【Leetcode 做题学算法周刊】第三期
McChen 人气:3首发于微信公众号《前端成长记》，写于 2019.11.13
背景
本文记录刷题过程中的整个思考过程，以供参考。主要内容涵盖：
- 题目分析设想
- 编写代码验证
- 查阅他人解法
- 思考总结
目录
- 35.搜索插入位置
- 38.报数
- 53.最大子序和
- 58.最后一个单词的长度
- 66.加一
Easy
35.搜索插入位置
题目地址
题目描述
给定一个排序数组和一个目标值，在数组中找到目标值，并返回其索引。如果目标值不存在于数组中，返回它将会被按顺序插入的位置。
你可以假设数组中无重复元素。
示例：
输入: [1,3,5,6], 5
输出: 2
输入: [1,3,5,6], 2
输出: 1
输入: [1,3,5,6], 7
输出: 4
输入: [1,3,5,6], 0
输出: 0题目分析设想
这道题目有点明显，题干说明了是排序数组，重点是排序数组，所以很明显的第一反应会使用二分法来解题。同时可以注意一下，数组中无重复元素。所以这道题我就按两个方案来作答：
- 暴力法，直接遍历
- 二分法，可以理解成不断折半排除不可能
编写代码验证
Ⅰ.暴力法
代码：
/**
* @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
}
};结果：
- 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)
- 时间复杂度
O(n)
Ⅱ.二分法
代码：
/**
* @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; // 起点
let right = nums.length - 1; // 终点
while(left < right) {
// 零填充右位移，使用位运算避免溢出，大部分情况下等于 (left + right / 2)
let i = parseInt((left + right) >>> 1) // 这里选择取左
if (nums[i] < target) { // 中位数小于目标值
left = i + 1 // 排除中位数左侧
} else {
right = i // 排除中位数右侧
}
}
return left
};结果：
- 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)
- 时间复杂度
O(log2(n))
查阅他人解法
基本上这道题就是针对二分法进行考察的，所以没有看到其他特别的解法。
思考总结
看见排序数组，查找下标，那么就可以果断选择二分法啦。
38.报数
题目地址
题目描述
报数序列是一个整数序列，按照其中的整数的顺序进行报数，得到下一个数。其前五项如下：
1. 1
2. 11
3. 21
4. 1211
5. 1112211 被读作 "one 1" ("一个一"),即 11。
11 被读作 "two 1s" ("两个一"),即 21。
21 被读作 "one 2", "one 1" （"一个二" , "一个一") , 即 1211。
给定一个正整数 n（1 ≤ n ≤ 30），输出报数序列的第 n 项。
注意：整数顺序将表示为一个字符串。
示例:
输入: 1
输出: "1"
输入: 4
输出: "1211"题目分析设想
这道题目有点绕，其实我们只看右侧项就可以，每次都是读上一次项。报数的规则实际上就是相同连续数字合并后进行每位的报数。最简单的想法是直接使用正则替换就可以了。当然也可以从递归和遍历的方式来作答，我们分别来看看。
- 正则法，替换相同连续数字为
长度 + 数字本身 - 递归法，不断转换成
n-1求解 - 遍历法，不断转换成
n+1求解
编写代码验证
Ⅰ.正则法
代码：
/**
* @param {number} n
* @return {string}
*/
var countAndSay = function(n) {
let str = '1'
for(let i = 1; i < n; i++) {
// 匹配项长度+第一位即为读数
str = str.replace(/(\d)\1*/g, (match) => (`${match.length}${match.charAt(0)}`))
}
return str
};结果：
- 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)
- 时间复杂度
O(n)
Ⅱ.递归法
代码：
/**
* @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 // 计数器
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) { // 最后一位，需要取数
res += `${count}${item}`
}
}
return res
};结果：
- 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)
- 时间复杂度
O(n^2)
Ⅲ.遍历法
代码：
/**
* @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
};结果：
- 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)
- 时间复杂度
O(n^2)
查阅他人解法
这里看到一个开怀一笑的解法，直接字典法，缺点很明显，但是当前情况下确实是最快的。
Ⅰ.正则法
代码：
/**
* @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]
};结果：
- 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)
- 时间复杂度
O(1)
思考总结
总体而言，这道题用正则去解答十分简单，考验的点在正则的匹配这块；当然递归或者遍历也是常规思路；字典法纯属一乐。推荐使用正则来解答此题。
53.最大子序和
题目地址
题目描述
给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。
示例:
输入: [-2,1,-3,4,-1,2,1,-5,4],
输出: 6
解释: 连续子数组 [4,-1,2,1] 的和最大，为 6。进阶:
如果你已经实现复杂度为 O(n) 的解法，尝试使用更为精妙的分治法求解。
题目分析设想
这道题首先基本解法肯定是暴力的遍历求解，直接遍历找出最大区间。当然这里我们也可以使用动态规划来思考问题，列出动态和转移方程式，等于求解 Max(d[0, i])。另外进阶里面提示分治法，分治法在之前有用过，我们也可以做为一个方向。所以大概有三种：
- 遍历求解，直接遍历算出各区间值
- 动态规划问题，求解动态问题，找到每个动态区间的最大值
- 分治，不断二分找区间内的最大子序和
注意一下，只要是寻找最大值最小值的，初始值需要定义为理论上的最大最小值。
编写代码验证
Ⅰ.遍历求解
代码：
/**
* @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
// 分别算出 i 开始的最大子序和
for(let j = i; j < nums.length; j++) {
sum += nums[j];
res = Math.max(res, sum)
}
}
return res
};结果：
- 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)
- 时间复杂度
O(n^2)
Ⅱ.动态规划
代码：
/**
* @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]) // 动态取得最大值
res = Math.max(res, dp)
}
return res
};结果：
- 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)
- 时间复杂度
O(n)
Ⅲ.分治
代码：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
// 不断分治
function countByDichotomy (start, end) {
// 存储左侧结果，右侧结果，两者更大值，以及两者相加的值
// 解释一下：最大子序列在左右两区间内要么过界要么不过界。
// 如果不过界，则最大值为 Max(left, right)
// 如果过界，则最大为左区间到中间的最大值加中间到右区间的最大值
if (end === start) { // 数组就一项
return {
lmax: nums[start], // 左半区间包含其右端点的最大子序和
rmax: nums[start], // 右半区间包含其左端点的最大子序和
sum: nums[start], // 总和
result: nums[start] // 区域内部的最大子序和
}
} else {
const mid = (start + end) >>> 1 // 这个取中位数写法之前解释过，避免溢出
const left = countByDichotomy(start, mid) // 左区间中计算结果
const right = countByDichotomy(mid + 1, end) // 右区间中计算结果
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;
};结果：
- 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)
- 时间复杂度
O(n)
查阅他人解法
查阅题解的过程中发现了以下几种有意思的思路：
- 动态规划，使用增益的思路。其实上面我们写的动态规划是一样的
- 贪心法，尝试多加一位，取较大值
- 分治中使用贪心法求区间
Ⅰ.动态规划
代码：
/**
* @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 保留并加上当前遍历数字
sum += nums[i]
} else { // sum 更新为当前遍历数字
sum = nums[i]
}
res = Math.max(res, sum)
}
return res
};结果：
- 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)
- 时间复杂度
O(n)
Ⅱ.贪心法
代码：
/**
* @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) { // 重新开始找子序串
sum = 0;
}
}
return res
};结果：
- 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)
- 时间复杂度
O(n)
Ⅲ.分治中使用贪心法求区间
代码：
/**
* @param {number[]} nums
* @return {number}
*/
var maxSubArray = function(nums) {
// 获取跨边界的和
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)
// 三者比较最大的就为最大子序和
return Math.max(leftSum, rightSum, midSum)
}
}
return countByDichotomy(0, nums.length - 1)
};结果：
- 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)
- 时间复杂度
O(nlog(n))
思考总结
个人认为动态规划在这套题里面解题思路清晰，贪心法也可以理解为基于遍历基础上做的延伸，而分治法需要画图加以理解。一般看到这种最大最长的题目，基本上就可以用动态规划问题来尝试作答了。
58.最后一个单词的长度
题目地址
题目描述
给定一个仅包含大小写字母和空格 ' ' 的字符串，返回其最后一个单词的长度。
如果不存在最后一个单词，请返回 0 。
说明：一个单词是指由字母组成，但不包含任何空格的字符串。
示例：
输入: "Hello World"
输出: 5题目分析设想
这道题看上去像是一道字符串题，我们可以从以下几个方面来尝试作答：
- 遍历，从末尾开始，效率高
- lastIndexOf，直接找空格
- 正则
- split
编写代码验证
Ⅰ.遍历
代码：
/**
* @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
};结果：
- 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)
- 时间复杂度
O(n)
Ⅱ.lastIndexOf
代码：
/**
* @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
};结果：
- 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)
- 时间复杂度
O(1)
Ⅲ.正则
代码：
/**
* @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
};结果：
- 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)
- 时间复杂度
O(1)
Ⅳ.split
代码：
/**
* @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
}
};结果：
- 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)
- 时间复杂度
O(1)
查阅他人解法
没有在题解中看到什么特别的解法，大部分都是基于类库解的，比如 Javascript 中 String 和 Array 的方法。或者是遍历实现的。
思考总结
直到现在也没有弄明白这道题的考察点在哪里？不过我建议感兴趣的同学，可以自己拓展实现 lastIndexOf ，参考 上一期 28题的数十种解法，应该能有不小收获。
66.加一
题目地址
题目描述
给定一个由整数组成的非空数组所表示的非负整数，在该数的基础上加一。
最高位数字存放在数组的首位， 数组中每个元素只存储单个数字。
你可以假设除了整数 0 之外，这个整数不会以零开头。
示例：
输入: [1,2,3]
输出: [1,2,4]
解释: 输入数组表示数字 123。
输入: [4,3,2,1]
输出: [4,3,2,2]
解释: 输入数组表示数字 4321。题目分析设想
这道题我有两个大方向，一是数组遍历进行求解，另外一种是数组转数字再处理。但是转数字可能会溢出，所以就只想到从遍历的角度来作答。
- 遍历，从后往前遍历找到不为9的项，后面填0就可以了
编写代码验证
Ⅰ.遍历
代码：
/**
* @param {number[]} digits
* @return {number[]}
*/
var plusOne = function(digits) {
for(let i = digits.length - 1; i >= 0; i--) {
// 找不到不为9的数，直接加1输出就可以了
if(digits[i] !== 9) {
digits[i]++
return digits
} else {
digits[i] = 0
}
}
digits.unshift(1)
return digits
};结果：
- 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)
- 时间复杂度
O(n)
查阅他人解法
发现思路基本都是遍历，但是具体实现会有些差距，这里只列举一个最简单的。
Ⅰ.遍历
代码：
/**
* @param {number[]} digits
* @return {number[]}
*/
var plusOne = function(digits) {
for(let i = digits.length - 1; i >= 0; i--) {
digits[i]++
// 取10的余数，做了赋值操作，为0就继续进位
digits[i] %= 10
if(digits[i] !== 0) {
return digits
}
}
digits.unshift(1)
return digits
};结果：
- 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)
- 时间复杂度
O(n)
思考总结
这道题可能大众的想法会转成数字再处理，但是做数字运算的时候，千万要记住考虑溢出的问题。另外因为是加1，所以倒序遍历就可以了。至于是判断末位为9还是对10取余，我觉得都是一个很好理解的思路，也避免了代码的繁琐。
（完）
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