From 23680873b2ce345f2fb40af6cb6762eb7cc1199f Mon Sep 17 00:00:00 2001 From: ridethepig Date: Sat, 1 Jul 2023 23:59:11 +0800 Subject: [PATCH] update log --- journals/2023_06_04.md | 2 + journals/2023_06_05.md | 3 + journals/2023_06_06.md | 4 + journals/2023_06_07.md | 6 + journals/2023_06_09.md | 4 + journals/2023_06_10.md | 2 + journals/2023_06_11.md | 1 + journals/2023_06_12.md | 4 + journals/2023_06_13.md | 3 + journals/2023_06_14.md | 2 + journals/2023_06_15.md | 1 + journals/2023_06_16.md | 2 + journals/2023_06_17.md | 4 + journals/2023_06_18.md | 2 + journals/2023_06_19.md | 4 + journals/2023_06_20.md | 4 + journals/2023_06_21.md | 1 + journals/2023_06_22.md | 1 + journals/2023_06_23.md | 2 + journals/2023_06_24.md | 1 + journals/2023_06_25.md | 2 + journals/2023_06_26.md | 5 + journals/2023_06_27.md | 1 + journals/2023_06_28.md | 11 ++ journals/2023_06_29.md | 9 ++ journals/2023_06_30.md | 3 + journals/2023_07_01.md | 5 + logseq/config.edn | 2 +- ...Organization_and_Design_1681729306797_0.md | 2 - pages/hls__ostep_1681115599584_0.md | 2 - pages/动态规划.md | 118 ++++++++++++++++++ pages/基础图论算法.md | 42 +++++++ pages/简单数学算法.md | 40 ++++++ 33 files changed, 290 insertions(+), 5 deletions(-) create mode 100644 journals/2023_06_04.md create mode 100644 journals/2023_06_05.md create mode 100644 journals/2023_06_06.md create mode 100644 journals/2023_06_07.md create mode 100644 journals/2023_06_09.md create mode 100644 journals/2023_06_10.md create mode 100644 journals/2023_06_11.md create mode 100644 journals/2023_06_12.md create mode 100644 journals/2023_06_13.md create mode 100644 journals/2023_06_14.md create mode 100644 journals/2023_06_15.md create mode 100644 journals/2023_06_16.md create mode 100644 journals/2023_06_17.md create mode 100644 journals/2023_06_18.md create mode 100644 journals/2023_06_19.md create mode 100644 journals/2023_06_20.md create mode 100644 journals/2023_06_21.md create mode 100644 journals/2023_06_22.md create mode 100644 journals/2023_06_23.md create mode 100644 journals/2023_06_24.md create mode 100644 journals/2023_06_25.md create mode 100644 journals/2023_06_26.md create mode 100644 journals/2023_06_27.md create mode 100644 journals/2023_06_28.md create mode 100644 journals/2023_06_29.md create mode 100644 journals/2023_06_30.md create mode 100644 journals/2023_07_01.md create mode 100644 pages/动态规划.md create mode 100644 pages/基础图论算法.md create mode 100644 pages/简单数学算法.md diff --git a/journals/2023_06_04.md b/journals/2023_06_04.md new file mode 100644 index 0000000..badbbaa --- /dev/null +++ b/journals/2023_06_04.md @@ -0,0 +1,2 @@ +- 小熊思想，我的评价是背了也没啥用，考试的时候一顿瞎扯 + - 练习时长两年半的思政练习生正式毕业 \ No newline at end of file diff --git a/journals/2023_06_05.md b/journals/2023_06_05.md new file mode 100644 index 0000000..93854c3 --- /dev/null +++ b/journals/2023_06_05.md @@ -0,0 +1,3 @@ +- 跑了好久的材料，姑且把pku-cs和thu-cs都搞完了 +- 新内存到了，32G真的好棒啊 +- 编译器是真的一点也写不下去啊，还特地把人喊过去就是为了告诉大家要快点写 \ No newline at end of file diff --git a/journals/2023_06_06.md b/journals/2023_06_06.md new file mode 100644 index 0000000..8840d90 --- /dev/null +++ b/journals/2023_06_06.md @@ -0,0 +1,4 @@ +- 莫名其妙的有点焦虑，然后就又多整了两个学院的材料 + - 然后全部寄出去了，花了我60，EMS这波属于是垄断抢钱 +- 编译器进展缓慢 +- 模式识别85，练习时长3个月的rk1到此结束 \ No newline at end of file diff --git a/journals/2023_06_07.md b/journals/2023_06_07.md new file mode 100644 index 0000000..5251cbf --- /dev/null +++ b/journals/2023_06_07.md @@ -0,0 +1,6 @@ +- NJU-CS投递完成，SJTU还剩个表，这周填完 + - 还有USTC-CS和计算所没填 + - 28号考软件工程，有点尴尬 +- 姑且是强迫自己坐下来写编译器，争取这周跑通前后端，下周做优化 + - 早知道考试去了，分高还省事 +- 大创结题了，基地正式毕业 \ No newline at end of file diff --git a/journals/2023_06_09.md b/journals/2023_06_09.md new file mode 100644 index 0000000..d4a212c --- /dev/null +++ b/journals/2023_06_09.md @@ -0,0 +1,4 @@ +- 论语还是很棒的，写了一晚上给了97 +- 说起来，他们去CUHK面试的人结束了，今年居然有笔试，面试也在问笔试 + - 就挺抽象的，属于是Regular的操作搬过来了？ + - 感觉给需要去面试的人的名额也不是很多 \ No newline at end of file diff --git a/journals/2023_06_10.md b/journals/2023_06_10.md new file mode 100644 index 0000000..4aecc8f --- /dev/null +++ b/journals/2023_06_10.md @@ -0,0 +1,2 @@ +- 无聊的软工实验，不知道为啥有这门课 +- 玩群星，浪费时间捏 \ No newline at end of file diff --git a/journals/2023_06_11.md b/journals/2023_06_11.md new file mode 100644 index 0000000..c00c832 --- /dev/null +++ b/journals/2023_06_11.md @@ -0,0 +1 @@ +- 玩群星，浪费时间捏 \ No newline at end of file diff --git a/journals/2023_06_12.md b/journals/2023_06_12.md new file mode 100644 index 0000000..6dbbd82 --- /dev/null +++ b/journals/2023_06_12.md @@ -0,0 +1,4 @@ +- CU的老师26号来西安，顺手发了三篇论文让我看 + - 然而是布线的论文，一脸懵逼 +- 提交了SJTU的申请表，姑且 + - 因为和PKUCS冲突了，所以还是填了SE，到时候去和ipads对线 \ No newline at end of file diff --git a/journals/2023_06_13.md b/journals/2023_06_13.md new file mode 100644 index 0000000..804ff2b --- /dev/null +++ b/journals/2023_06_13.md @@ -0,0 +1,3 @@ +- fdu入营，但是显然去不了，遂放弃offer +- 编译器终于能从前端到后端全部跑通了啊啊啊 +- 太极拳考试，30分钟下课 \ No newline at end of file diff --git a/journals/2023_06_14.md b/journals/2023_06_14.md new file mode 100644 index 0000000..3ec52b3 --- /dev/null +++ b/journals/2023_06_14.md @@ -0,0 +1,2 @@ +- 填了计算所的报名，虽然要推荐信，但是直接电子签了 + - 甚至还要单独填问卷选老师，就挺抽象的 \ No newline at end of file diff --git a/journals/2023_06_15.md b/journals/2023_06_15.md new file mode 100644 index 0000000..b58a47d --- /dev/null +++ b/journals/2023_06_15.md @@ -0,0 +1 @@ +- 继续在编译器上浪费时间 \ No newline at end of file diff --git a/journals/2023_06_16.md b/journals/2023_06_16.md new file mode 100644 index 0000000..fd82977 --- /dev/null +++ b/journals/2023_06_16.md @@ -0,0 +1,2 @@ +- 要不是垃圾试点班，我编译原理就已经考完了啊啊啊 +- 难绷地写着常数传播 \ No newline at end of file diff --git a/journals/2023_06_17.md b/journals/2023_06_17.md new file mode 100644 index 0000000..2dd521b --- /dev/null +++ b/journals/2023_06_17.md @@ -0,0 +1,4 @@ +- 软工实验，然后晚上写编译器 +- 姑且是把先进封装的introduction视频看完了 +- 早上去考了个游泳，意外的游泳馆还不错，三年来唯一一次去 + - 没想到三年没游泳的我居然没被淹死 \ No newline at end of file diff --git a/journals/2023_06_18.md b/journals/2023_06_18.md new file mode 100644 index 0000000..b02916f --- /dev/null +++ b/journals/2023_06_18.md @@ -0,0 +1,2 @@ +- 写编译器，姑且写了个DCE，不想写了草 +- 提交了计算所的材料，和同学进行一个扎堆报考 \ No newline at end of file diff --git a/journals/2023_06_19.md b/journals/2023_06_19.md new file mode 100644 index 0000000..8e9304b --- /dev/null +++ b/journals/2023_06_19.md @@ -0,0 +1,4 @@ +- 给编译器加了个简单的peephole优化，暂时先不写了，可能后面会再加个GVN和简单的循环分析吧 +- 填写了USTC-CS的报名 +- 姑且看完了第一篇论文 + - 发现好像也没那么离谱 \ No newline at end of file diff --git a/journals/2023_06_20.md b/journals/2023_06_20.md new file mode 100644 index 0000000..c4d2c08 --- /dev/null +++ b/journals/2023_06_20.md @@ -0,0 +1,4 @@ +- 10分钟的体育课，离谱 +- 看第二篇论文 +- 过了一个周末，为啥大家都有学上了，就我没有 + - 寻思着是不是应该进行一个新的复习，毕竟还是要去夏令营的 \ No newline at end of file diff --git a/journals/2023_06_21.md b/journals/2023_06_21.md new file mode 100644 index 0000000..50fa9bb --- /dev/null +++ b/journals/2023_06_21.md @@ -0,0 +1 @@ +- 努力了一下，把论文看完了 \ No newline at end of file diff --git a/journals/2023_06_22.md b/journals/2023_06_22.md new file mode 100644 index 0000000..684025b --- /dev/null +++ b/journals/2023_06_22.md @@ -0,0 +1 @@ +- 开始复习软工，看了一天ppt，好智障啊bbzl \ No newline at end of file diff --git a/journals/2023_06_23.md b/journals/2023_06_23.md new file mode 100644 index 0000000..bb6ac90 --- /dev/null +++ b/journals/2023_06_23.md @@ -0,0 +1,2 @@ +- 继续复习软工，又看了两章ppt +- 联系了老师，26号下午面谈 \ No newline at end of file diff --git a/journals/2023_06_24.md b/journals/2023_06_24.md new file mode 100644 index 0000000..2ca755a --- /dev/null +++ b/journals/2023_06_24.md @@ -0,0 +1 @@ +- 继续复习软工，把最抽象的测试看完了 \ No newline at end of file diff --git a/journals/2023_06_25.md b/journals/2023_06_25.md new file mode 100644 index 0000000..459a05e --- /dev/null +++ b/journals/2023_06_25.md @@ -0,0 +1,2 @@ +- 回头看了看之前的论文，还顺便看了两篇前置的论文 + - 感觉算法啥的倒是不难，但是细节感觉还是挺多的 \ No newline at end of file diff --git a/journals/2023_06_26.md b/journals/2023_06_26.md new file mode 100644 index 0000000..1f5fa77 --- /dev/null +++ b/journals/2023_06_26.md @@ -0,0 +1,5 @@ +- 最后一节软工课，有点离谱 + - 果然抽象还是得看西工大啊，推迟两周开学把夏令营什么的直接橄榄了 +- 下午去南山苑面谈，结果发现根本不是面试，早在上个月他回我邮件的时候就已经相当于拿到offer了 + - 草 + - 太草了 \ No newline at end of file diff --git a/journals/2023_06_27.md b/journals/2023_06_27.md new file mode 100644 index 0000000..71b7330 --- /dev/null +++ b/journals/2023_06_27.md @@ -0,0 +1 @@ +- 背了一天软工，睡觉做梦都是软工 \ No newline at end of file diff --git a/journals/2023_06_28.md b/journals/2023_06_28.md new file mode 100644 index 0000000..ca6a700 --- /dev/null +++ b/journals/2023_06_28.md @@ -0,0 +1,11 @@ +- 傻逼软工，我把116个问题全背下来了，结果考了问题集里面没有的东西 + - 课上也没有个例题，纯纯的傻逼，也不知道题目怎么做 +- 跟学长吃了个饭，聊了下香港相关的东西 + - 老师基本上没啥太大的问题，去也能去 + - 会比较牛马就是了，居然要做七次TA，也不一定能按时毕业 + - 香港会比较闷热，也不知道能不能顶得住 +- 姑且还是想认真准备一下PKU的夏令营，明天开始复习机试 + - 只能说，大概是各有各的牛马之处吧 + - 也有一部分原因是家长不想让我润掉，说什么要为国效力 + - 又不得不再骂一次西工大，太傻逼了，推迟两周，复习个锤子 + - 还要骂北大，机试不早说，只剩一周不到了啊啊啊 \ No newline at end of file diff --git a/journals/2023_06_29.md b/journals/2023_06_29.md new file mode 100644 index 0000000..7bf816d --- /dev/null +++ b/journals/2023_06_29.md @@ -0,0 +1,9 @@ +- 看了一下2017年的机试，感觉裸考10题能写个4-5题的样子，复习一下能写个6题 + - 大概3个模拟，1个搜索，1个最短路，1-2个dp，剩下的随缘 + - 但是好像今年时间比较短，也不知道形式和难度会不会变 + - 今年感觉300个人录取一半，有点小难绷 +- 究极难绷的事情出现了 + - 今年填的老师居然大热门，要跟pku本科生抢，草，我去hk成了天意所指是吧，啊？ + - 果然还是应该提前问一下的，草，不然就直接冲集成电路了 + - 好傻逼啊，我居然还莫名其妙把rk2卡掉了，所以老师把我放进来玩是吧，听我说谢谢你，因为有你，大家都变成了小丑 + - 算了继续复习去了，再骂一次傻逼西工大，把考试排这么靠后，一点缓冲都没有 \ No newline at end of file diff --git a/journals/2023_06_30.md b/journals/2023_06_30.md new file mode 100644 index 0000000..ecf7e29 --- /dev/null +++ b/journals/2023_06_30.md @@ -0,0 +1,3 @@ +- dp的经典模型算是复习完了，不过如果是要自己想思路的dp，那显然是不会写的 + - 开始看看图论 +- 摆烂，毁灭吧 \ No newline at end of file diff --git a/journals/2023_07_01.md b/journals/2023_07_01.md new file mode 100644 index 0000000..7dd8525 --- /dev/null +++ b/journals/2023_07_01.md @@ -0,0 +1,5 @@ +- PKU夏令营成为真正的小丑，北大爷自己还要抢名额三进二，我还是摆烂吧，去跟老师聊着玩玩 + - 学长建议去联系一下其他的老师，然后得到回复说是没法换导师、只能等九月，我直接立马告辞 + - 跑了三天材料，花费60r材料邮寄费用，最后换来旅游一趟，太tm小丑了，草 + - 正式宣布，PKU成为我最讨厌的大学：材料究极麻烦、不包住不包路费、夏令营还不能调剂、一堆本科生跑过来抢名额。真nm傻逼啊 +- 忍住恶心写了点图论和二叉树的题。 \ No newline at end of file diff --git a/logseq/config.edn b/logseq/config.edn index 9e14282..834e3fc 100644 --- a/logseq/config.edn +++ b/logseq/config.edn @@ -245,7 +245,7 @@ :ref/linked-references-collapsed-threshold 50 ;; Favorites to list on the left sidebar - :favorites [] + :favorites ["hls__Computer_Organization_and_Design_1681729306797_0" "hls__ostep_1680491762166_0" "hls__ostep_1681115599584_0"] ;; any number between 0 and 1 (the greater it is the faster the changes of the next-interval of card reviews) (default 0.5) ;; :srs/learning-fraction 0.5 diff --git a/pages/hls__Computer_Organization_and_Design_1681729306797_0.md b/pages/hls__Computer_Organization_and_Design_1681729306797_0.md index e8a9bdb..8e06a04 100644 --- a/pages/hls__Computer_Organization_and_Design_1681729306797_0.md +++ b/pages/hls__Computer_Organization_and_Design_1681729306797_0.md @@ -55,7 +55,6 @@ file-path:: ../../../../assets/Computer_Organization_and_Design_1681729306797_0. hl-page:: 47 hl-color:: yellow id:: 643eb311-6b10-4fa3-9aa3-dfd5a59acf2c - collapsed:: true - Semiconductor, silicon: add materials to silicon that allow tiny areas to transform into one of three devices: Excellent conductor, Excellent insulator and Transistor (conduct/insulate at some conditions) hl-page:: 48 ls-type:: annotation @@ -69,7 +68,6 @@ file-path:: ../../../../assets/Computer_Organization_and_Design_1681729306797_0. hl-page:: 51 hl-color:: yellow id:: 643ec3be-027e-48b5-90e0-cd4a5e901691 - collapsed:: true - response/execution time: time between the start and completion of a task hl-page:: 52 ls-type:: annotation diff --git a/pages/hls__ostep_1681115599584_0.md b/pages/hls__ostep_1681115599584_0.md index 90459ff..5df094a 100644 --- a/pages/hls__ostep_1681115599584_0.md +++ b/pages/hls__ostep_1681115599584_0.md @@ -7,7 +7,6 @@ file-path:: ../assets/ostep_1681115599584_0.pdf hl-page:: 311 hl-color:: yellow id:: 6433ca28-1bdf-433d-8ed9-0d54bf5ba940 - collapsed:: true - share the same address space and thus can access the same data - context switch: the address space remains the same hl-page:: 311 @@ -25,7 +24,6 @@ file-path:: ../assets/ostep_1681115599584_0.pdf id:: 6433cba2-61bd-4549-a29f-2ad85b3e30cd hl-color:: yellow - Why thread? - collapsed:: true - possible speedup through parallelization - enable overlap of IO in a single program - Though these could be done through multi-processing, threading makes share data easier diff --git a/pages/动态规划.md b/pages/动态规划.md new file mode 100644 index 0000000..d16cd02 --- /dev/null +++ b/pages/动态规划.md @@ -0,0 +1,118 @@ +- 考虑状态和转移两种东西 + - 可以把状态看作是DAG上的点，然后状态转移就是边 +- LCS问题 + - 两个序列`A[1..n]`和`B[1..m]`，求最长的子序列既是A的也是B的 + - 状态的定义：$f(i,j)=A[1:i]和B[1:j]的LCS$ + - 状态转移：如果`A[i]==B[j]`，那就直接接到后面`f[i,j] = f[i-1, j-1] + 1`；否则更新为`max(f[i-1, j], f[i, j-1])` +- LIS问题 + - 求最长子序列，子序列满足某些有序限制 + - 状态为：以第i个元素结尾的子序列的最长 + - 状态转移：在前面的子序列里面找一个最长且满足要求的子序列接在后面，也就是$f[i] = \max_{1 \le j \lt i, w[i] \lt w[j]}(f[j]) + 1$ +- 01背包 + - n个物品，每个物品有价值v和重量w两种属性，W容量的包。每个物品是唯一的，求能装进包里的物品的价值最大。 + - 状态：$f[i, c]$为前i个物品已经处理完成，容量为c情况下的最大价值 + - 状态转移：当前物品装或者不装的决策。`f[i,c] = max(f[i-1, c], f[i-1, c-w[i]] + v[i])`。如果没有装物品，那么容量不变，价值也不变；如果装了第i个物品，那么它的价值增加且容量减小，因为这里当前状态`f[i,c]`是固定的（写的是一个逆推的形式），因此从更小容量转移过来 + - 在具体做的时候，需要注意一下顺序和空间压缩。 + - 因为第i个物品的i是有顺序的，因此可以压缩掉一维。变成这样`f[c] = max(f[c], f[c-w[i]] + v[i])` + - 在滚动压缩的时候，需要保证逆推的顺序，否则容量较小的情况更新过后会影响到后面的推导。不过在非滚动数组的情况下，这则是不需要的，因为反正用的是i-1的状态 + ```c + for (int i = 1; i <= n; ++ i) + for (int c = W; c >= w[i]; -- c) + f[c] = max(f[c], f[c - w[i]] + v[i]) + ``` +- 完全背包 + - n个物品，每个物品有价值v和重量w两种属性，W容量的包。**每个物品可以取多次**，求能装进包里的物品的价值最大。 + - 状态是一样的，唯一的区别在于，完全背包需要枚举当前物品取的次数 + - 不过这也可以优化掉，因为如果是正向推的话，已经包含了取所有可能次数的情况。 + - **0-1背包和完全背包区别就在于容量维度的迭代顺序** + - ```c + for (int i = 1; i <= n; ++ i) + for (int c = w[i]; c <= W; ++ c) + f[c] = max(f[c], f[c - w[i]] + v[i]); + ``` +- 多重背包 + - n种物品，每个物品有价值v和重量w两种属性，W容量的包。每种物品有k个，求能装进包里的物品的价值最大。 + - 转化为01背包求解。因为每种物品k个就等于有k个属性相同的物品分别取或者不取。 +- 二维背包 + - 这道题是很明显的 0-1 背包问题，可是不同的是选一个物品会消耗两种价值（经费、时间），只需在状态中增加一维存放第二种价值即可，同时枚举的时候也变成了两个量。 + - 也就是状态方程变成了`f[i, c, d] = f[i-1, c - c[i], d-d[i]] + v[i]` +- 背包状态数 + - 把最大值换成求和，初始状态变成1（因为可以啥也不装） + - `f[i, c] += f[i-1, c-w[i]]` +- 背包方案 + - 一种方案是，另外开一个数组记录状态`[i, c]`下有没有取i + ``` + int v = V; // 记录当前的存储空间 + + // 因为最后一件物品存储的是最终状态，所以从最后一件物品进行循环 + for (从最后一件循环至第一件) { + if (g[i][v]) { + 选了第 i 项物品; + v -= 第 i 项物品的重量; + } else { + 未选第 i 项物品; + } + } + ``` + - 另一种方案则是，不优化空间，然后倒着推算更新点（如果状态和前一个物品不一样，那肯是发生了转移） + ``` + for (int i = n; i > 0; -- i) { + if (dp[i][res] != dp[i-1][res]) { + sel[i] = 1; + res -= w[i]; + } + } + ``` +- 区间dp + - 具有明显的可划分性质 + - 经典的合并石子题：有n个数排成一个环，进行n-1次合并操作，每次操作将相邻的两堆合并成一堆，能获得新的一堆中的石子数量的和的得分。你需要最大化你的得分。 + - 状态：`f[l, r]`表示区间`[l:r]`合并所能得到的最大分数 + - 方程：枚举合并点k，取最大值。$f[l, r] = max_{i\le k \lt j}(f[i, k] + f[k+1, j]) + sum(a[i : j])$ + - 可以用前缀和来优化求和的过程 + - 这里的阶段划分并不是自然的（LIS、LCS自然就是LTR或者RTL，背包也就是依次取或者不取一个物品），需要用区间长度进行划分。 + - 对于该问题，还需要解决围成环这个问题，比较好的解决方法是展开成链式之后复制一遍，最后在n个长度为n的区间里面取最大值 + - 实现如下 + ```c + for (int len = 1; len <= n; ++ len) { + for (int i = 1; i + len - 1 <= 2 * n; ++ i) { // 实际上是j<=2*n + int j = len + i - 1; + for (int k = i; k < j; ++ k) { + f[i][j] = max(f[i][j], f[i][k] + f[k+1][j] + sum[j] - sum[i-1]); + } + } + } + // ... + ans = [&]() { + int mx = 0; + for (int i = 1; i <= n; ++ i) mx = max(mx, f[i][i + n - 1]); + return mx; + }(); + ``` + - 能量项链也是完全一样的思路，除了值的计算方法稍有区别。 +- 树形dp + - 就是在树上做dp，一般而言，状态肯定有某一维是“以节点u为根的子树”这样的东西。然后遍历子树求解就好了。 + - 例题1：POJ1463。有若干结点，结点之间有路相连，构成树形结构，如果在一个结点上放置一个士兵，与这个结点相连的路就可以被监视，现在要监视所有的路，问至少要多少士兵。 + - 状态：$f[u, 0/1]$为节点u放置或者不放置士兵情况下的最小值 + - 状态转移：如果当前节点不放，那么子节点就必须放置，也就是`f[u][0] = sum(f[v][1])`；如果当前节点放置，那么子节点可以放，也可以不放，对每个子节点的两种状态求最小值然后加起来（再加上自己1）：`f[u][1] = sum(min(f[v][0],f[v][1]) + 1`。 + - 舞会那个题的思路也是类似的，就不赘述了 +- Floyd最短路 + - 状态：$f[k, i, j]$表示只经过编号不超过k的节点，从i到j的最短路长度 + - 状态转移：`f[k,i,j] = min(f[k-1, i, j], f[k-1, i, k] + f[k-1, k, j])`。决策就是要不要经过k这个点。 + - 显然第一维可以推掉，所以实际上数组是两维度的 + - 实现 + ```c + int dis[maxn][maxn]; + memset(dis, 0x3f, sizeof(dis)); + for (int i = 1; i <= n; ++ i) dis[i][i] = 0; + for (int i = 1; i <= m; ++ i) { + int u = read(), v = read(), w = read(); + dis[u][v] = dis[v][u] = w; + } + for (int k = 1; k <= n; ++ k){ + for (int i = 1; i <= n; ++ i) { + for (int j = 1; j <= n; ++ j){ + f[i][j] = min(f[i][j], f[i][k] + f[k][j]); + } + } + } + ``` \ No newline at end of file diff --git a/pages/基础图论算法.md b/pages/基础图论算法.md new file mode 100644 index 0000000..dae69b5 --- /dev/null +++ b/pages/基础图论算法.md @@ -0,0 +1,42 @@ +- 链星 + ```c + inline void add_edge(int u, int v, int w) { + edge[cnt].next = head[u]; edge[cnt].v = v; edge[cnt].w = w; head[u] = cnt++; + } + ``` +- Dijkstra最短路 + - 要求：边权非负（不仅仅是没有负环） + - 随手敲一个 + ```c + priority_queue, greater> pq; + pq.push({s, 0}); + dis[s] = 0; + while(!pq.empty()) { + int u = pq.top().id; + pq.pop(); + if (vis[u]) continue; + vis[u] = true; + for (int i = head[u]; i; i = edge[i].next) { + int v = edge[i].to; + if (dis[v] > dis[u] + edge[i].w) { + dis[v] = dis[u] + edge[i].w; + pq.push({v, dis[v]}); + } + } + } + ``` +- Kruscal生成树 + - ```c++ + std::sort(e + 1, e + e_cnt + 1); + int ans = 0, t_cnt = 0; + for (int i = 1; i <= n; ++ i) fa[i] = i; + for (int i = 1; i <= e_cnt; ++ i) { + int fau = findfa(e[i].u); + int fav = findfa(e[i].v); + if (fau != fav) { + fa[fav] = fau; // attention! use fa[find(v)], not fa[v] + ans += e[i].w; + t_cnt ++; + } + } + ``` \ No newline at end of file diff --git a/pages/简单数学算法.md b/pages/简单数学算法.md new file mode 100644 index 0000000..64e791c --- /dev/null +++ b/pages/简单数学算法.md @@ -0,0 +1,40 @@ +- 素数判定：$\sqrt{n}$算法，直接枚举所有小于根号n的数字，取模判定 +- 素数筛法：思路很简单，把所有素数的倍数标记为非素数即可。可能需要long long。 +- 质因数分解：一句话描述，从2开始到根号n，逮到一个因数就死命除掉 + ```c + vector prime_factor(int n){ + vector retval; + for (int i = 2; i * i <= n; ++ i){ + if (n % i == 0) { + retval.push_back(i); + while(n % i == 0) n /= i; + } + } + if (n != 1) retval.push_back(i); + } + ``` +- 快速幂： + ```c + int fpow(int a, int b) { // a^b + int ans = 1; + while (b) { + if (b & 1) ans *= a; + a*= a; + b >>= 1; + } + } + ``` +- GCD辗转相除，没啥好说的，其实也可以用编译器函数 + ```c + int gcd(int a, int b) { + return b == 0 ? a : gcd(b, a % b); + } + inline int gcd(int a, int b) { + while (b) { + int tmp = a; + a = b; + b = tmp % b; + } + } + ``` + - 另外，对于 C++14，我们可以使用自带的 `__gcd(a,b)` 函数来求最大公约数。而对于 C++ 17，我们可以使用 [``](https://en.cppreference.com/w/cpp/header/numeric) 头中的 [`std::gcd`](https://en.cppreference.com/w/cpp/numeric/gcd) 与 [`std::lcm`](https://en.cppreference.com/w/cpp/numeric/lcm) 来求最大公约数和最小公倍数。 \ No newline at end of file