📚 A* Strategies for Decision Mathematics 1 AB | 决策数学1 AB高分技巧
Decision Mathematics 1 is a distinctive module in Further Maths that focuses on algorithms, networks, and optimisation. To score top marks, you need not only to memorise step-by-step procedures but also to interpret questions, avoid careless errors, and present your working clearly. This article shares high-scoring techniques that will help you tackle every topic with confidence.
决策数学1是进阶数学中独特的一个模块，重点研究算法、网络和优化。要拿到高分，你不仅需要熟记分步程序，还要理解题目、避免粗心错误，并清晰展示解题过程。本文分享高分技巧，助你自信应对每个专题。
1. Understanding the Big Picture of D1 | 理解D1的整体框架
Before diving into individual algorithms, build a mental map of the entire specification. D1 typically covers algorithms (sorting, searching), graph theory (trees, paths), network flows, critical path analysis, linear programming, and matching. Seeing how these topics connect helps you select the right method quickly.
在深入学习每个算法之前，先建立整个课程内容的思维导图。D1通常涵盖算法（排序、搜索）、图论（树、路径）、网络流、关键路径分析、线性规划和匹配。看出这些专题之间的联系，能帮助你快速选择合适的解题方法。
For example, both the minimum spanning tree and shortest path problems operate on weighted graphs, but they ask different questions. Keeping a topic overview in mind prevents you from confusing Dijkstra’s algorithm with Prim’s algorithm under exam pressure.
例如，最小生成树和最短路径问题都基于加权图，但问题不同。心中有一个专题总览，可以避免在考试压力下把Dijkstra算法和Prim算法搞混。
2. Sorting Algorithms: Bubble, Shuttle, and Quick Sort | 排序算法：冒泡排序、穿梭排序和快速排序
Sorting algorithms are examined both for their mechanics and for efficiency comparisons. Make sure you can perform each sort by hand on a small list (usually 6–8 numbers). Always write the list at each pass or pivot selection – even if the question only asks for the number of comparisons, clear working earns method marks.
排序算法既考查操作过程，也考查效率对比。确保你能够手工对一个小型列表（通常6–8个数字）执行每种排序。即使题目只要求给出比较次数，也要写出每一趟或每个枢轴的选择过程——清晰的解题步骤能获得方法分。
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Bubble sort: work from left to right, compare adjacent pairs, swap if out of order. After the first pass, the largest number ‘bubbles’ to the end. You may be asked to show each pass or only the state after a given number of passes.
冒泡排序：从左向右比较相邻对，若逆序则交换。第一趟之后，最大的数“浮”到末尾。题目可能要求展示每一趟，或只展示特定趟数之后的状态。
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Shuttle sort (insertion sort): take the second number, insert it into the correct position among the elements already sorted, then take the next, and so on. Show each insertion clearly with arrows or underlining.
穿梭排序（插入排序）：取第二个数，将其插入前面已排序部分的正确位置，然后取下一个数，以此类推。每次插入要用箭头或下划线清晰标出。
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Quick sort: select a pivot (usually the middle or first item), partition into sublists of numbers less than and greater than the pivot. Repeat recursively. Clearly indicate the pivot and the sublists at each stage. Keep track of comparisons: many marks are lost by forgetting to count comparisons during the partitioning step.
快速排序：选择一个枢轴（通常是中间项或首项），将列表划分为小于枢轴和大于枢轴的子列表。递归进行。清晰标出每个阶段的枢轴和子列表。记录比较次数：许多失分是因为在划分步骤中忘记计数比较。
For all sorts, use abbreviations such as L and R for left and right pointers to save time, but define them once. In the exam, box your final sorted list and state the total number of comparisons / swaps explicitly.
对于所有排序，可用L和R等缩写表示左右指针以节省时间，但要定义一次。考试中，将最终排序列表框起来，并明确写出总比较/交换次数。
3. Graph Terminology and Notation | 图论术语与符号
Master the vocabulary: vertices (nodes), edges (arcs), degree (valency), directed, undirected, weighted, complete, connected, path, cycle, tree, spanning tree, and network. Many students lose marks by mislabelling or misinterpreting graph features.
掌握术语：顶点（节点）、边（弧）、度（价）、有向、无向、加权、完全图、连通图、路径、回路、树、生成树和网络。很多学生因错误标注或错误理解图的性质而失分。
Often, you must draw a graph from a distance matrix or a description. Practise sketching neat, well-labelled diagrams. Use straight edges for undirected graphs and arrowheads for directed ones. If a vertex has a loop, add a curved edge returning to the same vertex.
通常你需要根据距离矩阵或描述画图。练习画出整洁、标注清晰的草图。无向图用直线边，有向图用箭头。如果顶点有自环，则添加一条返回同一顶点的弯曲边。
When a question asks for the ‘order’ of a node, it means the number of edges incident to it; for directed graphs, distinguish in-degree and out-degree.
当题目要求节点的“阶”时，是指与之关联的边数；对于有向图，要区分入度和出度。
4. Minimum Spanning Trees (Kruskal and Prim)
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