There are n + k - 1 diagonals, on each of them running time is at most O(n) due to the given inequalities, so the total running time is O((n + k)n) = O(n2). We then use CHT to get values for all $$$j$$$ on $$$i$$$-th row in $$$O(n)$$$ time. First, for each suffix, we compute the number of Guernseys minus the number of Holsteins and store it in the suffix array. k). If we fix $$$j$$$ then in the formula above, $$$sum[j] \cdot j - wsum[j]$$$ is a constant that we can ignore and focus on $$$-sum(k) \cdot j + wsum(k) + dp[i - 1][k]$$$ and for each $$$k$$$ define a line $$$hx + m$$$ where $$$h = -sum(k)$$$ and $$$m = wsum(k) + dp[i - 1][k]$$$. You said "at most n" what brings 0 bits of information since k<=n. Alien's optimization? Read This article before solving Knuth optimization problems. We can have much fewer cases to take care for. Dynamic Programming II; Codeforces Mysterious Present; Chain Reaction; Python Indentation; Find the Bug Find the Bug #8; Vanilla Problems 0/1 Knapsack; References Overlapping Subproblems; Travelling Salesman Problem; Knapsack Problem Define $$$dp_{i,j}$$$ to be the minimum cost if we split the first $$$i$$$ plants into $$$j$$$ groups. use this archive https://web.archive.org/web/20181030143808/http://wcipeg.com/wiki/Convex_hull_trick. I found a good Tutorial on 2d-dp Matrix Exponentiation. What is wrong here? But in some specific case as $$$Knapsack_{\ 0/1}$$$ problem, where we can have some good observations with optimizing algorithm by remove as many not-good cases as possibles. optimizing the optimization technique itself? https://web.archive.org/web/20181030143808/http://wcipeg.com/wiki/Convex_hull_trick. We define dp[i] to be the minimum number of Guernsey majority or tied districts with the first i pastures. Ofcourse in some cases it will break the $$$space-optimization$$$ tricks, and we have to store data by another ways to reduce the time (like using global variables, passing reference data), Sometimes by changing DP-states will results in another way of computing the results, thus will change the complexity, Data structure stream #3: New Year Prime Contest 2021, The only programming contests Web 2.0 platform, What is the sufficient condition of applying, https://codeforces.com/blog/entry/8192#comment-491779), https://www.hackerrank.com/contests/monthly/challenges/alien-languages, https://www.youtube.com/watch?v=OrH2ah4ylv4, https://cp-algorithms.com/dynamic_programming/divide-and-conquer-dp.html, Educational Codeforces Round 102 (Rated for Div. can someone help me plz <3. General Idea for Solving Chess based problems, Number of subarrays with sum less than K, using Fenwick tree, AtCoder Regular Contest #111 Livesolve [A-D], Codeforces Round #318 [RussianCodeCup Thanks-Round] Editorial, Why rating losses don't matter much (alternate timelines part II), Educational Codeforces Round 99 Editorial. (i know that this can be used for reduce one state of the dp performing a binary search on a constant and add this on every transition until the realized number of transition for reach the final state become the desired). Normally Iterative-DP runs faster than Recursive-DP. Say the state is as follows: I am finding it hard to reduce it to any less than O(n * m) for finding dp[n][m], I guess you should ask it after the Long Challenge. We define dp[i] to be the minimum number of Guernsey majority or tied districts with the first i pastures. orz indy256 meta-san. This shows that when we advance $$$j$$$ to $$$j+1$$$ we can ignore any $$$k<\hat k$$$ which allows us to apply divide and conquer. dp[a] > dp[b] : suffix[a] >= suffix[b] which is true if a will never be the optimal value for k in the future. Applying that to NKLEAVES we get: where $$$C = sum[j] \cdot j - wsum[j]$$$ is a constant when we fix $$$j$$$, $$$F(k) = wsum(k) + dp[i - 1][k]$$$, $$$b(k) = -sum(k)$$$, $$$a(j) = j$$$. Codeforces. What is the meaning of table , how to apply them , suppose row 1 in table 1 , what to do ? orz indy256 meta-san. So dp[i] = min(f(k, i)) for k < i, where f(k, i) = dp[k] + (suffix[k] - suffix[i + 1] >= 0). A2 Online Judge (or Virtual Online Contests) is an online judge with hundreds of problems and it helps you to create, run and participate in virtual contests using problems from the following online judges: A2 Online Judge, Live Archive, Codeforces, Timus, SPOJ, TJU, SGU, PKU, ZOJ, URI. After some simplification, we have: where $$$sum(k) = \sum\limits_1^k w(i)$$$ and $$$wsum(k) = \sum\limits_1^k i \cdot w(i)$$$ which we can precompute. For ex. dp[a] > dp[b] : suffix[a] >= suffix[b] which is true if a will never be the optimal value for k in the future. Problem 6 [ leetcode 32 ] [ dynamic programming optimization techniques competitive-programming data-structures Codeforces dynamic-programming greedy-algorithms codeforces-solutions Updated. How to bring the dp of NKLEAVES to the form of convex hull optimization from. In combinatorics, C ( n-1, m-1 ) programming ] dynamic query with dynamic records in SQL Global. By indy256, 7 years ago, Several recent problems on Codeforces concerned dynamic programming optimization techniques of convex optimization. Shriram Krishnamurth that covers the subtle distinction between the two techniques ( in English ) all... 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