From 603b1de58bbf36c724a262824ee42d86936d0e60 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:38 +0800 Subject: [PATCH] =?UTF-8?q?Update=20Leetcode=20=E9=A2=98=E8=A7=A3=20-=20?= =?UTF-8?q?=E6=95=B0=E7=BB=84=E4=B8=8E=E7=9F=A9=E9=98=B5.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充矩阵查找与寻找重复数等题目的思路解析及配图,更新有序矩阵第 K 小、数组的度等题目的解法说明,并在文末补充参考资料。 --- notes/Leetcode 题解 - 数组与矩阵.md | 48 +++++++++++++++++++------- notes/pics/lc-array-dup-cycle.png | Bin 0 -> 154369 bytes notes/pics/lc-array-matrix-search.png | Bin 0 -> 155410 bytes 3 files changed, 36 insertions(+), 12 deletions(-) create mode 100644 notes/pics/lc-array-dup-cycle.png create mode 100644 notes/pics/lc-array-matrix-search.png diff --git a/notes/Leetcode 题解 - 数组与矩阵.md b/notes/Leetcode 题解 - 数组与矩阵.md index 7e6a43f1..669830fb 100644 --- a/notes/Leetcode 题解 - 数组与矩阵.md +++ b/notes/Leetcode 题解 - 数组与矩阵.md @@ -15,6 +15,7 @@ * [12. 分隔数组](#12-分隔数组) * [13. 合并区间](#13-合并区间) * [14. 下一个排列](#14-下一个排列) + * [参考资料](#参考资料) @@ -104,13 +105,24 @@ public int findMaxConsecutiveOnes(int[] nums) { [Leetcode](https://leetcode.com/problems/search-a-2d-matrix-ii/description/) / [力扣](https://leetcode-cn.com/problems/search-a-2d-matrix-ii/description/) ```text -[ - [ 1, 5, 9], - [10, 11, 13], - [12, 13, 15] -] +Input: +matrix = [ + [ 1, 4, 7, 11, 15], + [ 2, 5, 8, 12, 19], + [ 3, 6, 9, 16, 22], + [10, 13, 14, 17, 24], + [18, 21, 23, 26, 30] +], target = 14 + +Output: true ``` +题目描述:矩阵的每一行从左到右递增,每一列从上到下递增,判断 target 是否在矩阵中。 + +从右上角开始比较。每次比较的元素都位于剩余范围的右上角,是剩余范围内所在行的最大值、所在列的最小值:target 比它小,这一列下面的元素都更大,可以排除这一列;target 比它大,这一行左边的元素都更小,可以排除这一行。每次比较排除一行或一列,时间复杂度为 O(M + N)。 + +

+ ```java public boolean searchMatrix(int[][] matrix, int target) { if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false; @@ -144,7 +156,7 @@ return 13. 解题参考:[Share my thoughts and Clean Java Code](https://leetcode-cn.com/problems/kth-smallest-element-in-a-sorted-matrix/discuss/85173) -二分查找解法: +二分查找解法:在 [matrix[0][0], matrix[m - 1][n - 1]] 这个值域上二分,统计矩阵中不大于 mid 的元素个数 cnt。cnt < k 说明第 k 小的数比 mid 大,否则不大于 mid。循环结束时 lo 是使 cnt >= k 的最小值,这个值一定是矩阵中的元素。 ```java public int kthSmallest(int[][] matrix, int k) { @@ -165,7 +177,7 @@ public int kthSmallest(int[][] matrix, int k) { } ``` -堆解法: +堆解法:每一列从上到下递增,可以看成 n 个有序链表做多路归并。先把第一行放入小根堆,每次弹出堆顶后放入它下面的元素,弹出 k - 1 次后堆顶就是第 k 小的数。 ```java public int kthSmallest(int[][] matrix, int k) { @@ -206,7 +218,7 @@ Output: [2,3] 最直接的方法是先对数组进行排序,这种方法时间复杂度为 O(NlogN)。本题可以以 O(N) 的时间复杂度、O(1) 空间复杂度来求解。 -主要思想是通过交换数组元素,使得数组上的元素在正确的位置上。 +主要思想是通过交换数组元素,把值 x 放到下标 x - 1 上:nums[i] 不在正确的位置时,就和它应该去的位置交换,直到当前位置正确或者目标位置上已经是同样的值(说明遇到了重复的数)。放完之后,唯一一个 nums[i] != i + 1 的位置上,nums[i] 是重复的数,i + 1 是丢失的数。例如 [1, 2, 2, 4] 中,下标 2 上是 2,重复的数为 2,丢失的数为 3。 ```java public int[] findErrorNums(int[] nums) { @@ -238,7 +250,7 @@ private void swap(int[] nums, int i, int j) { 要求不能修改数组,也不能使用额外的空间。 -二分查找解法: +二分查找解法:对值域 [1, n] 二分,统计数组中不大于 mid 的元素个数 cnt。重复的数大于 mid 时,1 \~ mid 中每个数最多出现一次,cnt 不超过 mid;重复的数不大于 mid 时,大于 mid 的每个数最多出现一次,这类元素最多 n - mid 个,数组共 n + 1 个元素,cnt 至少为 mid + 1。因此 cnt > mid 说明重复的数在 [1, mid] 中,否则在 [mid + 1, n] 中。例如 [1, 3, 4, 2, 2] 中 mid = 2 时 cnt = 3,重复的数不大于 2。时间复杂度为 O(NlogN)。 ```java public int findDuplicate(int[] nums) { @@ -256,7 +268,9 @@ public int findDuplicate(int[] nums) { } ``` -双指针解法,类似于有环链表中找出环的入口: +双指针解法:把 i → nums[i] 看成链表中的一条边。从下标 0 出发沿边一直走,每一步都落在 [1, n] 的下标上,不会停下,有限个节点中必然会进入环。环的入口至少有两条边指向它(来自环外和环内),也就是至少有两个下标上的值等于它,所以入口就是重复的数。用快慢指针先在环内相遇,再让一个指针回到起点,两个指针每次各走一步,相遇处就是环的入口,与[剑指 Offer 23 链表中环的入口结点](23.%20链表中环的入口结点.md)的做法相同。时间复杂度为 O(N)。 + +

```java public int findDuplicate(int[] nums) { @@ -288,7 +302,7 @@ Explanation: The [1, 3, 2] has three different positive integers ranging from 1 题目描述:数组元素为 1\~n 的整数,要求构建数组,使得相邻元素的差值不相同的个数为 k。 -让前 k+1 个元素构建出 k 个不相同的差值,序列为:1 k+1 2 k 3 k-1 ... k/2 k/2+1. +让前 k+1 个元素构建出 k 个不相同的差值,序列为:1 k+1 2 k 3 k-1 ... k/2 k/2+1,相邻差值依次为 k、k-1、……、1。之后的元素按 k+2、k+3、……、n 递增排列,内部的差值都是 1;前一段的最后一个元素在 k/2 附近,与 k+2 的差值不超过 k,也已经出现过,因此不会产生新的差值。例如 n = 5、k = 3 时得到 [1, 4, 2, 3, 5],差值为 3、2、1、2,衔接处 3 → 5 的差值 2 已经出现过。 ```java public int[] constructArray(int n, int k) { @@ -317,6 +331,8 @@ Output: 6 题目描述:数组的度定义为元素出现的最高频率,例如上面的数组度为 3。要求找到一个最小的子数组,这个子数组的度和原数组一样。 +子数组的度要和原数组一样,就要包含某个出现次数最多的元素的全部出现位置,最短的就是从它第一次出现到最后一次出现的一段。记录每个元素的出现次数、第一次和最后一次出现的位置,在出现次数最多的元素中取这段长度的最小值。上面的数组中 2 出现 3 次,位置 1 到 6,答案为 6。 + ```java public int findShortestSubArray(int[] nums) { Map numsCnt = new HashMap<>(); @@ -403,6 +419,8 @@ S[0] = {A[0], A[5], A[6], A[2]} = {5, 6, 2, 0} 题目描述:S[i] 表示一个集合,集合的第一个元素是 A[i],第二个元素是 A[A[i]],如此嵌套下去。求最大的 S[i]。 +数组是 0 \~ n-1 的一个排列,每个下标只被一个元素指向,所以 i → A[i] 把数组分成若干个互不相交的环,S[i] 就是 i 所在的环。同一个环上的起点得到的集合大小相同,遍历过的位置标记为 -1 后不再访问,每个元素只访问一次,时间复杂度为 O(N)。 + ```java public int arrayNesting(int[] nums) { int max = 0; @@ -435,7 +453,9 @@ We can split into two chunks, such as [1, 0], [2, 3, 4]. However, splitting into [1, 0], [2], [3], [4] is the highest number of chunks possible. ``` -题目描述:分隔数组,使得对每部分排序后数组就为有序。 +题目描述:arr 是 0 \~ n-1 的一个排列,把它分成尽量多的块,使得对每块分别排序后整个数组有序。 + +前 i + 1 个元素能单独成为若干块,当且仅当它们恰好是 0 \~ i,也就是前缀的最大值等于 i。从左往右维护前缀最大值 right,每遇到 right == i 就可以切一刀。例如 [1, 0, 2, 3, 4] 在下标 1、2、3、4 处都满足条件,答案为 4。 ```java public int maxChunksToSorted(int[] arr) { @@ -529,3 +549,7 @@ private void swap(int[] nums, int i, int j) { nums[j] = t; } ``` + +## 参考资料 + +- [LeetCode 题库](https://leetcode.com/problemset/) diff --git a/notes/pics/lc-array-dup-cycle.png b/notes/pics/lc-array-dup-cycle.png new file mode 100644 index 0000000000000000000000000000000000000000..377baffa5883aa73a6f070032dca33fb24743213 GIT binary patch literal 154369 zcmYIwbzGF&_w~>n(hW)}-5sKU(xB2vmxv&UNOveLjWh^|fRu4>=6TN9d+oK>-sgFvseX?Dmj)MsKoBV1mw$jjV8D-P8rZ1tA6&g9X86xF z7X>{RT{9Oe=VxZlPZ4+B?+Wnoi$x_EWd!akSN2_vD?rt#gL&_RS~nzHCj`Zk@esU;kh)LQAaR|HBd$QD^K}IWDgi&!SW? 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