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z^;m9F+kmvAjnOKnIDnA$0=THl@f#pT$J9#xN~8h4R_spi{F}Y9GGzJhnv`F~B;nz> zkA%MyQ^2c_LBltIVv?BcMKO5>P&3&&Bp`SxQ@+LmVUh7aU2v9}s;QV)i`yT{e&o{a ao;Hj-d>8Zc<<$egkEWWgYW9r>Fa8&bnM4!- diff --git a/problems/0435.无重叠区间.md b/problems/0435.无重叠区间.md index f4b77e88..0637ab5b 100644 --- a/problems/0435.无重叠区间.md +++ b/problems/0435.无重叠区间.md @@ -48,7 +48,7 @@ 按照左边界排序,就要从右向左遍历,因为左边界数值越大越好(越靠右),这样就给前一个区间的空间就越大,所以可以从右向左遍历。 -如果按照左边界排序,还从左向右遍历的话,要处理各个区间右边界的各种情况,就很复杂了。 +如果按照左边界排序,还从左向右遍历的话,其实也可以,逻辑会有所不同。 一些同学做这道题目可能真的去模拟去重复区间的行为,这是比较麻烦的,还要去删除区间。 @@ -126,7 +126,67 @@ public: **所以我把本题的难点也一一列出,帮大家不仅代码看的懂,想法也理解的透彻!** +# 补充 + +本题其实和[贪心算法:用最少数量的箭引爆气球](https://mp.weixin.qq.com/s/HxVAJ6INMfNKiGwI88-RFw)非常像,弓箭的数量就相当于是非交叉区间的数量,只要把弓箭那道题目代码里射爆气球的判断条件加个等号(认为[0,1][1,2]不是相邻区间),然后用总区间数减去弓箭数量 就是要移除的区间数量了。 + +把[贪心算法:用最少数量的箭引爆气球](https://mp.weixin.qq.com/s/HxVAJ6INMfNKiGwI88-RFw)代码稍做修改,别可以AC本题。 + +```C++ +class Solution { +public: + // 按照区间右边界排序 + static bool cmp (const vector& a, const vector& b) { + return a[1] < b[1]; + } + int eraseOverlapIntervals(vector>& intervals) { + if (intervals.size() == 0) return 0; + sort(intervals.begin(), intervals.end(), cmp); + + int result = 1; // points 不为空至少需要一支箭 + for (int i = 1; i < intervals.size(); i++) { + if (intervals[i][0] >= intervals[i - 1][1]) { + result++; // 需要一支箭 + } + else { // 气球i和气球i-1挨着 + intervals[i][1] = min(intervals[i - 1][1], intervals[i][1]); // 更新重叠气球最小右边界 + } + } + return intervals.size() - result; + } +}; +``` + +这里按照 作弊案件遍历,或者按照右边界遍历,都可以AC,具体原因我还没有仔细看,后面有空再补充。 +```C++ +class Solution { +public: + // 按照区间左边界排序 + static bool cmp (const vector& a, const vector& b) { + return a[0] < b[0]; + } + int eraseOverlapIntervals(vector>& intervals) { + if (intervals.size() == 0) return 0; + sort(intervals.begin(), intervals.end(), cmp); + + int result = 1; // points 不为空至少需要一支箭 + for (int i = 1; i < intervals.size(); i++) { + if (intervals[i][0] >= intervals[i - 1][1]) { + result++; // 需要一支箭 + } + else { // 气球i和气球i-1挨着 + intervals[i][1] = min(intervals[i - 1][1], intervals[i][1]); // 更新重叠气球最小右边界 + } + } + return intervals.size() - result; + } +}; + +``` + 循序渐进学算法,认准「代码随想录」就够了,值得介绍给身边的朋友同学们! > 我是[程序员Carl](https://github.com/youngyangyang04),组队刷题可以找我,本文[leetcode刷题攻略](https://github.com/youngyangyang04/leetcode-master)已收录,更多[精彩算法文章](https://mp.weixin.qq.com/mp/appmsgalbum?__biz=MzUxNjY5NTYxNA==&action=getalbum&album_id=1485825793120387074&scene=173#wechat_redirect)尽在:[代码随想录](https://img-blog.csdnimg.cn/20200815195519696.png),期待你的关注! + +是不是尽可能重叠,其实它都在那里,没有尽可能这一说 diff --git a/problems/0494.目标和.md b/problems/0494.目标和.md index 7eb5d3ca..83e27804 100644 --- a/problems/0494.目标和.md +++ b/problems/0494.目标和.md @@ -70,33 +70,68 @@ public: ## 动态规划 -使用背包要明确dp[i]表示的是什么,i表示的又是什么? +如何转化为01背包问题呢。 -填满i(包括i)这么大容积的包,有dp[i]种方法。 +假设加法的总和为x,那么减法对应的总和就是sum - x。 +所以我们要求的是 x - (sum - x) = S + +x = (S + sum) / 2 + +此时问题就转化为,装满容量为x背包,有几种方法。 + +大家看到(S + sum) / 2 应该担心计算的过程中向下取整有没有影响。 + +这么担心就对了,例如sum 是5,S是2的话其实就是无解的,所以: + +``` +if ((S + sum) % 2 == 1) return 0; // 此时没有方案,两个int相加的时候要各位小心数值溢出的问题 +``` + +看到这种表达式,应该本能的反应,两个int相加数值可能溢出的问题,当然本题并没有溢出。 + +在回归到01背包问题, + +这次和之前遇到的背包问题不一样了,之前都是求容量为j的背包,最多能装多少。 + +本题是装满有几种方法。 + +* 确定dp数组以及下标的含义 + +dp[j] 表示:填满j(包括j)这么大容积的包,有dp[i]种方法 + +* 确定递推公式 + +有哪些来源可以推出dp[j]呢,只有dp[j - nums[i]]。 + +那么dp[j] 应该是 dp[j] + dp[j - nums[i]] (**这块需要好好讲讲**) + +* dp数组如何初始化 +* 确定遍历顺序 ``` -// 时间复杂度O(n^2) -// 空间复杂度可以说是O(n),也可以说是O(1),因为每次申请的辅助数组的大小是一个常数 class Solution { public: int findTargetSumWays(vector& nums, int S) { int sum = 0; for (int i = 0; i < nums.size(); i++) sum += nums[i]; if (S > sum) return 0; // 此时没有方案 - if ((S + sum) % 2) return 0; // 此时没有方案,两个int相加的时候要各位小心数值溢出的问题 + if ((S + sum) % 2 == 1) return 0; // 此时没有方案,两个int相加的时候要各位小心数值溢出的问题 int bagSize = (S + sum) / 2; int dp[1001] = {1}; for (int i = 0; i < nums.size(); i++) { for (int j = bagSize; j >= nums[i]; j--) { - if (j - nums[i] >= 0) dp[j] += dp[j - nums[i]]; + dp[j] += dp[j - nums[i]]; } } return dp[bagSize]; } }; ``` +* 时间复杂度O(n * m),n为正数个数,m为背包容量 +* 空间复杂度:O(n),也可以说是O(1),因为每次申请的辅助数组的大小是一个常数 + dp数组中的数值变化:(从[0 - 4]) ``` diff --git a/problems/0763.划分字母区间.md b/problems/0763.划分字母区间.md index 6a0716a3..b0b3c3c8 100644 --- a/problems/0763.划分字母区间.md +++ b/problems/0763.划分字母区间.md @@ -1,22 +1,46 @@ -## 题目链接 -https://leetcode-cn.com/problems/partition-labels/ +> 看起来有点难,看仅仅是看起来难而已 -## 思路 +# 763.划分字母区间 -一想到分割字符串就想到了回溯,但本题其实不用那么复杂。 +题目链接: https://leetcode-cn.com/problems/partition-labels/ + +字符串 S 由小写字母组成。我们要把这个字符串划分为尽可能多的片段,同一字母最多出现在一个片段中。返回一个表示每个字符串片段的长度的列表。 + +示例: +输入:S = "ababcbacadefegdehijhklij" +输出:[9,7,8] +解释: +划分结果为 "ababcbaca", "defegde", "hijhklij"。 +每个字母最多出现在一个片段中。 +像 "ababcbacadefegde", "hijhklij" 的划分是错误的,因为划分的片段数较少。 +  +提示: + +* S的长度在[1, 500]之间。 +* S只包含小写字母 'a' 到 'z' 。 + +# 思路 + +一想到分割字符串就想到了回溯,但本题其实不用回溯去暴力搜索。 + +题目要求同一字母最多出现在一个片段中,那么如何把同一个字母的都圈在同一个区间里呢? + +如果没有接触过这种题目的话,还挺有难度的。 + +在遍历的过程中相当于是要找每一个字母的边界,**如果找到之前遍历过的所有字母的最远边界,说明这个边界就是分割点了**。此时前面出现过所有字母,最远也就到这个边界了。 可以分为如下两步: * 统计每一个字符最后出现的位置 -* 从头遍历字符,如果找到之前字符最大出现位置下标和当前下标相等,则找到了分割点 +* 从头遍历字符,并更新字符的最远出现下标,如果找到字符最远出现位置下标和当前下标相等了,则找到了分割点 如图: - +![763.划分字母区间](https://img-blog.csdnimg.cn/20201222191924417.png) 明白原理之后,代码并不复杂,如下: -``` +```C++ class Solution { public: vector partitionLabels(string S) { @@ -38,4 +62,16 @@ public: } }; ``` -> 更多算法干货文章持续更新,可以微信搜索「代码随想录」第一时间围观,关注后,回复「Java」「C++」 「python」「简历模板」「数据结构与算法」等等,就可以获得我多年整理的学习资料。 + +* 时间复杂度:O(n) +* 空间复杂度:O(1) 使用的hash数组是固定大小 + +# 总结 + +这道题目leetcode标记为贪心算法,说实话,我没有感受到贪心,找不出局部最优推出全局最优的过程。就是用最远出现距离模拟了圈字符的行为。 + +但这道题目的思路是很巧妙的,所以有必要介绍给大家做一做,感受一下。 + +就酱,循序渐进寻算法,认准「代码随想录」,直接介绍给身边的朋友同学们! + + diff --git a/problems/1049.最后一块石头的重量II.md b/problems/1049.最后一块石头的重量II.md index 7540b4c5..17bcdfc8 100644 --- a/problems/1049.最后一块石头的重量II.md +++ b/problems/1049.最后一块石头的重量II.md @@ -37,10 +37,11 @@ dp[j]有两个来源方向,一个是dp[j]自己,一个是dp[j - stones[i]] for循环遍历石头的数量嵌套一个for循环遍历背包容量,且因为是01背包,每一个物品只使用一次,所以遍历背包容量的时候要倒序。 -具体原因我在 +具体原因我在[01背包一维数组实现](https://github.com/youngyangyang04/leetcode-master/blob/master/problems/%E8%83%8C%E5%8C%85%E7%90%86%E8%AE%BA%E5%9F%BA%E7%A1%8001%E8%83%8C%E5%8C%85-2.md)详细讲解过了。大家感兴趣可以去看一下。 -``` +最后C++代码如下: +```C++ class Solution { public: int lastStoneWeightII(vector& stones) {