From 73190703ea48db968186f2d53b89ffad04f770ee Mon Sep 17 00:00:00 2001 From: krahets Date: Wed, 12 Jul 2023 03:52:33 +0800 Subject: [PATCH] Add playing cards sorting example to algos_are_everywhere --- .../unbounded_knapsack_problem.md | 4 +-- .../playing_cards_sorting.png | Bin 0 -> 189154 bytes .../algorithms_are_everywhere.md | 25 +++++++++++------- docs/chapter_introduction/summary.md | 2 ++ .../assembling_blocks.jpg | Bin docs/chapter_introduction/what_is_dsa.md | 16 ++++++----- 6 files changed, 29 insertions(+), 18 deletions(-) create mode 100644 docs/chapter_introduction/algorithms_are_everywhere.assets/playing_cards_sorting.png rename docs/chapter_introduction/{algorithms_are_everywhere.assets => what_is_dsa.assets}/assembling_blocks.jpg (100%) diff --git a/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md b/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md index ebd73044b..caa943c7a 100644 --- a/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md +++ b/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md @@ -97,7 +97,7 @@ $$ 由于当前状态是从左边和上边的状态转移而来,**因此状态压缩后应该对 $dp$ 表中的每一行采取正序遍历**,这个遍历顺序与 0-1 背包正好相反。请通过以下动画来理解为什么要改为正序遍历。 === "<1>" - ![unbounded_knapsack_dp_comp_step1](unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png) + ![完全背包的状态压缩后的动态规划过程](unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png) === "<2>" ![unbounded_knapsack_dp_comp_step2](unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png) @@ -296,7 +296,7 @@ $$ 下图展示了零钱兑换的动态规划过程。 === "<1>" - ![coin_change_dp_step1](unbounded_knapsack_problem.assets/coin_change_dp_step1.png) + ![零钱兑换问题的动态规划过程](unbounded_knapsack_problem.assets/coin_change_dp_step1.png) === "<2>" ![coin_change_dp_step2](unbounded_knapsack_problem.assets/coin_change_dp_step2.png) diff --git a/docs/chapter_introduction/algorithms_are_everywhere.assets/playing_cards_sorting.png 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zWYWXX?T8n&&pbE#-;9jZi8uTOn_j40N^+#n0FAT*ZeXCl)pUWuU<{b)OiT^HnwRUe zDtg5cHV~^`R0en)B3(}DI!=*3lS6768pIbOQ&*3j;yu=x*T;K~K0LqIM5| za&F`WCckjV$pi0EdDC3fR)0YowTBugypo2C*#erCGyTIqIlfmlCjk5tBXF~KYI;We zuXtuw*dNgzF;|%y_``>_%&n(SfEOkX&5gHO0jsQ}pQnWn6fzc6z%I(5^0du&UV%x^ zP)Q^b!vu+gV%+b9<}m%&FFM;5eVu0g^6}VW!|8vzGY{Q-wWu4rxdPtnR)}`id@EUl zquSfq+1cAGuM^MC8aLy{lzjBU#`SJ$_K6{w;c2n;qi&yz2R@48E65~39jdYwHJ5lb zGMNmRwz-HfaBd@z<8K_@>*G@!n;TX?e(i^$np@VrW`QeR?sDoh#1Ir*Oi0SSPflqx z`CXDmR`@~7LwOw*w$9>do}Ly&)Ki5L)y*v3299n z$*F9hiU?AH4Z9bLnEW8_?vs?fb~3>GT~&%5)|=kHru^VA#qpyKvVk9p+iqlP$&1$O8X*2nn|Zp@2`+i>n?x9|nuH)_wfgE)~tv;eA4GxXd z-7rvE-UJiOxd22jT1twzfo$w?2brw# zU0do" @@ -33,6 +27,17 @@ 查阅字典这个小学生必备技能,实际上就是著名的「二分查找」。从数据结构的角度,我们可以把字典视为一个已排序的「数组」;从算法的角度,我们可以将上述查字典的一系列操作看作是「二分查找」算法。 +**例二:整理扑克**。我们在打斗地主时,每局都需要整理扑克牌,使其从小到大排列,实现流程如下: + +1. 将扑克牌划分为“有序”和“无序”两部分,并假设初始状态下最左 1 张扑克牌已经有序。 +2. 在无序区间抽出一张扑克牌,插入至有序区间的正确位置;完成后最左 2 张扑克已经有序。 +3. 在无序区间抽出一张扑克牌,插入至有序区间的正确位置;完成后最左 3 张扑克已经有序。 +4. 不断循环以上操作,直至所有扑克牌都有序后终止。 + +以上整理扑克牌的方法本质上就是「插入排序」,它在处理小型数据集时非常高效,因此插入排序常作为编程语言的排序库函数的重要组成部分。 + +![扑克排序步骤](algorithms_are_everywhere.assets/playing_cards_sorting.png) + **例三:货币找零**。假设我们在超市购买了 $69$ 元的商品,给收银员付了 $100$ 元,则收银员需要给我们找 $31$ 元。他会很自然地完成以下思考: 1. 可选项是比 $31$ 元面值更小的货币,包括 $1$ , $5$ , $10$ , $20$ 元。 @@ -43,7 +48,7 @@ 在以上步骤中,我们每一步都采取当前看来最好的选择(尽可能用大面额的货币),最终得到了可行的找零方案。从数据结构与算法的角度看,这种方法本质上是「贪心算法」。 -![货币找零](algorithms_are_everywhere.assets/greedy_change.png) +![货币找零过程](algorithms_are_everywhere.assets/greedy_change.png) 小到烹饪一道菜,大到星际航行,几乎所有问题的解决都离不开算法。计算机的出现使我们能够通过编程将数据结构存储在内存中,同时编写代码调用 CPU 和 GPU 执行算法。这样一来,我们就能把生活中的问题转移到计算机上,以更高效的方式解决各种复杂问题。 diff --git a/docs/chapter_introduction/summary.md b/docs/chapter_introduction/summary.md index 5901832b0..cb24607ef 100644 --- a/docs/chapter_introduction/summary.md +++ b/docs/chapter_introduction/summary.md @@ -2,6 +2,8 @@ - 算法在日常生活中无处不在,并不是遥不可及的高深知识。实际上,我们已经在不知不觉中学会了许多算法,用以解决生活中的大小问题。 - 查阅字典的原理与二分查找算法相一致。二分查找体现了分而治之的重要算法思想。 +- 整理扑克的过程与插入排序算法非常类似。插入排序适合排序小型数据集。 +- 货币找零的步骤本质上是贪心算法,每一步都采取当前看来的最好选择。 - 算法是在有限时间内解决特定问题的一组指令或操作步骤,而数据结构是计算机中组织和存储数据的方式。 - 数据结构与算法紧密相连。数据结构是算法的基石,而算法则是发挥数据结构作用的舞台。 - 乐高积木对应于数据,积木形状和连接方式代表数据结构,拼装积木的步骤则对应算法。 diff --git a/docs/chapter_introduction/algorithms_are_everywhere.assets/assembling_blocks.jpg b/docs/chapter_introduction/what_is_dsa.assets/assembling_blocks.jpg similarity index 100% rename from docs/chapter_introduction/algorithms_are_everywhere.assets/assembling_blocks.jpg rename to docs/chapter_introduction/what_is_dsa.assets/assembling_blocks.jpg diff --git a/docs/chapter_introduction/what_is_dsa.md b/docs/chapter_introduction/what_is_dsa.md index a6ebb1028..6b15f1eaf 100644 --- a/docs/chapter_introduction/what_is_dsa.md +++ b/docs/chapter_introduction/what_is_dsa.md @@ -28,16 +28,20 @@ ![数据结构与算法的关系](what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png) -类比「LEGO 乐高」和「数据结构与算法」,则对应关系如下表所示。 +我们可以把数据结构与算法类比为拼装积木。一套积木,除了包含许多零件之外,还附有详细的组装说明书。我们按照说明书一步步操作,就能组装出精美的积木模型。 + +![拼装积木](what_is_dsa.assets/assembling_blocks.jpg) + +两者的详细对应关系如下表所示。
-| 数据结构与算法 | LEGO 乐高 | -| -------------- | ------------------------------- | -| 输入数据 | 未拼装的积木 | +| 数据结构与算法 | LEGO 乐高 | +| -------------- | ---------------------------------------- | +| 输入数据 | 未拼装的积木 | | 数据结构 | 积木组织形式,包括形状、大小、连接方式等 | -| 算法 | 把积木拼成目标形态的一系列操作步骤 | -| 输出数据 | 积木模型 | +| 算法 | 把积木拼成目标形态的一系列操作步骤 | +| 输出数据 | 积木模型 |