14 课，从数数的道理讲到算法优化——每课拆子任务、带手推演算和答案
| 01 计数原理：加法与乘法 | Counting Principles: Addition & Multiplication |
| 02 排列：顺序有关系的计数 | Permutations (Order Matters) |
| 03 组合：顺序没关系的计数 | Combinations (Order Does Not Matter) |
| 04 杨辉三角：数字金字塔 | Pascal's Triangle |
| 05 倍增法：快速幂 | Doubling Method: Fast Power (Exponentiation by Squaring) |
| 06 一元一次与二元一次方程 | Linear Equations (One / Two Variables) |
| 07 平面几何：面积计算 | Plane Geometry: Areas (Rectangle, Triangle, Circle) |
| 08 最小生成树：Kruskal 算法 | Minimum Spanning Tree: Kruskal's Algorithm |
| 09 Prim 算法：从一点长成一棵树 | Prim's Algorithm (Grow a Tree from One Vertex) |
| 10 Dijkstra：单源最短路 | Dijkstra's Algorithm (Single-Source Shortest Path) |
| 11 Floyd：任意两点最短路 | Floyd-Warshall Algorithm (All-Pairs Shortest Paths) |
| 12 图论工具箱：选对工具 | Graph Algorithm Toolbox (Choosing the Right Tool) |
| 13 时间和空间复杂度分析 | Time and Space Complexity Analysis |
| 14 算法优化：同样的事做得更快 | Algorithm Optimization (Doing the Same Job Faster) |
| 加法原理（分类做，相加） | Addition Principle (Categories → Add) |
| 乘法原理（分步做，相乘） | Multiplication Principle (Steps → Multiply) |
| 排列 / 顺序有关系 | Permutation (Order Matters) |
| A(n,k) 排列数 | Arrangement Number A(n, k) |
| 全排列 / 阶乘 n! | Permutations of All n Elements / Factorial n! |
| 组合 / 顺序没关系 | Combination (Order Does Not Matter) |
| C(n,k) 组合数 | Combination Number C(n, k) |
| 握手问题 | Handshake Problem |
| 杨辉三角 | Pascal's Triangle |
| 倍增法 | Doubling / Exponentiation by Squaring |
| 快速幂 | Fast Power (a^b in O(log b)) |
| 二进制拆分指数 | Binary Expansion of the Exponent |
| 一元一次方程 | Linear Equation in One Variable |
| 二元一次方程 / 方程组 | Linear Equation in Two Variables / System of Equations |
| 消元法 | Elimination |
| 面积 / 周长 | Area / Perimeter |
| 圆面积 πr² / 周长 2πr | Circle Area πr² / Circumference 2πr |
| 生成树 | Spanning Tree |
| 最小生成树（MST） | Minimum Spanning Tree (MST) |
| 环 / 成环判断 | Cycle / Cycle Detection |
| 并查集 / 同组表 | Union-Find (Disjoint Set) |
| Kruskal 算法 | Kruskal's Algorithm |
| Prim 算法 | Prim's Algorithm |
| 单源最短路 | Single-Source Shortest Path |
| Dijkstra 算法 | Dijkstra's Algorithm |
| 松弛操作 | Edge Relaxation |
| 全源最短路 | All-Pairs Shortest Paths |
| Floyd-Warshall 算法 | Floyd-Warshall Algorithm |
| 时间复杂度 | Time Complexity |
| 空间复杂度 | Space Complexity |
| 大 O 记号 | Big O Notation |
| 前缀和 | Prefix Sum |
| 等差数列求和公式 | Sum of an Arithmetic Series |
| 滚动数组 | Rolling Array |
| 空间换时间 | Space for Time |