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Dynamic Programming
D&C and Knuth Optimization
Problemset
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Recursion Fundamentals
0/42
Dynamic Programming Fundamentals
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1D DP
0/41
Multi-Dimensional DP
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Knapsack
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Knapsack Variations
0/46
Prefix Sums
0/44
Longest Increasing Subsequence
0/47
LCS and Edit Distance
0/41
Interval DP
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DP on Trees
0/43
Bitmask DP
0/42
Digit DP
0/42
Game Theory DP
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Probability DP
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D&C and Knuth Optimization
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1
Intro
2
When Naive DP Fails
3
Vocabulary - Quadrangle Inequality
4
Quiz: Quadrangle Inequality
5
Why QI Implies Monotonicity
6
Quiz: Monotonicity Implication
7
D&C and Knuth Overview
8
What Is D&C Optimization?
9
The D&C Recursion
10
D&C Recursion - Walkthrough
11
Why D&C Is O(n log n)
12
Quiz: D&C Complexity
13
Visualizing D&C
14
Codeforces 321E Ciel and Gondola - Problem Statement
15
Codeforces 321E Ciel and Gondola - The DP
16
Codeforces 321E Ciel and Gondola - Why QI Holds
17
Codeforces 321E Ciel and Gondola - Implementation
18
Codeforces 321E Ciel and Gondola - Walkthrough
19
Lessons from D&C Optimization
20
Challenge: Proving QI
21
What Is Knuth's Optimization?
22
The Double Bound
23
The Iteration Order
24
Knuth's Optimization - Walkthrough
25
Why O(n²) Total
26
Visualizing Knuth
27
Optimal BST - Problem Statement
28
Optimal BST - The DP
29
Optimal BST - Why QI Holds
30
Optimal BST - Implementation
31
Optimal BST - Walkthrough
32
Lessons from Knuth's Optimization
33
Breaking a String - Problem Statement
34
Breaking a String - Implementation
35
Printing Neatly - Problem Statement
36
Server Allocation - Problem Statement
37
Server Allocation - Implementation
38
D&C vs Knuth
39
Quiz: Knuth vs D&C
40
Common Mistakes
41
Challenge: When QI Fails
42
Challenge: Combining with Other Techniques
43
Pattern - Quadrangle Optimizations
44
Implementation Checklist
45
Practice - Identify the Optimization
46
What's Next
47
Section Recap
Convex Hull Trick
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Monotonic Queue Optimization
0/45
Aliens Trick (WQS Binary Search)
0/41
Slope Trick
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Broken Profile DP (Plug DP)
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16.1
Intro
4 minutes
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Tasks
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