From 480d256d26e790041d07d694da583c70a86d9edc Mon Sep 17 00:00:00 2001 From: Chiayi Date: Tue, 25 Jan 2022 11:31:48 +0800 Subject: [PATCH] problem: 0128 longest consecutive sequence --- .../0128 Longest Consecutive Sequence.md | 199 ++++++++++++++++++ .../Untitled 1.png | Bin 0 -> 72969 bytes .../Untitled 2.png | Bin 0 -> 71666 bytes .../Untitled.png | Bin 0 -> 25702 bytes 4 files changed, 199 insertions(+) create mode 100644 0128 Longest Consecutive Sequence/0128 Longest Consecutive Sequence.md create mode 100644 0128 Longest Consecutive Sequence/Untitled 1.png create mode 100644 0128 Longest Consecutive Sequence/Untitled 2.png create mode 100644 0128 Longest Consecutive Sequence/Untitled.png diff --git a/0128 Longest Consecutive Sequence/0128 Longest Consecutive Sequence.md b/0128 Longest Consecutive Sequence/0128 Longest Consecutive Sequence.md new file mode 100644 index 0000000..9069970 --- /dev/null +++ b/0128 Longest Consecutive Sequence/0128 Longest Consecutive Sequence.md @@ -0,0 +1,199 @@ +# 0128. Longest Consecutive Sequence + +- Difficulty: medium +- Link: https://leetcode.com/problems/longest-consecutive-sequence/ +- Topics: Array-String + +# Clarification + +1. Check the inputs and outputs + - INPUT: List[int] + - OUTPUT: integer +2. Check the main goal + - time complexity $O(n)$ + +# Naive Solution + +> in $O(nlogn)$ +> + +### Thought Process + +1. sort Array +2. iterate + 1. if 下一個 = 當前 + 1:count ++ + 2. if 下一個 = 當前:往下一個 loop + 3. else: + - 比對 maxCount 與 count,更新 maxCount + - 將 count 重置回 1 +- Implement + + ```python + class Solution: + def longestConsecutive(self, nums: List[int]) -> int: + """ + 1. sort array + 2. iterate it + """ + + if len(nums) == 0: + return 0 + if len(nums) == 1: + return 1 + + nums.sort() + maxCount = 1 + count = 1 + for i in range(0, len(nums) - 1): + if nums[i+1] == nums[i]: + continue + if nums[i+1] == nums[i] + 1: + count += 1 + else: + count = 1 + if count > maxCount: + maxCount = count + return maxCount + ``` + + +### Complexity + +- Time complexity: $O(nlogn)$ + + ![Untitled](./Untitled.png) + +- Space complexity:$O(1)$ + +### Problems & Improvement + +- time complexity $O(n)$ + +# Improvement + +> $O(n)$ +> + +### Thought Process + +1. use a set +2. iterate the array + 1. 該個 num 是否為 sequence 的起始點 ( num - 1 是否在 set 之中) + + [為起始點 (num - 1不在set中)] + + - 紀錄新的 sequence + - 並向後尋找,後面的值是否在 set 之中 + + [非起始點 (num - 1 在 set 中)]: continue + +3. 計算每個 sequence 的數量 +4. 回傳最長者 +- Implement + + ```python + class Solution: + def longestConsecutive(self, nums: List[int]) -> int: + """ + 1. use a set + 2. iterate the array + 1. 該個 num 是否為 sequence 的起始點 ( num - 1 是否在 set 之中) + + [為起始點 (num - 1不在set中)] + + - 紀錄新的 sequence + - 並向後尋找,後面的值是否在 set 之中 + + [非起始點 (num - 1 在 set 中)]: continue + + 3. 計算每個 sequence 的數量 + 4. 回傳最長者 + """ + numSet = set(nums) + sequence = [] + for num in numSet: + if num - 1 in numSet: continue + newSequence = [] + newSequence.append(num) + nextNum = num + 1 + while nextNum in numSet: + newSequence.append(nextNum) + nextNum += 1 + sequence.append(newSequence) + + maxCount = 0 + for i in range(len(sequence)): + if len(sequence[i]) > maxCount: + maxCount = len(sequence[i]) + + return maxCount + ``` + + +### Complexity + +- Time complexity: $O(n)$ + + ![Untitled](./Untitled%201.png) + +- Space complexity: $O(n)$ + + ![Untitled](./Untitled%202.png) + + +# Check special cases, check error + +- 只需要記住數量,不需要記得實際數字,所以可以不用記 sequence + - Space Complexity: $O(1)$ + - implement + + ```python + class Solution: + def longestConsecutive(self, nums: List[int]) -> int: + """ + 1. use a set + 2. iterate the array + 1. 該個 num 是否為 sequence 的起始點 ( num - 1 是否在 set 之中) + + [為起始點 (num - 1不在set中)] + + - 並向後尋找,後面的值是否在 set 之中 + - 記住找到多長 + - 比較當前最長 + + [非起始點 (num - 1 在 set 中)]: continue + + 4. 回傳最長者 + """ + numSet = set(nums) + maxCount = 0 + for num in numSet: + if num - 1 in numSet: continue + nextNum = num + 1 + while nextNum in numSet: + nextNum += 1 + count = nextNum - num + maxCount = max(maxCount, count) + return maxCount + ``` + +- 算 nextNum 時就像是在加長度了,所以不用多一個變數去存 nextNum + + ```python + class Solution: + def longestConsecutive(self, nums: List[int]) -> int: + numSet = set(nums) + longest = 0 + for num in numSet: + if num - 1 in numSet: continue + length = 0 + while num + length in numSet: + length += 1 + longest = max(longest, length) + return longest + ``` + + +# Note + +- [Leetcode 128 - LONGEST CONSECUTIVE SEQUENCE](https://www.youtube.com/watch?v=P6RZZMu_maU) \ No newline at end of file diff --git a/0128 Longest Consecutive Sequence/Untitled 1.png b/0128 Longest Consecutive Sequence/Untitled 1.png new file mode 100644 index 0000000000000000000000000000000000000000..2e7f633b3a1747453daf6b32fd2a56f346babe30 GIT binary patch literal 72969 zcmd42bx<5p)F(Ow5(pYRSRlB&I|O$IcL}b+T|$rm0fM_b!{CDq79hC0ySuyXR-9LE%q@b@i3 zbu0oBXP{L6_mx|4eFb=xG%Ct0|Giv+MEL3{OO1-#q2@LC;egpqUc(??6oQQOIrzf@ zd8%COw2ej*l@1n2V>^EYLmcU|s|RKXvMQMVBQ>TtQm(!F`x35J^575RC7(9(M*#m$ z(CU&2{~(UU6%>mFyNL|~1r=;`3Q0=t-&vTy5@5Ghq4-Gm?{XziOVIc zi>BRh1N6>?Augvsm|Xyarb;RZR;?3%f}n$fM4K?=5uRkWD+J@BjXyXIX42 ztFOPaVc#R-XJ_lXR3i4Klq!R{W?Fo%C6p$65_M!EKc9$C6Pb!Gzr-igCR{B-Qilz6 z9fX5~Bu_`xkFuGN$5W=~n;;9EkfqDDaz`u6Ok+yl{VQ4o)k#joNlV&56;-9fqL0*A 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