Data Structures & Algorithms / Ordered structures and graph reasoning

Data Structures & Algorithms β€” Ordered structures and graph reasoning

Stable sorting, search trees, heaps, traversal, weighted paths, recursion, and selection.

6 lessons Β· No account required

What you will learn

  • Stable sorting, search trees, heaps, traversal, weighted paths, recursion, and selection.

  1. Sorting, stability, and merge invariants

    Preserve a sorted permutation, define equal-key behavior, and account for preparation and copying costs.

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  2. Binary search trees and traversals

    Use subtree ordering rather than local guesses, and express search cost in terms of actual height.

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  3. Heaps, priorities, and streaming top-k

    Use the heap invariant for extremum access and keep tie-breaking, replacement, and stale entries explicit.

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  4. Graph representation, BFS, and DFS

    Define vertices and edges explicitly, then preserve discovery and unfinished-traversal invariants.

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  5. Weighted shortest paths and relaxation

    Choose an algorithm from weight assumptions and preserve current-distance authority when priority entries become obsolete.

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  6. Recursion, divide and conquer, and selection

    Prove decreasing subproblems, distinguish call depth from total work, and select only as much order as the task needs.

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