pieces-to-obtain-a-string) [🔗](https://leetcode.com/problems/move-pieces-to-obtain-a-string) |

‎problem/0041.md

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| 287 | 寻找重复数 | [[✓]](/problem/0287.md) | [`位运算`](/tag/bit-manipulation.md) [`数组`](/tag/array.md) [`双指针`](/tag/two-pointers.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/find-the-duplicate-number) [🔗](https://leetcode.com/problems/find-the-duplicate-number) |
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| 448 | 找到所有数组中消失的数字 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) | 🟢 | [🀄️](https://leetcode.cn/problems/find-all-numbers-disappeared-in-an-array) [🔗](https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array) |
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| 765 | 情侣牵手 | | [`贪心`](/tag/greedy.md) [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) `2+` | 🔴 | [🀄️](https://leetcode.cn/problems/couples-holding-hands) [🔗](https://leetcode.com/problems/couples-holding-hands) |
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| 2336 | 无限集中的最小数字 | | [`设计`](/tag/design.md) [`哈希表`](/tag/hash-table.md) [`有序集合`](/tag/ordered-set.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/smallest-number-in-infinite-set) [🔗](https://leetcode.com/problems/smallest-number-in-infinite-set) |
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| 2554 | 从一个范围内选择最多整数 I | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) `2+` | 🟠 | [🀄️](https://leetcode.cn/problems/maximum-number-of-integers-to-choose-from-a-range-i) [🔗](https://leetcode.com/problems/maximum-number-of-integers-to-choose-from-a-range-i) |
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| 2336 | 无限集中的最小数字 | [[✓]](/problem/2336.md) | [`设计`](/tag/design.md) [`哈希表`](/tag/hash-table.md) [`有序集合`](/tag/ordered-set.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/smallest-number-in-infinite-set) [🔗](https://leetcode.com/problems/smallest-number-in-infinite-set) |
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| 2554 | 从一个范围内选择最多整数 I | [[✓]](/problem/2554.md) | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) `2+` | 🟠 | [🀄️](https://leetcode.cn/problems/maximum-number-of-integers-to-choose-from-a-range-i) [🔗](https://leetcode.com/problems/maximum-number-of-integers-to-choose-from-a-range-i) |
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| 2557 | 从一个范围内选择最多整数 II 🔒 | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/maximum-number-of-integers-to-choose-from-a-range-ii) [🔗](https://leetcode.com/problems/maximum-number-of-integers-to-choose-from-a-range-ii) |
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| 2598 | 执行操作后的最大 MEX | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/smallest-missing-non-negative-integer-after-operations) [🔗](https://leetcode.com/problems/smallest-missing-non-negative-integer-after-operations) |
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| 2996 | 大于等于顺序前缀和的最小缺失整数 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`排序`](/tag/sorting.md) | 🟢 | [🀄️](https://leetcode.cn/problems/smallest-missing-integer-greater-than-sequential-prefix-sum) [🔗](https://leetcode.com/problems/smallest-missing-integer-greater-than-sequential-prefix-sum) |

‎problem/0392.md

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| 792 | 匹配子序列的单词数 | | [`字典树`](/tag/trie.md) [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) `4+` | 🟠 | [🀄️](https://leetcode.cn/problems/number-of-matching-subsequences) [🔗](https://leetcode.com/problems/number-of-matching-subsequences) |
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| 1055 | 形成字符串的最短路径 🔒 | | [`贪心`](/tag/greedy.md) [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/shortest-way-to-form-string) [🔗](https://leetcode.com/problems/shortest-way-to-form-string) |
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| 2486 | 追加字符以获得子序列 | | [`贪心`](/tag/greedy.md) [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/append-characters-to-string-to-make-subsequence) [🔗](https://leetcode.com/problems/append-characters-to-string-to-make-subsequence) |
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| 2825 | 循环增长使字符串子序列等于另一个字符串 | | [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/make-string-a-subsequence-using-cyclic-increments) [🔗](https://leetcode.com/problems/make-string-a-subsequence-using-cyclic-increments) |
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| 2825 | 循环增长使字符串子序列等于另一个字符串 | [[✓]](/problem/2825.md) | [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) | 🟠 | [🀄️](https://leetcode.cn/problems/make-string-a-subsequence-using-cyclic-increments) [🔗](https://leetcode.com/problems/make-string-a-subsequence-using-cyclic-increments) |

‎problem/0502.md

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<!-- prettier-ignore -->
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| 题号 | 标题 | 题解 | 标签 | 难度 | 力扣 |
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| :------: | :------ | :------: | :------ | :------: | :------: |
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| 2542 | 最大子序列的分数 | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`排序`](/tag/sorting.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/maximum-subsequence-score) [🔗](https://leetcode.com/problems/maximum-subsequence-score) |
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| 2542 | 最大子序列的分数 | [[✓]](/problem/2542.md) | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`排序`](/tag/sorting.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/maximum-subsequence-score) [🔗](https://leetcode.com/problems/maximum-subsequence-score) |
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| 2813 | 子序列最大优雅度 | | [`栈`](/tag/stack.md) [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) `3+` | 🔴 | [🀄️](https://leetcode.cn/problems/maximum-elegance-of-a-k-length-subsequence) [🔗](https://leetcode.com/problems/maximum-elegance-of-a-k-length-subsequence) |

‎problem/0790.md

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## 解题思路
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这道题的核心在于如何利用动态规划来枚举所有可能的铺法。
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如图所示:
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![](../image/790.png)
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- `dp[0] = 1`:空棋盘有一种铺法。
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- `dp[1] = 1`:一个 `2 * 1` 的棋盘只能用一个竖直的多米诺骨牌铺满。
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- `dp[2] = 2`:两个竖直多米诺骨牌或两个水平多米诺骨牌。
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- `dp[3] = 5`:
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- `dp[3] = dp[2] + dp[1] + 2 * dp[0]`
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- 在 `dp[2]` 后面加一个竖直的多米诺骨牌:`2`
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- 在 `dp[1]` 后面加两个水平的多米诺骨牌:`1`
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- 在 `dp[0]` 后面加两个 L 形托米诺骨牌:`2`
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- `dp[4] = 11`:
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- `dp[4] = dp[3] + dp[2] + 2 * dp[1] + 2 * dp[0]`
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- 在 `dp[3]` 后面加一个竖直的多米诺骨牌:`5`
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- 在 `dp[2]` 后面加两个水平的多米诺骨牌:`2`
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- 在 `dp[1]` 后面加两个 L 形托米诺骨牌:`2`
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- 在 `dp[0]` 后面加一个水平的多米诺骨牌和两个 L 形托米诺骨牌:`2`
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- `dp[5] = 24`:
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- `dp[5] = dp[4] + dp[3] + 2 * dp[2] + 2 * dp[1] + 2 * dp[0]`
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- 在 `dp[4]` 后面加一个竖直的多米诺骨牌:`11`
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- 在 `dp[3]` 后面加两个水平的多米诺骨牌:`5`
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- 在 `dp[2]` 后面加两个 L 形托米诺骨牌:`4`
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- 在 `dp[1]` 后面加一个水平的多米诺骨牌和两个 L 形托米诺骨牌:`2`
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- 在 `dp[0]` 后面加两个水平的多米诺骨牌和两个 L 形托米诺骨牌:`2`
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由此可以得到递推关系:
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```
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dp[n] = dp[n-1] + dp[n-2] + 2 * (dp[n-3] + ... + d[0])
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= dp[n-1] + dp[n-2] + dp[n-3] + dp[n-3] + 2 * (dp[n-4] + ... + d[0])
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= dp[n-1] + dp[n-3] + (dp[n-2] + dp[n-3] + 2 * (dp[n-4] + ... + d[0]))
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= dp[n-1] + dp[n-3] + dp[n-1]
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= 2 * dp[n-1] + dp[n-3]
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```
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#### 复杂度分析
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- **时间复杂度**:`O()`,
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- **空间复杂度**:`O()`,
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- **时间复杂度**:`O(n)`,动态规划需要遍历 `n`。
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- **空间复杂度**:
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- 常规 DP:需要存储 `n + 1` 个状态,空间复杂度为 `O(n)`。
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- 优化 DP:只需要三个变量,空间复杂度为 `O(1)`。
87128

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## 代码
89130

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::: code-tabs
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@tab 动态规划
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90134
```javascript
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/**
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* @param {number} n
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* @return {number}
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*/
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var numTilings = function (n) {
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const MOD = 1e9 + 7;
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let dp = new Array(n + 1).fill(0);
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dp[0] = 1;
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dp[1] = 1;
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dp[2] = 2;
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for (let i = 3; i <= n; i++) {
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dp[i] = (2 * dp[i - 1] + dp[i - 3]) % MOD;
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}
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return dp[n];
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};
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```
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@tab 动态规划(空间优化)
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```javascript
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/**
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* @param {number} n
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* @return {number}
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*/
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var numTilings = function (n) {
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const MOD = 1e9 + 7;
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if (n === 0) return 1;
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if (n === 1) return 1;
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if (n === 2) return 2;
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let dp0 = 1,
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dp1 = 1,
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dp2 = 2;
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for (let i = 3; i <= n; i++) {
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let curr = (2 * dp2 + dp0) % MOD;
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dp0 = dp1;
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dp1 = dp2;
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dp2 = curr;
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}
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return dp2;
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};
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```
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:::

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