📚 Edexcel Further Maths Decision Maths 1: Algorithms & Graphs (AB) | Edexcel 进阶数学决策数学 1：算法与图论（AB）
Decision Mathematics 1 (D1) introduces the core ideas of algorithms, graph theory and network optimisation used in Edexcel Further Mathematics. This revision guide focuses on the 'AB' topics: algorithms, graphs, networks and their applications, including sorting, searching, minimum spanning trees, shortest path problems, route inspection and critical path analysis.
决策数学 1（D1）介绍 Edexcel 进阶数学中使用的算法、图论和网络优化的核心思想。本复习指南聚焦 'AB' 主题：算法、图、网络及其应用，包括排序、查找、最小生成树、最短路径问题、路线检查和关键路径分析。
1. What Is an Algorithm? | 什么是算法？
An algorithm is a finite sequence of precise instructions that solves a problem. In D1, an algorithm must have well-defined inputs and outputs, must terminate after a finite number of steps, and each step must be clear enough to be carried out without ambiguity.
算法是解决问题的一组有限且精确的指令序列。在 D1 中，算法必须有明确的输入和输出，必须在有限步后终止，并且每一步都必须足够清晰，执行时没有歧义。
When you trace an algorithm, you should record the state of variables at each stage. Common operations include assignment (x ← y), comparison (if), and loops (for, while). These operations are the building blocks of every algorithm you will meet in the D1 exam.
跟踪算法时，你应该记录每个阶段变量的状态。常见操作包括赋值（x ← y）、比较（if）和循环（for、while）。这些操作是 D1 考试中你会遇到的每一种算法的基本构件。
An example is the first-fit bin packing algorithm, which places each item into the first bin that can hold it. Although this is not always optimal, it is quick to apply and testable as a simple algorithm.
一个例子是首次适应装箱算法，它将每个物品放入第一个能容纳它的箱子中。虽然该算法不一定总是最优，但它操作快捷，适合作为简单算法进行考查。
2. Sorting Algorithms | 排序算法
Bubble sort repeatedly compares adjacent items and swaps them if they are in the wrong order. A pass is one full scan through the list. After each pass, the largest unsorted item is usually placed in its final position.
冒泡排序反复比较相邻项目，如果顺序错误就交换它们。一趟是对列表的一次完整扫描。每趟结束后，未排序部分中最大的项通常被放到最终位置。
The maximum number of comparisons for bubble sort on n items is n(n − 1)/2. The maximum number of swaps is also n(n − 1)/2, which occurs when the list is in reverse order.
冒泡排序在 n 个项目上的最大比较次数为 n(n − 1)/2。最大交换次数也是 n(n − 1)/2，这种情况发生在列表完全逆序时。
Quick sort chooses a pivot, then places items smaller than the pivot in one sublist and items larger in another. The pivot is then fixed, and the process repeats on each sublist until all items are sorted.
快速排序选择一个基准项，然后将小于基准项的项放在一个子列表中，大于基准项的项放在另一个子
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