【Leetcode 做題學演算法週刊】第三期
阿新 • • 發佈：2019-11-13
首發於微信公眾號《前端成長記》，寫於 2019.11.13
背景
本文記錄刷題過程中的整個思考過程，以供參考。主要內容涵蓋：
- 題目分析設想
- 編寫程式碼驗證
- 查閱他人解法
- 思考總結
目錄
- 35.搜尋插入位置
- 38.報數
- 53.最大子序和
- 58.最後一個單詞的長度
- 66.加一
Easy
35.搜尋插入位置
題目地址
題目描述
給定一個排序陣列和一個目標值，在陣列中找到目標值，並返回其索引。如果目標值不存在於陣列中，返回它將會被按順序插入的位置。
你可以假設陣列中無重複元素。
示例：
輸入: [1,3,5,6], 5 輸出: 2 輸入: [1,3,5,6], 2 輸出: 1 輸入: [1,3,5,6], 7 輸出: 4 輸入: [1,3,5,6], 0 輸出: 0
題目分析設想
這道題目有點明顯，題幹說明了是排序陣列，重點是排序陣列，所以很明顯的第一反應會使用二分法來解題。同時可以注意一下，陣列中無重複元素。所以這道題我就按兩個方案來作答：
- 暴力法，直接遍歷
- 二分法，可以理解成不斷折半排除不可能
編寫程式碼驗證
Ⅰ.暴力法
程式碼：
/** * @param {number[]} nums * @param {number} target * @return {number} */ var searchInsert = function(nums, target) { if (nums.length === 0 || nums[0] > target) return 0; if(nums[nums.length - 1] < target) return nums.length; for(let i = 0; i < nums.length; i++) { if(nums[i] >= target) return i } };
結果：
- 62/62 cases passed (60 ms)
- Your runtime beats 92.48 % of javascript submissions
- Your memory usage beats 63.22 % of javascript submissions (33.8 MB)
- 時間複雜度
O(n)
Ⅱ.二分法
程式碼：
/** * @param {number[]} nums * @param {number} target * @return {number} */ var searchInsert = function(nums, target) { if (nums.length === 0 || nums[0] > target) return 0; if(nums[nums.length - 1] < target) return nums.length; let left = 0; // 起點 let right = nums.length - 1; // 終點 while(left < right) { // 零填充右位移，使用位運算避免溢位，大部分情況下等於 (left + right / 2) let i = parseInt((left + right) >>> 1) // 這裡選擇取左 if (nums[i] < target) { // 中位數小於目標值 left = i + 1 // 排除中位數左側 } else { right = i // 排除中位數右側 } } return left };
結果：
- 62/62 cases passed (52 ms)
- Your runtime beats 99.31 % of javascript submissions
- Your memory usage beats 61.31 % of javascript submissions (33.8 MB)
- 時間複雜度
O(log2(n))
查閱他人解法
基本上這道題就是針對二分法進行考察的，所以沒有看到其他特別的解法。
思考總結
看見排序陣列，查詢下標，那麼就可以果斷選擇二分法啦。
38.報數
題目地址
題目描述
報數序列是一個整數序列，按照其中的整數的順序進行報數，得到下一個數。其前五項如下：
1. 1
2. 11
3. 21
4. 1211
5. 1112211 被讀作 "one 1" ("一個一"),即 11。
11 被讀作 "two 1s" ("兩個一"),即 21。
21 被讀作 "one 2", "one 1" （"一個二" , "一個一") , 即 1211。
給定一個正整數 n（1 ≤ n ≤ 30），輸出報數序列的第 n 項。
注意：整數順序將表示為一個字串。
示例:
輸入: 1
輸出: "1"
輸入: 4
輸出: "1211"題目分析設想
這道題目有點繞，其實我們只看右側項就可以，每次都是讀上一次項。報數的規則實際上就是相同連續數字合併後進行每位的報數。最簡單的想法是直接使用正則替換就可以了。當然也可以從遞迴和遍歷的方式來作答，我們分別來看看。
- 正則法，替換相同連續數字為
長度 + 數字本身 - 遞迴法，不斷轉換成
n-1求解 - 遍歷法，不斷轉換成
n+1求解
編寫程式碼驗證
Ⅰ.正則法
程式碼：
/**
* @param {number} n
* @return {string}
*/
var countAndSay = function(n) {
let str = '1'
for(let i = 1; i < n; i++) {
// 匹配項長度+第一位即為讀數
str = str.replace(/(\d)\1*/g, (match) => (`${match.length}${match.charAt(0)}`))
}
return str
};結果：
- 18/18 cases passed (56 ms)
- Your runtime beats 98.81 % of javascript submissions
- Your memory usage beats 32.53 % of javascript submissions (35.6 MB)
- 時間複雜度
O(n)
Ⅱ.遞迴法
程式碼：
/**
* @param {number} n
* @return {string}
*/
var countAndSay = function(n) {
if (n === 1) return '1'
debugger
let str = countAndSay(n - 1)
let item = str.charAt(0)
let count = 0 // 計數器
let res = ''
for(let i = 0; i < str.length; i++) {
if(str.charAt(i) === item) {
count++
} else {
res += `${count}${item}`
item = str.charAt(i)
count = 1
}
if (i === str.length - 1) { // 最後一位，需要取數
res += `${count}${item}`
}
}
return res
};結果：
- 18/18 cases passed (64 ms)
- Your runtime beats 92.23 % of javascript submissions
- Your memory usage beats 28.23 % of javascript submissions (35.7 MB)
- 時間複雜度
O(n^2)
Ⅲ.遍歷法
程式碼：
/**
* @param {number} n
* @return {string}
*/
var countAndSay = function(n) {
let str = '1'
for(let i = 1; i < n; i++) {
str = countEach(str)
}
function countEach(str) {
let count = 0
let res = ''
for(let i = 0; i < str.length; i++) {
if(i === 0 || str.charAt(i) === str.charAt(i - 1)) {
count++
} else {
res += `${count}${str.charAt(i - 1)}`
count = 1
}
if (i === str.length - 1) {
res += `${count}${str.charAt(i)}`
}
}
return res
}
return str
};結果：
- 18/18 cases passed (60 ms)
- Your runtime beats 96.98 % of javascript submissions
- Your memory usage beats 41.69 % of javascript submissions (35.5 MB)
- 時間複雜度
O(n^2)
查閱他人解法
這裡看到一個開懷一笑的解法，直接字典法，缺點很明顯，但是當前情況下確實是最快的。
Ⅰ.正則法
程式碼：
/**
* @param {number} n
* @return {string}
*/
var countAndSay = function(n) {
const map = {
1:"1",
2:"11",
3:"21",
4:"1211",
5:"111221",
6:"312211",
7:"13112221",
8:"1113213211",
9:"31131211131221",
10:"13211311123113112211",
11:"11131221133112132113212221",
12:"3113112221232112111312211312113211",
13:"1321132132111213122112311311222113111221131221",
14:"11131221131211131231121113112221121321132132211331222113112211",
15:"311311222113111231131112132112311321322112111312211312111322212311322113212221",
16:"132113213221133112132113311211131221121321131211132221123113112221131112311332111213211322211312113211",
17:"11131221131211132221232112111312212321123113112221121113122113111231133221121321132132211331121321231231121113122113322113111221131221",
18:"31131122211311123113321112131221123113112211121312211213211321322112311311222113311213212322211211131221131211132221232112111312111213111213211231131122212322211331222113112211",
19:"1321132132211331121321231231121113112221121321132122311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112111331121113122112132113213211121332212311322113212221",
20:"11131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113121113123112112322111213211322211312113211",
21:"311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311122122111312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221131112311311121321122112132231121113122113322113111221131221",
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
24:"3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211132221121311121312211213211312111322211213211321322113311213212322211231131122211311123113321112131221123113112211121312211213211321222113222112132113223113112221121113122113121113123112112322111213211322211312113211",
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
26:"1113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123211211131211121311121321123113111231131122112213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122113221122112133221121113122113121113222123211211131211121311121321123113213221121113122113121113222113221113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211",
27:"31131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322123211211131211121332211231131122211311122122111312211213211312111322211231131122211311123113322112111331121113112221121113122113111231133221121113122113121113222123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221123113112221131112311332111213122112311311123112111331121113122112132113311213211321222122111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311123113322113223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331221122311311222112111312211311123113322112132113213221133122211332111213112221133211322112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122211331121321232221121113122113121122132112311321322112111312211312111322211213111213122112132113121113222112132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212321121113121112133221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213212312311211131122211213211331121321122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311222113111221221113122112132113121113222112132113213221133122211332111213322112132113213221132231131122211311123113322112111312211312111322212321121113122123211231131122113221123113221113122112132113213211121332212311322113212221",
28:"13211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221232112111312211312113211223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321322113311213212322211322132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212311322123123112111321322123122113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132132211331221122311311222112111312211311123113322112111312211312111322212311322123123112112322211211131221131211132221132213211321322113311213212322211231131122211311123113321112131221123113112211121312211213211321222113222112132113223113112221121113122113121113123112112322111213211322211312113211",
29:"11131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211132221121311121312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221231122212213211321322112311311222113311213212322211211131221131211132221232112111312111213322112131112131221121321131211132221121321132132212321121113121112133221121321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122111213122112311311222113111221131221221321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311222112111331121113112221121113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212321121113121112133221132211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112132132112211131221131211132221121321132132212321121113121112133221123113112221131112311332111213211322111213111213211231131211132211121311222113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131211131221223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112211213322112312321123113213221123113112221133112132123222112311311222113111231132231121113112221121321133112132112211213322112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212311222122132113213221123113112221133112132123222112311311222113111231133211121321132211121311121321122112133221123113112221131112311332211322111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221",
30:"3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321223112111311222112132113213221133122211311221122111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331222113321112131122211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112112322211322311311222113111231133211121312211231131112311211232221121113122113121113222123211211131221132211131221121321131211132221123113112211121312211231131122113221122112133221121321132132211331121321231231121113121113122122311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312211322311211133112111312211213211311123113223112111321322123122113222122211211232221121113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123112221221321132132211231131122211331121321232221121113122113121113222123211211131211121332211213111213122112132113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231131112311311221122132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132122311211131122211213211321222113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111312211322311211133112111312212221121123222112132113213221133112132123222113223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211"
}
return map[n]
};結果：
- 18/18 cases passed (56 ms)
- Your runtime beats 98.81 % of javascript submissions
- Your memory usage beats 98.5 % of javascript submissions (33.5 MB)
- 時間複雜度
O(1)
思考總結
總體而言，這道題用正則去解答十分簡單，考驗的點在正則的匹配這塊；當然遞迴或者遍歷也是常規思路；字典法純屬一樂。推薦使用正則來解答此題。
53.最大子序和
題目地址
題目描述
給定一個整數陣列 nums ，找到一個具有最大和的連續子陣列（子陣列最少包含一個元素），返回其最大和。
示例:
輸入: [-2,1,-3,4,-1,2,1,-5,4],
輸出: 6
解釋: 連續子陣列 [4,-1,2,1] 的和最大，為 6。進階:
如果你已經實現複雜度為 O(n) 的解法，嘗試使用更為精妙的分治法求解。
題目分析設想
這道題首先基本解法肯定是暴力的遍歷求解，直接遍歷找出最大區間。當然這裡我們也可以使用動態規劃來思考問題，列出動態和轉移方程式，等於求解 Max(d[0, i])。另外進階裡面提示分治法，分治法在之前有用過，我們也可以做為一個方向。所以大概有三種：
- 遍歷求解，直接遍歷算出各區間值
- 動態規劃問題，求解動態問題，找到每個動態區間的最大值
- 分治，不斷二分找區間內的最大子序和
注意一下，只要是尋找最大值最小值的，初始值需要定義為理論上的最大最小值。
編寫程式碼驗證
Ⅰ.遍歷求解
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
let res = Number.MIN_SAFE_INTEGER
for(let i = 0; i < nums.length; i++) {
let sum = 0
// 分別算出 i 開始的最大子序和
for(let j = i; j < nums.length; j++) {
sum += nums[j];
res = Math.max(res, sum)
}
}
return res
};結果：
- 202/202 cases passed (272 ms)
- Your runtime beats 7.61 % of javascript submissions
- Your memory usage beats 41.88 % of javascript submissions (35.1 MB)
- 時間複雜度
O(n^2)
Ⅱ.動態規劃
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
let res = dp = nums[0] // 初始值
for(let i = 1; i < nums.length; i++) {
dp = Math.max(dp + nums[i], nums[i]) // 動態取得最大值
res = Math.max(res, dp)
}
return res
};結果：
- 202/202 cases passed (68 ms)
- Your runtime beats 90.14 % of javascript submissions
- Your memory usage beats 45 % of javascript submissions (35.1 MB)
- 時間複雜度
O(n)
Ⅲ.分治
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
// 不斷分治
function countByDichotomy (start, end) {
// 儲存左側結果，右側結果，兩者更大值，以及兩者相加的值
// 解釋一下：最大子序列在左右兩區間內要麼過界要麼不過界。
// 如果不過界，則最大值為 Max(left, right)
// 如果過界，則最大為左區間到中間的最大值加中間到右區間的最大值
if (end === start) { // 陣列就一項
return {
lmax: nums[start], // 左半區間包含其右端點的最大子序和
rmax: nums[start], // 右半區間包含其左端點的最大子序和
sum: nums[start], // 總和
result: nums[start] // 區域內部的最大子序和
}
} else {
const mid = (start + end) >>> 1 // 這個取中位數寫法之前解釋過，避免溢位
const left = countByDichotomy(start, mid) // 左區間中計算結果
const right = countByDichotomy(mid + 1, end) // 右區間中計算結果
return {
lmax: Math.max(left.lmax, left.sum + right.lmax),
rmax: Math.max(right.rmax, left.rmax + right.sum),
sum: left.sum + right.sum,
result: Math.max(left.rmax + right.lmax, Math.max(left.result, right.result))
}
}
}
return countByDichotomy(0, nums.length - 1).result;
};結果：
- 202/202 cases passed (60 ms)
- Your runtime beats 97.89 % of javascript submissions
- Your memory usage beats 5.01 % of javascript submissions (36.7 MB)
- 時間複雜度
O(n)
查閱他人解法
查閱題解的過程中發現了以下幾種有意思的思路：
- 動態規劃，使用增益的思路。其實上面我們寫的動態規劃是一樣的
- 貪心法，嘗試多加一位，取較大值
- 分治中使用貪心法求區間
Ⅰ.動態規劃
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
let res = nums[0]
let sum = nums[0] // 增益
for(let i = 1; i < nums.length; i++) {
if (sum > 0) { // 正向增益， sum 保留並加上當前遍歷數字
sum += nums[i]
} else { // sum 更新為當前遍歷數字
sum = nums[i]
}
res = Math.max(res, sum)
}
return res
};結果：
- 202/202 cases passed (60 ms)
- Your runtime beats 97.89 % of javascript submissions
- Your memory usage beats 47.5 % of javascript submissions (35.1 MB)
- 時間複雜度
O(n)
Ⅱ.貪心法
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
let res = Number.MIN_SAFE_INTEGER // 初始值
let sum = 0
for(let i = 0; i < nums.length; i++) {
sum += nums[i]
res = Math.max(res, sum)
if (sum < 0) { // 重新開始找子序串
sum = 0;
}
}
return res
};結果：
- 202/202 cases passed (68 ms)
- Your runtime beats 90.14 % of javascript submissions
- Your memory usage beats 45 % of javascript submissions (35.1 MB)
- 時間複雜度
O(n)
Ⅲ.分治中使用貪心法求區間
程式碼：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
// 獲取跨邊界的和
function getMaxCross (start, mid, end) {
let leftRes = Number.MIN_SAFE_INTEGER
let leftSum = 0
for(let i = mid; i >= start; i--) {
leftSum += nums[i]
leftRes = Math.max(leftRes, leftSum)
}
let rightRes = Number.MIN_SAFE_INTEGER
let rightSum = 0
for(let i = mid + 1; i <= end; i++) {
rightSum += nums[i]
rightRes = Math.max(rightRes, rightSum)
}
return leftRes + rightRes
}
function countByDichotomy (start, end) {
if (start === end) {
return nums[start]
} else {
const mid = (start + end) >>> 1
const leftSum = countByDichotomy(start, mid)
const rightSum = countByDichotomy(mid + 1, end)
const midSum = getMaxCross(start, mid, end)
// 三者比較最大的就為最大子序和
return Math.max(leftSum, rightSum, midSum)
}
}
return countByDichotomy(0, nums.length - 1)
};結果：
- 202/202 cases passed (72 ms)
- Your runtime beats 80.56 % of javascript submissions
- Your memory usage beats 49.38 % of javascript submissions (35.1 MB)
- 時間複雜度
O(nlog(n))
思考總結
個人認為動態規劃在這套題裡面解題思路清晰，貪心法也可以理解為基於遍歷基礎上做的延伸，而分治法需要畫圖加以理解。一般看到這種最大最長的題目，基本上就可以用動態規劃問題來嘗試作答了。
58.最後一個單詞的長度
題目地址
題目描述
給定一個僅包含大小寫字母和空格 ' ' 的字串，返回其最後一個單詞的長度。
如果不存在最後一個單詞，請返回 0 。
說明：一個單詞是指由字母組成，但不包含任何空格的字串。
示例：
輸入: "Hello World"
輸出: 5題目分析設想
這道題看上去像是一道字串題，我們可以從以下幾個方面來嘗試作答：
- 遍歷，從末尾開始，效率高
- lastIndexOf，直接找空格
- 正則
- split
編寫程式碼驗證
Ⅰ.遍歷
程式碼：
/**
* @param {string} s
* @return {number}
*/
var lengthOfLastWord = function(s) {
if(!s.length) return 0
let i = s.length - 1
while(i >= 0 && s.charAt(i) === ' ') {
i--
}
if(i < 0) return 0 // 全是空格
let j = i
while(j >= 0 && s.charAt(j) != ' ') {
j--
}
return i - j
};結果：
- 59/59 cases passed (64 ms)
- Your runtime beats 81.14 % of javascript submissions
- Your memory usage beats 29.72 % of javascript submissions (33.8 MB)
- 時間複雜度
O(n)
Ⅱ.lastIndexOf
程式碼：
/**
* @param {string} s
* @return {number}
*/
var lengthOfLastWord = function(s) {
if(!s.length) return 0
s = s.trim()
const idx = s.lastIndexOf(' ')
return idx === -1 ? s.length : s.length - 1 - idx
};結果：
- 59/59 cases passed (48 ms)
- Your runtime beats 99.48 % of javascript submissions
- Your memory usage beats 36.52 % of javascript submissions (33.7 MB)
- 時間複雜度
O(1)
Ⅲ.正則
程式碼：
/**
* @param {string} s
* @return {number}
*/
var lengthOfLastWord = function(s) {
if(!s.length) return 0
const match = s.match(/([a-zA-Z]+)\s*$/)
let res = 0
if (match) {
res = match.pop()
return res.length
}
return res
};結果：
- 59/59 cases passed (80 ms)
- Your runtime beats 26.65 % of javascript submissions
- Your memory usage beats 5.95 % of javascript submissions (34.2 MB)
- 時間複雜度
O(1)
Ⅳ.split
程式碼：
/**
* @param {string} s
* @return {number}
*/
var lengthOfLastWord = function(s) {
if(!s.length) return 0
s = s.trim()
const arr = s.split(' ')
if (arr.length) {
let str = arr.pop()
return str.length
} else {
return 0
}
};結果：
- 59/59 cases passed (60 ms)
- Your runtime beats 90.57 % of javascript submissions
- Your memory usage beats 13.8 % of javascript submissions (34 MB)
- 時間複雜度
O(1)
查閱他人解法
沒有在題解中看到什麼特別的解法，大部分都是基於類庫解的，比如 Javascript 中 String 和 Array 的方法。或者是遍歷實現的。
思考總結
直到現在也沒有弄明白這道題的考察點在哪裡？不過我建議感興趣的同學，可以自己拓展實現 lastIndexOf ，參考 上一期 28題的數十種解法，應該能有不小收穫。
66.加一
題目地址
題目描述
給定一個由整陣列成的非空陣列所表示的非負整數，在該數的基礎上加一。
最高位數字存放在陣列的首位， 陣列中每個元素只儲存單個數字。
你可以假設除了整數 0 之外，這個整數不會以零開頭。
示例：
輸入: [1,2,3]
輸出: [1,2,4]
解釋: 輸入陣列表示數字 123。
輸入: [4,3,2,1]
輸出: [4,3,2,2]
解釋: 輸入陣列表示數字 4321。題目分析設想
這道題我有兩個大方向，一是陣列遍歷進行求解，另外一種是陣列轉數字再處理。但是轉數字可能會溢位，所以就只想到從遍歷的角度來作答。
- 遍歷，從後往前遍歷找到不為9的項，後面填0就可以了
編寫程式碼驗證
Ⅰ.遍歷
程式碼：
/**
* @param {number[]} digits
* @return {number[]}
*/
var plusOne = function(digits) {
for(let i = digits.length - 1; i >= 0; i--) {
// 找不到不為9的數，直接加1輸出就可以了
if(digits[i] !== 9) {
digits[i]++
return digits
} else {
digits[i] = 0
}
}
digits.unshift(1)
return digits
};結果：
- 109/109 cases passed (60 ms)
- Your runtime beats 93.72 % of javascript submissions
- Your memory usage beats 26.35 % of javascript submissions (33.8 MB)
- 時間複雜度
O(n)
查閱他人解法
發現思路基本都是遍歷，但是具體實現會有些差距，這裡只列舉一個最簡單的。
Ⅰ.遍歷
程式碼：
/**
* @param {number[]} digits
* @return {number[]}
*/
var plusOne = function(digits) {
for(let i = digits.length - 1; i >= 0; i--) {
digits[i]++
// 取10的餘數，做了賦值操作，為0就繼續進位
digits[i] %= 10
if(digits[i] !== 0) {
return digits
}
}
digits.unshift(1)
return digits
};結果：
- 109/109 cases passed (64 ms)
- Your runtime beats 85.29 % of javascript submissions
- Your memory usage beats 94.34 % of javascript submissions (33.4 MB)
- 時間複雜度
O(n)
思考總結
這道題可能大眾的想法會轉成數字再處理，但是做數字運算的時候，千萬要記住考慮溢位的問題。另外因為是加1，所以倒序遍歷就可以了。至於是判斷末位為9還是對10取餘，我覺得都是一個很好理解的思路，也避免了程式碼的繁瑣。
（完）
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