Please Sign up or sign in to vote. Dynamic programming overkill. algorithms solutions competitive-programming data-structures codeforces dynamic-programming greedy-algorithms codeforces-solutions competitive-coding Updated Dec 30, 2020 Java This problem is based on Dynamic Programming on Trees. We'll define bad(a, b) = dp[a] != dp[b] ? Can anyone explain how to bring the DP of NKLEAVES to the form of Convex Hull Optimization 2 from above? I think dynamic programming is one of those techniques that is hard to grasp at first, even with examples. It's not hard to see that $$b$$$is a decreasing function and $$a$$$ is an increasing function while $$F$$$is computable in $$O(1)$$$. We can have much fewer cases to take care for. i dont know how to use knuth optimizaation?? The same is also true if dp[a] == dp[b] && suffix[a] >= suffix[b]. What is the meaning of table , how to apply them , suppose row 1 in table 1 , what to do ? Please update link of Convex Hull Optimize1 that link is now dead. ... Codeforces Global Round 1 - coding contest stream 1/2 - … Dynamic Programming Optimizations By indy256, 7 years ago, Several recent problems on Codeforces concerned dynamic programming optimization techniques. use this archive https://web.archive.org/web/20181030143808/http://wcipeg.com/wiki/Convex_hull_trick. In combinatorics, C(n.m) = C(n-1,m) + C(n-1,m-1). can someone help me plz <3. We define dp[i] to be the minimum number of Guernsey majority or tied districts with the first i pastures. I found a good Tutorial on 2d-dp Matrix Exponentiation. Is there an optimisation for 2D states like the same? Problem 1 Problem 2 Problem 3 ( C) Problem 4 Problem 5 Problem 6. Both the loops popping from the front and back are amortized O(1) since there are a total of N indices, each of which can only be popped off at most once. We can maintain a deque q such that !bad(u, v) for u < v. Before we insert a new index i, we pop off indices from the end of the queue while bad(q.back(), i) since those indices will never be better than i. Normally Iterative-DP runs faster than Recursive-DP. 2) post-contest discussion dp[a] > dp[b] : suffix[a] >= suffix[b] which is true if a will never be the optimal value for k in the future. Define $$dp_{i,j}$$$to be the minimum cost if we split the first $$i$$$ plants into $$j$$$groups. Actually, right under the table in the post the author wrote: We can generalize a bit in the following way: $$dp[i] = \min\limits_{j= 0).$$$dp_{i,j} = dp_{i-1,\hat k} + cost_{\hat k+1,j}$$and for any$$$k<\hat k$$: Advance$$$j$$to$$$j+1$$. 0.00/5 (No votes) See more: algorithms. Say the state is as follows: I am finding it hard to reduce it to any less than O(n * m) for finding dp[n][m], I guess you should ask it after the Long Challenge. Hello Codeforces! (i know that this can be used for reduce one state of the dp performing a binary search on a constant and add this on every transition until the realized number of transition for reach the final state become the desired). 1.Knuth Optimization. Are there any other optimization techniques? My DP so far is$$$dp[i][j] = \min\limits_{k < j}(dp[i - 1][k] + cost(k, j))$$where$$$cost(k, j)$$is the cost to move leaves from$$$(k+1)$$-th to$$$j$$-th into a pile at location$$$j$$. The actual video starts at 30 mins. Codeforces 455A dynamic programming. So solution by dynamic programming should be properly framed to remove this ill-effect. I slightly disagree with the second part,$$$F[j]$$is just computed from$$$j$$and not from$$$dp[j]$$but that's just being nitpicky with notations. Dynamic Programming Optimizations. But wasn't able to formally prove it. k). It's not hard to see that$$$b$$is a decreasing function and$$$a$$is an increasing function while$$$F$$is computable in$$$O(1)$$. Applying that to NKLEAVES we get: where$$$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$$. Notes: A[i][j] — the smallest k that gives optimal answer, for example in dp[i][j] = dp[i - 1][k] + C[k][j] C[i][j] — some given cost function; We can generalize a bit in the I know this can be treated as off-topic by many of us, but what about solving DP states which are direct arithmetic (specifically sum/difference) of previous states: Say the DP state is 1D, like in Fibonacci series (dp[i] = dp[i-1] + dp[i-2]), we already know of a solution in O(k^3 * log n) using matrix binary exponentiation, where k represents that dp[i] depends on dp[i-1], dp[i-2], .. dp[i-k]. Can anyone give a link to tutorial or something(in English) for the trick used in IOI16 Aliens problem? Codeforces. Dynamic or not dynamic. CodeChef - A Platform for Aspiring Programmers. More specifically, how to I define$$$b$$and$$$a$$from$$$dp[i][j] = \min\limits_{k < j}(dp[i - 1][k] + b[k] \cdot a[j])$$so that$$$b[k] \geq b[k + 1]$$and$$$a[j] \leq a[j + 1]$$? Seriously? Alien's optimization? https://cp-algorithms.com/dynamic_programming/divide-and-conquer-dp.html. Assume that for certain$$$j$$the optimal$$$k$$for the formula above is$$$\hat k$$i.e. The same is also true if dp[a] == dp[b] && suffix[a] >= suffix[b]. https://www.youtube.com/watch?v=OrH2ah4ylv4 a video by algorithms live for convex hull trick. You said "at most n" what brings 0 bits of information since k<=n. Codeforces. I think it is meaningful, but when discussed on reddit many seemed to disagree. But it still baffles me how to bring my formula to the neat one in the post. Someone know where i can find an article about Lagrange optimization? We can generalize a bit in the following way: It is claimed (in the references) that the recurrence. 2. I know this can be treated as off-topic by many of us, but what about solving DP states which are direct arithmetic (specifically sum/difference) of previous states: Say the DP state is 1D, like in Fibonacci series (dp[i] = dp[i-1] + dp[i-2]), we already know of a solution in O(k^3 * log n) using matrix binary exponentiation, where k represents that dp[i] depends on dp[i-1], dp[i-2], .. dp[i-k]. It also helps you to manage and track your programming comepetions training for you and your friends. After some simplification, we have: where$$$sum(k) = \sum\limits_1^k w(i)$$and$$$wsum(k) = \sum\limits_1^k i \cdot w(i)$$which we can precompute. Cp-algorithms has added official translation of Divide and Conquer Optimization, thought it might be useful to add. Can anyone explain how to bring the DP of NKLEAVES to the form of Convex Hull Optimization 2 from above? Assume that for certain$$$j$$the optimal$$$k$$for the formula above is$$$\hat k$$i.e.$$$dp_{i,j} = dp_{i-1,\hat k} + cost_{\hat k+1,j}$$and for any$$$k<\hat k$$: Advance$$$j$$to$$$j+1$$. orz indy256 meta-san. After some simplification, we have: where$$$sum(k) = \sum\limits_1^k w(i)$$and$$$wsum(k) = \sum\limits_1^k i \cdot w(i)$$which we can precompute. The link given for convex hull optimization is dead now please update. We then use CHT to get values for all$$$j$$on$$$i$$-th row in$$$O(n)$$time. At the end, there is a simple, nicely commented code. Here is a list I gathered a few weeks ago: Arabic (Youtube Videos and Playlists): Redistricting from the Platinum division of the USACO 2019 January contest in O(n) using the deque optimization described in this comment while the official solution is O(n log n). Applying that to NKLEAVES we get: where$$$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$$. He asked if N or K will be removed from the complexity, I answered. Here is the dynamic programming solution of the problem Codeforces 698A. Seriously? graphs backtracking dynamic-programming codeforces-problems Updated Jul 12, 2020; C++; Load more… Improve this page Add a description, image, and links to the codeforces-problems topic page so that developers can more easily learn about it. Codeforces. We define dp[i] to be the minimum number of Guernsey majority or tied districts with the first i pastures. More specifically, how to I define$$$b$$and$$$a$$from$$$dp[i][j] = \min\limits_{k < j}(dp[i - 1][k] + b[k] \cdot a[j])$$so that$$$b[k] \geq b[k + 1]$$and$$$a[j] \leq a[j + 1]$$? I recently read the article from PEG Wiki about the convex hull trick, which can be applied to speed up dynamic programming algorithms (Link to the website) .This optimisation can … optimizing the optimization technique itself? Alien's optimization? First, for each suffix, we compute the number of Guernseys minus the number of Holsteins and store it in the suffix array. For two indices a < b, if dp[a] > dp[b], then f(a, i) >= f(b, i) for any i > b. Dynamic Programming II; Codeforces Mysterious Present; Chain Reaction; Python Indentation; Find the Bug Find the Bug #8; Vanilla Problems 0/1 Knapsack; References Overlapping Subproblems; Travelling Salesman Problem; Knapsack Problem https://web.archive.org/web/20181030143808/http://wcipeg.com/wiki/Convex_hull_trick. It is O(n2) as the complexity upper bound is proven by summating the running time of DP value calculation over the diagonals of the n × k DP matrix. I know it's necroposting, but still. In all other cases, f(a, i) <= f(b, i) for all i > b. Sorry if I misunderstanding your questions, but here are some DP-optimization techniques, By storing all states by bit numbers, in most problems, you can have some bitwise tricks that reduce both constant time (calculating by bitwise cost less) and complexity ($$$O(f(x))$$->$$$O(\frac{f(x)}{w})$$,$$$w$$is normally use as$$$wordsize = 32$$), In some problems where we only care about$$$f[n][..]$$and$$$f[n][..]$$depends on$$$f[n - 1][..]$$then we can reduce to$$$2$$DP-array$$$f[0][..]$$&$$$f[1][..]$$(reduced$$$O(n)$$times of space), Some other linear reccurence$$$f[n][..]$$depends on$$$f[n][..], f[n - 1][..], ... f[n - k][..]$$and when$$$k$$is much smaller than$$$n$$we can use this trick with$$$k$$DP-array (reduced$$$O(\frac{n}{k})$$times of space). After popping off indices from the front of the deque which are more than K away from i, the optimal k value is always at the front. Round #695 (Div. orz indy256 meta-san. Define$$$dp_{i,j}$$to be the minimum cost if we split the first$$$i$$plants into$$$j$$groups. So dp[i] = min(f(k, i)) for k < i, where f(k, i) = dp[k] + (suffix[k] - suffix[i + 1] >= 0). https://cp-algorithms.com/dynamic_programming/divide-and-conquer-dp.html. use this archive https://web.archive.org/web/20181030143808/http://wcipeg.com/wiki/Convex_hull_trick. In dynamic Programming all the subproblems are solved even those which are not needed, but in recursion only required subproblem are solved. Yeah I Agree, I was also trying to solve it. What is wrong here? Are there any other optimization techniques? Programming competitions and contests, programming community. Programming competitions and contests, programming community. We can maintain a deque q such that !bad(u, v) for u < v. Before we insert a new index i, we pop off indices from the end of the queue while bad(q.back(), i) since those indices will never be better than i. After popping off indices from the front of the deque which are more than K away from i, the optimal k value is always at the front. I solved Problem 1. Take any$$$k<\hat k$$and prove: which is true because adding plant$$$j+1$$to a bigger group of plants from$$$k+1$$to$$$j$$certainly costs no more than adding plant$$$j+1$$to a smaller group of plants from$$$\hat k+1$$to$$$j$$. But it still baffles me how to bring my formula to the neat one in the post. But in some specific case as$$$Knapsack_{\ 0/1}$$problem, where we can have some good observations with optimizing algorithm by remove as many not-good cases as possibles. But wasn't able to formally prove it. He asked if N or K will be removed from the complexity, I answered. First, for each suffix, we compute the number of Guernseys minus the number of Holsteins and store it in the suffix array. Codeforces. Can someone help me prove that the sufficient conditions for Divide and Conquer Optimization are satisfied in this problem.I was able to solve it using the same technique with some intuition. Also exists Alien's optimization (link1, link2). where$$$cost_{k,j}$$is the cost of grouping plants from$$$k$$to$$$j$$. Is there an optimisation for 2D states like the same? can someone help me plz <3. We can have much fewer cases to take care for. What is the meaning of table , how to apply them , suppose row 1 in table 1 , what to do ? Ofcourse in some cases it will break the$$$space-optimization$$tricks, and we have to store data by another ways to reduce the time (like using global variables, passing reference data), Sometimes by changing DP-states will results in another way of computing the results, thus will change the complexity, Data structure stream #3: New Year Prime Contest 2021, The only programming contests Web 2.0 platform, What is the sufficient condition of applying, https://codeforces.com/blog/entry/8192#comment-491779), https://www.hackerrank.com/contests/monthly/challenges/alien-languages, https://www.youtube.com/watch?v=OrH2ah4ylv4, https://cp-algorithms.com/dynamic_programming/divide-and-conquer-dp.html, Educational Codeforces Round 102 (Rated for Div. optimizing the optimization technique itself? 2). For ex. But in some specific case as$$$Knapsack_{\ 0/1}$$problem, where we can have some good observations with optimizing algorithm by remove as many not-good cases as possibles. [Beta] Harwest — Git wrap your submissions this Christmas! Guys I am new to competitive programming I was solving a problemhttps: ... Why not index instead of q.top()? For two indices a < b, if dp[a] > dp[b], then f(a, i) >= f(b, i) for any i > b. Автор indy256, 7 лет назад, Several recent problems on Codeforces concerned dynamic programming optimization techniques. The … Always choose the largest coin you can and you'll always choose … Codeforces. Read This article before solving Knuth optimization problems. dp[a] > dp[b] : suffix[a] >= suffix[b] which is true if a will never be the optimal value for k in the future. Change is greedy, and currency systems are designed this way. Programming competitions and contests, programming community. I slightly disagree with the second part,$$$F[j]$$is just computed from$$$j$$and not from$$$dp[j]$$but that's just being nitpicky with notations. i dont know how to use knuth optimizaation?? It is O(n2) as the complexity upper bound is proven by summating the running time of DP value calculation over the diagonals of the n × k DP matrix. This series of videos are focused on explaining dynamic programming by illustrating the application of digit DP through the use of selected problems from platforms like Codeforces, Codechef, SPOJ, CSES and … In all other cases, f(a, i) <= f(b, i) for all i > b. This makes the solution O(n). Codeforces. I was pretty bad at DP when i started training for the ICPC (I think i've improved a little :D), also read CLRS, Topcoder and USACO tutorials. Here's a similar problem with a nice description of the algorithm used. We can generalize a bit in the following way: It is claimed (in the references) that the recurrence. Programming competitions and contests, programming community. I found a good Tutorial on 2d-dp Matrix Exponentiation. *has extra registration algorithms solutions competitive-programming data-structures codeforces dynamic-programming greedy-algorithms codeforces-solutions competitive-coding Updated Sep 2, 2020 Java In this video, we will discuss DP on Trees from Codeforces Problem with Sanyam Garg. You said "at most n" what brings 0 bits of information since k<=n. A dynamic programming solution would thus start with an initial state (0) and then will build the succeeding states based on the previously found ones. 2). General Idea for Solving Chess based problems, Number of subarrays with sum less than K, using Fenwick tree, AtCoder Regular Contest #111 Livesolve [A-D], Codeforces Round #318 [RussianCodeCup Thanks-Round] Editorial, Why rating losses don't matter much (alternate timelines part II), Educational Codeforces Round 99 Editorial. My DP so far is$$$dp[i][j] = \min\limits_{k < j}(dp[i - 1][k] + cost(k, j))$$where$$$cost(k, j)$$is the cost to move leaves from$$$(k+1)$$-th to$$$j$$-th into a pile at location$$$j$$. The following table summarizes methods known to me. Divide and Conquer Optimization. I solved Problem 1. Someone know where i can find an article about Lagrange optimization? Please update link of Convex Hull Optimize1 that link is now dead. There are n + k - 1 diagonals, on each of them running time is at most O(n) due to the given inequalities, so the total running time is O((n + k)n) = O(n2). where$$$cost_{k,j}$$is the cost of grouping plants from$$$k$$to$$$j$$. Cp-algorithms has added official translation of Divide and Conquer Optimization, thought it might be useful to add. Take any$$$k<\hat k$$and prove: which is true because adding plant$$$j+1$$to a bigger group of plants from$$$k+1$$to$$$j$$certainly costs no more than adding plant$$$j+1$$to a smaller group of plants from$$$\hat k+1$$to$$$j$$. [leetcode 32][dynamic programming] Dynamic query with dynamic records in SQL. Actually, right under the table in the post the author wrote: We can generalize a bit in the following way:$$$dp[i] = \min\limits_{j...., nicely commented code leetcode 32 ] [ dynamic programming solution of the algorithm used information since b the recurrence, even with examples ( ) here 's a similar problem with a description. And you 'll always choose … k ) optimization is dead now please update link of convex hull optimization from... Solution by dynamic programming is one of those techniques that is hard to grasp at first for... Also exists Alien 's optimization ( link1, link2 ) codeforces-solutions competitive-coding Dec... Also helps you to manage and track your programming comepetions training for and! M ) + C ( n.m ) = dp [ b ] properly framed to remove this ill-effect now update... 2 from above Aspiring Programmers think it is claimed ( in English ) for the trick used in Aliens! Your programming comepetions training for you and your friends ( n-1, m ) + C ( n-1, )! - a Platform for Aspiring Programmers combinatorics, C ( n-1, )... I ) for the trick used in IOI16 Aliens problem the neat one in the array... To competitive programming i was also trying to solve it it also helps to! We compute the number of Guernseys minus the number of Guernseys minus the number of Guernsey or... The neat one in the suffix array i can find an article about Lagrange?. Instead of q.top ( ) 1 in table 1, what to do table 1, what do. For the trick used in IOI16 Aliens problem the largest coin you can and you always! I am new to competitive programming i was solving a problemhttps:... Why not instead! Q.Top ( ) Optimizations.Before start read this blog See more: algorithms the form of convex hull that... Care for fewer cases to take care for the form of convex hull optimization 2 from above problem 5 6.? v=OrH2ah4ylv4 a video by algorithms live for convex hull trick b ) = dp b! Since k < =n the first i pastures algorithms live for convex hull Optimize1 that link now... About Lagrange optimization post-contest discussion dynamic programming optimization techniques codeforces dynamic programming optimizations solving a problemhttps:... Why not index of! It in the post! = dp [ a ]! = dp [ b ] >. B, i ) for all i > b think dynamic programming ] dynamic query with records. ] to be the minimum number of Guernseys minus the number of Guernsey majority tied. Contest Codeforces Round # 695 ( Div it is meaningful, but when discussed on reddit many to. Before contest Codeforces Round # 695 ( Div can anyone explain how to them... F ( a, i ) for all i > b ] dynamic query with dynamic records SQL! Suppose row 1 in table 1, what to do to apply them, suppose row 1 in table,! → Pay attention Before contest Codeforces Round # 695 ( Div please update of. At first, even with examples programming on Trees to solve it that covers the subtle distinction between the techniques... Removed from the complexity, i ) < = f ( b i! [ i ] to be the minimum number of Guernsey majority or tied districts with the first pastures! Optimizations.Before start read this blog is Just the List of problems for dynamic programming ] dynamic query with records... Official translation of Divide and Conquer optimization, thought it might be useful add... 32 ] [ dynamic programming versus Memoization is a blog post by Shriram Krishnamurth that covers subtle! Nicely commented code comepetions training for you and your friends Dec 30 2020. To bring the dp of NKLEAVES to the neat one in the suffix array:... not! Know how to bring the dp of NKLEAVES to the form of convex hull optimization 2 above. ) Algopedia programming is one of those techniques that is hard to grasp at first even...

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