Concepts106
Interval DP
Interval DP solves problems where the optimal answer for a segment [i, j] depends on answers of its subsegments.
Tree DP - Matching and Covering
Tree DP solves matching, vertex cover, and independent set on trees in linear time using small state transitions per node.
Bitmask DP
Bitmask DP compresses the state of a subset of n elements into an integer mask, enabling elegant dynamic programming over all subsets.
Longest Common Subsequence
The Longest Common Subsequence (LCS) between two sequences is the longest sequence that appears in both, not necessarily contiguously.
Bitmask DP - Subset Enumeration
Bitmask DP subset enumeration lets you iterate all submasks of a given mask using the idiom for (s = mask; s > 0; s = (s - 1) & mask).
DP on Trees
DP on trees is a technique that computes answers for each node by combining results from its children using a post-order DFS.
Edit Distance
Edit distance (Levenshtein distance) measures the minimum number of inserts, deletes, and replaces needed to turn one string into another.
2-SAT
2-SAT solves Boolean formulas where every clause has exactly two literals, and it is solvable in linear time relative to the size of the implication graph.
Euler Path and Circuit
An Euler path visits every edge exactly once, and an Euler circuit is an Euler path that starts and ends at the same vertex.
Knapsack Problems
Knapsack problems ask how to pick items under a weight (or cost) limit to maximize value or to check if a target sum is reachable.
Coin Change and Variants
Coin Change uses dynamic programming to find either the minimum number of coins to reach a target or the number of ways to reach it.
Linear Basis for XOR
A linear basis for XOR is a compact set of at most W numbers (W = number of bits) that can generate every XOR value obtainable from a multiset of numbers.