https://jasper-aa64.github.io/tags/dp/Recent content in Dp on JasperHugoen-usTue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/matrix-1-fast-exponentiation/Tue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/matrix-1-fast-exponentiation/Matrix fast power for linear recurrences (4 patterns), 4 semiring templates (count/bool/min-plus/max-plus), matrix+segment tree for range-add Fibonacci queries, Kitamasa O(k²logn) and NTT O(k log²k logn).https://jasper-aa64.github.io/posts/matrix-4-problems/Tue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/matrix-4-problems/Hard matrix problems: Fibonacci squared subarray sum with segment-tree 4-tuple and companion matrix; cycle-decomposition partition state space for random-swap sorting, first-step analysis, and Gaussian elimination.https://jasper-aa64.github.io/posts/number-theory-3-1-sieve-problems/Tue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/number-theory-3-1-sieve-problems/Greedy optimality for divisibility-chain coin systems, DP over the maximum denomination, and a sieve-style transition by adding one larger coin.https://jasper-aa64.github.io/posts/combinatorics-order-theory/Sun, 26 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-order-theory/Chromatic polynomial, chordal/interval graphs, PEO product formula, order polynomials (chain/antichain/tree/DAG/divisor lattice), MacMahon formula, Dilworth, Mirsky, Hall’s marriage theorem, Erdős–Szekeres, missile interception.https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Polynomial representations, FFT/DFT over complex numbers, Triple Sums, Fuzzy Search (difference convolution), FFT template, Lagrange interpolation (O(n²) and O(n) equidistant), sum of k-th powers, Assigning Prizes polynomial DP.https://jasper-aa64.github.io/posts/combinatorics-1-1-permutations-combinations/Fri, 24 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-1-1-permutations-combinations/Hockey Stick identity, addition/multiplication principles, binomial identities, example problems: bitonic sequences, multiset permutations, multi-layer coloring DP, CCPC Subpermutation.https://jasper-aa64.github.io/posts/combinatorics-d1-diophantine-equations/Fri, 24 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-d1-diophantine-equations/Stars and bars, bounded Diophantine equations via inclusion-exclusion, prefix-sum DP, D&C NTT, equal-cap formula, and a full worked example on CF 2127F.