Algorithms and Complexity
Big-O, searching, sorting, recursion, greedy and DP - with the maths actually explained
6 lessons · 1.2 hours of reading
· Intermediate · 3 free
The algorithms paper, taught by working out the numbers instead of quoting them. You will be able to derive a running time, spot the off-by-one in binary search, and say exactly when greedy fails and DP is needed.
Lessons
1
Big-O without hand-waving
What the notation really claims, why constants are dropped, and a table of n against operations.
2
Searching: linear and binary
Binary search in full, including the two bugs that break almost every first attempt.
3
Bubble, selection and insertion sort
Three O(n squared) sorts nobody uses in production - and the real reasons they are taught.
4
Merge sort and quick sort
Divide and conquer, the recurrences solved properly, and why quick sort is the default.
5
Recursion and how to reason about it
Base case, recursive case, the call stack, and why naive Fibonacci is catastrophically slow.
6
Greedy versus dynamic programming
Coin change worked both ways, showing exactly where greedy breaks and DP does not.
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