From cf14ed112866261c7aa061d68aa76527e929df54 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:34 +0800 Subject: [PATCH] =?UTF-8?q?Update=20Leetcode=20=E9=A2=98=E8=A7=A3=20-=20?= =?UTF-8?q?=E5=93=88=E5=B8=8C=E8=A1=A8.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 更新最长连续序列的 HashSet 实现与说明,为和为 K 的子数组补充前缀和注意要点并新增配图,调整两数之和等题目的解题说明并补充参考资料。 --- notes/Leetcode 题解 - 哈希表.md | 69 ++++++++++++++++-------------- notes/pics/lc-hash-prefix-sum.png | Bin 0 -> 124761 bytes 2 files changed, 37 insertions(+), 32 deletions(-) create mode 100644 notes/pics/lc-hash-prefix-sum.png diff --git a/notes/Leetcode 题解 - 哈希表.md b/notes/Leetcode 题解 - 哈希表.md index bd05c61b..9e0f8f90 100644 --- a/notes/Leetcode 题解 - 哈希表.md +++ b/notes/Leetcode 题解 - 哈希表.md @@ -6,14 +6,15 @@ * [3. 最长和谐序列](#3-最长和谐序列) * [4. 最长连续序列](#4-最长连续序列) * [5. 和为 K 的子数组](#5-和为-k-的子数组) + * [参考资料](#参考资料) -哈希表使用 O(N) 空间复杂度存储数据,并且以 O(1) 时间复杂度求解问题。 +哈希表使用 O(N) 空间复杂度存储数据,查找、插入的平均时间复杂度为 O(1),用空间换时间。 -- Java 中的 **HashSet** 用于存储一个集合,可以查找元素是否在集合中。如果元素有穷,并且范围不大,那么可以用一个布尔数组来存储一个元素是否存在。例如对于只有小写字符的元素,就可以用一个长度为 26 的布尔数组来存储一个字符集合,使得空间复杂度降低为 O(1)。 +- Java 中的 HashSet 用于存储一个集合,可以查找元素是否在集合中。如果元素有穷,并且范围不大,那么可以用一个布尔数组来存储一个元素是否存在。例如对于只有小写字符的元素,就可以用一个长度为 26 的布尔数组来存储一个字符集合,使得空间复杂度降低为 O(1)。 -- Java 中的 **HashMap** 主要用于映射关系,从而把两个元素联系起来。HashMap 也可以用来对元素进行计数统计,此时键为元素,值为计数。和 HashSet 类似,如果元素有穷并且范围不大,可以用整型数组来进行统计。在对一个内容进行压缩或者其它转换时,利用 HashMap 可以把原始内容和转换后的内容联系起来。例如在一个简化 url 的系统中(535\. Encode and Decode TinyURL (Medium),[Leetcode](https://leetcode.com/problems/encode-and-decode-tinyurl/description/) / [力扣](https://leetcode-cn.com/problems/encode-and-decode-tinyurl/description/)),利用 HashMap 就可以存储精简后的 url 到原始 url 的映射,使得不仅可以显示简化的 url,也可以根据简化的 url 得到原始 url 从而定位到正确的资源。 +- Java 中的 HashMap 主要用于映射关系,从而把两个元素联系起来。HashMap 也可以用来对元素进行计数统计,此时键为元素,值为计数。和 HashSet 类似,如果元素有穷并且范围不大,可以用整型数组来进行统计。在对一个内容进行压缩或者其它转换时,利用 HashMap 可以把原始内容和转换后的内容联系起来。例如在一个简化 url 的系统中(535\. Encode and Decode TinyURL (Medium),[Leetcode](https://leetcode.com/problems/encode-and-decode-tinyurl/description/) / [力扣](https://leetcode-cn.com/problems/encode-and-decode-tinyurl/description/)),利用 HashMap 就可以存储精简后的 url 到原始 url 的映射,使得不仅可以显示简化的 url,也可以根据简化的 url 得到原始 url 从而定位到正确的资源。 ## 1. 数组中两个数的和为给定值 @@ -22,7 +23,7 @@ [Leetcode](https://leetcode.com/problems/two-sum/description/) / [力扣](https://leetcode-cn.com/problems/two-sum/description/) -可以先对数组进行排序,然后使用双指针方法或者二分查找方法。这样做的时间复杂度为 O(NlogN),空间复杂度为 O(1)。 +可以先对数组进行排序,然后使用双指针方法或者二分查找方法,时间复杂度为 O(NlogN)。需要注意的是,题目要求返回原数组的下标,排序会打乱下标,因此要把元素和原下标一起排序,空间复杂度为 O(N)。 用 HashMap 存储数组元素和索引的映射,在访问到 nums[i] 时,判断 HashMap 中是否存在 target - nums[i],如果存在说明 target - nums[i] 所在的索引和 i 就是要找的两个数。该方法的时间复杂度为 O(N),空间复杂度为 O(N),使用空间来换取时间。 @@ -68,7 +69,7 @@ Output: 5 Explanation: The longest harmonious subsequence is [3,2,2,2,3]. ``` -和谐序列中最大数和最小数之差正好为 1,应该注意的是序列的元素不一定是数组的连续元素。 +和谐序列中最大数和最小数之差正好为 1,需要注意的是序列的元素不一定是数组的连续元素。统计每个数出现的次数,对每个 num,只有 num + 1 也存在时,两者的次数之和才是以它们为最小、最大值的和谐序列长度。 ```java public int findLHS(int[] nums) { @@ -97,42 +98,33 @@ Given [100, 4, 200, 1, 3, 2], The longest consecutive elements sequence is [1, 2, 3, 4]. Return its length: 4. ``` -要求以 O(N) 的时间复杂度求解。 +要求以 O(N) 的时间复杂度求解,因此不能排序。 + +把所有数放进 HashSet,只从每段连续序列的起点开始向后数:num - 1 不在集合中时,num 是起点,依次查找 num + 1、num + 2……直到断开。例如 4 不是起点(3 在集合中),跳过;1 是起点,向后数到 4,长度为 4。每个数只会在它所在序列的起点被数到一次,总的时间复杂度为 O(N)。 ```java public int longestConsecutive(int[] nums) { - Map countForNum = new HashMap<>(); + Set set = new HashSet<>(); for (int num : nums) { - countForNum.put(num, 1); + set.add(num); } - for (int num : nums) { - forward(countForNum, num); + int longest = 0; + for (int num : set) { + if (set.contains(num - 1)) { + continue; // num 不是一段连续序列的起点 + } + int end = num; + while (set.contains(end + 1)) { + end++; + } + longest = Math.max(longest, end - num + 1); } - return maxCount(countForNum); -} - -private int forward(Map countForNum, int num) { - if (!countForNum.containsKey(num)) { - return 0; - } - int cnt = countForNum.get(num); - if (cnt > 1) { - return cnt; - } - cnt = forward(countForNum, num + 1) + 1; - countForNum.put(num, cnt); - return cnt; -} - -private int maxCount(Map countForNum) { - int max = 0; - for (int num : countForNum.keySet()) { - max = Math.max(max, countForNum.get(num)); - } - return max; + return longest; } ``` +需要注意的是,遍历的是 set 而不是 nums:nums 中同一个起点重复出现很多次时,遍历 nums 会把同一段序列重复数很多遍。 + ## 5. 和为 K 的子数组 560\. Subarray Sum Equals K (Medium) @@ -148,6 +140,15 @@ Output: 2 用 sum 表示从数组开头到当前位置的前缀和,以当前位置结尾、和为 k 的子数组,对应前面某个位置的前缀和为 sum - k。遍历时用哈希表记录每个前缀和出现的次数即可。数组中有负数,窗口变大时和不一定变大,因此不能用滑动窗口。 +有两处容易写错: + +- 开始时放入前缀和 0、次数 1,表示数组开始之前的空前缀,这样从下标 0 开始的子数组也能被统计; +- 先查询 sum - k、再登记当前的 sum,保证配对的是更早的前缀,否则 k = 0 时当前前缀会和自己配对。 + +哈希表记录的是次数而不是是否出现,因为同一个前缀和可能出现多次,每一次都对应一个不同的子数组。例如 nums = [1, -1, 0]、k = 0: + +

+ ```java public int subarraySum(int[] nums, int k) { Map cnt = new HashMap<>(); @@ -161,3 +162,7 @@ public int subarraySum(int[] nums, int k) { return ret; } ``` + +## 参考资料 + +- [LeetCode 题库](https://leetcode.com/problemset/) diff --git a/notes/pics/lc-hash-prefix-sum.png b/notes/pics/lc-hash-prefix-sum.png new file mode 100644 index 0000000000000000000000000000000000000000..78be46094668d65fed6fbf2a5a366bf238d5fcce GIT binary patch literal 124761 zcmXV2cOcaN|39LkkgXy`GDC&TBf0Fo%Lqxz-dlsLkR9P{Ix;JpvPZcjE3!FzkHg{j zywC63AD?{c#{2zxKgVM{pM`3wD^OBgq(C4LluC;7+6V->CIUg4a+(zW z6=mpZVD4(=Y-jHL9C6R<-YubnsfDHFZm_vR^UrenA%V?j6E>_Rnq; z`@!Yzq$E}EiM@dFJL2LOVp3E6^!*YZ4~xdrn+#Akt?l_@FpOU1xi(+z4t$YKLaM#j z*il-#dhu3CaG7ybU1hE&75pk%^eC;zMql~6gwA!9T~neUBaOLMrS8BEKZph1e6G4%!;$LKv*ha|o=P#- zlq`b79mW^S_`Aw%lXLmHx=2XzR*v|lZy%agcU?|~?$Y7nxS!$CtJgA_`H0VnegH>J zM%p-$cugr`rUds1i`(4uHN2^*FUsw}`<3jmkv@IPb7OcVcU?s>27Vbouu9G~XZCL} zOR4jX_7h(J;(OiaP$ZK4+vOKcY^`ow3a=Ek=mjXPx_-Om*(Cc?A9v+)Q4kP_^ptnk 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