C++博客-Felicia-随笔分类-动态规划

C++博客-Felicia-随笔分类-动态规划http://www.cppblog.com/Felicia/category/4908.htmlzh-cnMon, 19 May 2008 13:28:44 GMTMon, 19 May 2008 13:28:44 GMT60[动态规划]O(n^2 / logn)的LCShttp://www.cppblog.com/Felicia/archive/2007/10/19/34618.htmlFeliciaFeliciaFri, 19 Oct 2007 08:56:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/19/34618.htmlhttp://www.cppblog.com/Felicia/comments/34618.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/19/34618.html#Feedback3http://www.cppblog.com/Felicia/comments/commentRss/34618.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/34618.html唐文斌曾经翻译过一篇论文，专门讨论这个问题。

下面是练习题（n = 10000 的LCS）
http://acm.whu.edu.cn/oak/problem/problem.jsp?problem_id=1210

和我的解答

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Felicia 2007-10-19 16:56 发表评论

]]>[动态规划] pku1458 最长公共子序列http://www.cppblog.com/Felicia/archive/2007/10/16/34380.htmlFeliciaFeliciaTue, 16 Oct 2007 14:46:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/16/34380.htmlhttp://www.cppblog.com/Felicia/comments/34380.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/16/34380.html#Feedback2http://www.cppblog.com/Felicia/comments/commentRss/34380.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/34380.html这里给出一个O(n^2)的算法，人人都会的。
但是，我想说，我所知道的最好算法，是O(n^2 / logn)的。

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Felicia 2007-10-16 22:46 发表评论

]]>[动态规划]pku1080http://www.cppblog.com/Felicia/archive/2007/10/12/34069.htmlFeliciaFeliciaFri, 12 Oct 2007 14:25:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/12/34069.htmlhttp://www.cppblog.com/Felicia/comments/34069.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/12/34069.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/34069.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/34069.html
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Felicia 2007-10-12 22:25 发表评论

]]>[动态规划]pku1338http://www.cppblog.com/Felicia/archive/2007/10/09/33851.htmlFeliciaFeliciaTue, 09 Oct 2007 13:53:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/09/33851.htmlhttp://www.cppblog.com/Felicia/comments/33851.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/09/33851.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33851.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33851.html具体实现见代码。

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Felicia 2007-10-09 21:53 发表评论

]]>[动态规划]pku3420http://www.cppblog.com/Felicia/archive/2007/10/08/33740.htmlFeliciaFeliciaMon, 08 Oct 2007 01:19:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/08/33740.htmlhttp://www.cppblog.com/Felicia/comments/33740.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/08/33740.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33740.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33740.html
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Felicia 2007-10-08 09:19 发表评论

]]>[动态规划]pku1191http://www.cppblog.com/Felicia/archive/2007/10/08/33737.htmlFeliciaFeliciaMon, 08 Oct 2007 01:12:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/08/33737.htmlhttp://www.cppblog.com/Felicia/comments/33737.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/08/33737.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/33737.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33737.html
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Felicia 2007-10-08 09:12 发表评论

]]>[动态规划]pku1179http://www.cppblog.com/Felicia/archive/2007/10/05/33515.htmlFeliciaFeliciaFri, 05 Oct 2007 08:47:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/05/33515.htmlhttp://www.cppblog.com/Felicia/comments/33515.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/05/33515.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33515.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33515.html
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Felicia 2007-10-05 16:47 发表评论

]]>[动态规划]pku1189http://www.cppblog.com/Felicia/archive/2007/10/04/33440.htmlFeliciaFeliciaThu, 04 Oct 2007 12:47:00 GMThttp://www.cppblog.com/Felicia/archive/2007/10/04/33440.htmlhttp://www.cppblog.com/Felicia/comments/33440.htmlhttp://www.cppblog.com/Felicia/archive/2007/10/04/33440.html#Feedback4http://www.cppblog.com/Felicia/comments/commentRss/33440.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33440.html
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Felicia 2007-10-04 20:47 发表评论

]]>[动态规划]pku1185http://www.cppblog.com/Felicia/archive/2007/09/30/33271.htmlFeliciaFeliciaSun, 30 Sep 2007 14:09:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/30/33271.htmlhttp://www.cppblog.com/Felicia/comments/33271.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/30/33271.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33271.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33271.html
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Felicia 2007-09-30 22:09 发表评论

]]>[动态规划]pku1163http://www.cppblog.com/Felicia/archive/2007/09/29/33228.htmlFeliciaFeliciaSat, 29 Sep 2007 14:43:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/29/33228.htmlhttp://www.cppblog.com/Felicia/comments/33228.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/29/33228.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33228.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33228.html
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Felicia 2007-09-29 22:43 发表评论

]]>[动态规划]动态规划总结 by Amberhttp://www.cppblog.com/Felicia/archive/2007/09/29/33222.htmlFeliciaFeliciaSat, 29 Sep 2007 12:25:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/29/33222.htmlhttp://www.cppblog.com/Felicia/comments/33222.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/29/33222.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/33222.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/33222.html
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Felicia 2007-09-29 20:25 发表评论

]]>[动态规划]pku3133http://www.cppblog.com/Felicia/archive/2007/09/24/32806.htmlFeliciaFeliciaMon, 24 Sep 2007 13:12:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/24/32806.htmlhttp://www.cppblog.com/Felicia/comments/32806.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/24/32806.html#Feedback2http://www.cppblog.com/Felicia/comments/commentRss/32806.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/32806.html状态压缩DP的好题！
分析见内

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Felicia 2007-09-24 21:12 发表评论

]]>[动态规划]pku1038http://www.cppblog.com/Felicia/archive/2007/09/12/32060.htmlFeliciaFeliciaWed, 12 Sep 2007 12:44:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/12/32060.htmlhttp://www.cppblog.com/Felicia/comments/32060.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/12/32060.html#Feedback2http://www.cppblog.com/Felicia/comments/commentRss/32060.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/32060.html由于第i+1行只和第i行有关，故可以用滚动数组优化。

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Felicia 2007-09-12 20:44 发表评论

]]>[动态规划]pku3375http://www.cppblog.com/Felicia/archive/2007/09/11/32030.htmlFeliciaFeliciaTue, 11 Sep 2007 14:28:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/11/32030.htmlhttp://www.cppblog.com/Felicia/comments/32030.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/11/32030.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/32030.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/32030.html
有很多细节不好考虑，应该是我的水平原因。最后我向updog要了数据才过的。而且代码写的不好。将就看一下吧。

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Felicia 2007-09-11 22:28 发表评论

]]>[动态规划]pku1170http://www.cppblog.com/Felicia/archive/2007/09/04/31516.htmlFeliciaFeliciaTue, 04 Sep 2007 00:37:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/04/31516.htmlhttp://www.cppblog.com/Felicia/comments/31516.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/04/31516.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/31516.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31516.html这个是IOI95的DP题。用一个b位的6进制数i表示状态。这个6进制数的每一位分别表示相应物品的数量。f[i]表示状态i下的最小花费。同样也可以用6进制数j表示优惠。那么，f[i]就能转移到f[i - j]，如果优惠j可用的话。代价是使用优惠j时减少的花费。最后的答案就是min(f[i])，0 <= i <= start（start是初始状态）。

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Felicia 2007-09-04 08:37 发表评论

]]>[动态规划]pku1160http://www.cppblog.com/Felicia/archive/2007/09/03/31493.htmlFeliciaFeliciaMon, 03 Sep 2007 14:44:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/03/31493.htmlhttp://www.cppblog.com/Felicia/comments/31493.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/03/31493.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/31493.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31493.html接下来就可以DP。设f[i][j]为前i个邮局，建在前j个村子的最小代价。那么f[i][j]可以转移到f[i + 1][j + k]，(1 <= k 且 j + k <= n)，代价是min_cost[j + 1][j + k]。

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Felicia 2007-09-03 22:44 发表评论

]]>[动态规划]pku1088http://www.cppblog.com/Felicia/archive/2007/09/02/31411.htmlFeliciaFeliciaSun, 02 Sep 2007 12:02:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/02/31411.htmlhttp://www.cppblog.com/Felicia/comments/31411.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/02/31411.html#Feedback2http://www.cppblog.com/Felicia/comments/commentRss/31411.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31411.html
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Felicia 2007-09-02 20:02 发表评论

]]>[动态规划]pku1737http://www.cppblog.com/Felicia/archive/2007/09/02/31386.htmlFeliciaFeliciaSun, 02 Sep 2007 05:53:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/02/31386.htmlhttp://www.cppblog.com/Felicia/comments/31386.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/02/31386.html#Feedback6http://www.cppblog.com/Felicia/comments/commentRss/31386.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31386.html
void calc(int n)
{
f[n] = 0;
for (int i = 1; i < n; i++)
f[n] += f[i] * f[n - i] * (pow(i) - 1) * C(n - 2, i - 1);
//pow(x) == 2^x
}

因为数据较多，所以预先算出f[1] -- f[50]，再输出。要用高精度。我用了标程。

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Felicia 2007-09-02 13:53 发表评论

]]>[动态规划]pku1946http://www.cppblog.com/Felicia/archive/2007/09/01/31353.htmlFeliciaFeliciaSat, 01 Sep 2007 03:42:00 GMThttp://www.cppblog.com/Felicia/archive/2007/09/01/31353.htmlhttp://www.cppblog.com/Felicia/comments/31353.htmlhttp://www.cppblog.com/Felicia/archive/2007/09/01/31353.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/31353.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31353.html设f[i][j][k]表示前i-1头奶牛已领跑，现在由第i头奶牛领跑，一共跑了j圈，奶牛i耗费了k的体力。
则f[i][j][k]可以转移到f[i][j + p][k + p^2]（耗费1分钟，奶牛i以p圈/分钟的速度继续领跑），也可转移到f[i + 1][j][j]（换成奶牛i + 1领跑，不耗费时间）。
时间复杂度为O(nde^2.5)。

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Felicia 2007-09-01 11:42 发表评论

]]>[动态规划]pku1947http://www.cppblog.com/Felicia/archive/2007/08/31/31321.htmlFeliciaFeliciaFri, 31 Aug 2007 10:27:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/31/31321.htmlhttp://www.cppblog.com/Felicia/comments/31321.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/31/31321.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/31321.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31321.htmlf[x][i](1 <= i <= p)表示以x为根的子树，变成剩下i个点的子树，且剩余子树包含根结点，需要去掉的最少边数。
那么父结点的f值可以由它所有的儿子的f值做背包得到。
最后的答案是min(min(f[i][p]) + 1 (2 <= i <= n), f[1][p])

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Felicia 2007-08-31 18:27 发表评论

]]>[动态规划]pku1848http://www.cppblog.com/Felicia/archive/2007/08/30/31236.htmlFeliciaFeliciaThu, 30 Aug 2007 13:47:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/30/31236.htmlhttp://www.cppblog.com/Felicia/comments/31236.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/30/31236.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/31236.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31236.html分析较长且带有图示，请阅读全文。

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Felicia 2007-08-30 21:47 发表评论

]]>[动态规划]pku1112http://www.cppblog.com/Felicia/archive/2007/08/29/31169.htmlFeliciaFeliciaWed, 29 Aug 2007 09:15:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/29/31169.htmlhttp://www.cppblog.com/Felicia/comments/31169.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/29/31169.html#Feedback2http://www.cppblog.com/Felicia/comments/commentRss/31169.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31169.html分析较长，请阅读全文。

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Felicia 2007-08-29 17:15 发表评论

]]>[动态规划]pku2411http://www.cppblog.com/Felicia/archive/2007/08/28/31052.htmlFeliciaFeliciaTue, 28 Aug 2007 13:03:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/28/31052.htmlhttp://www.cppblog.com/Felicia/comments/31052.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/28/31052.html#Feedback12http://www.cppblog.com/Felicia/comments/commentRss/31052.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31052.html如果行数比较多的话，可以用矩阵乘法优化。因为每行的状态转移都是相同的。设烈数为m，行数为n，可以做到O(2^(3m)logn)。

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Felicia 2007-08-28 21:03 发表评论

]]>[动态规划]pku2288http://www.cppblog.com/Felicia/archive/2007/08/28/31050.htmlFeliciaFeliciaTue, 28 Aug 2007 12:47:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/28/31050.htmlhttp://www.cppblog.com/Felicia/comments/31050.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/28/31050.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/31050.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/31050.html
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Felicia 2007-08-28 20:47 发表评论

]]>[动态规划]pku1141http://www.cppblog.com/Felicia/archive/2007/08/27/30936.htmlFeliciaFeliciaMon, 27 Aug 2007 07:55:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/27/30936.htmlhttp://www.cppblog.com/Felicia/comments/30936.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/27/30936.html#Feedback1http://www.cppblog.com/Felicia/comments/commentRss/30936.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/30936.html
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Felicia 2007-08-27 15:55 发表评论

]]>[动态规划]pku1050http://www.cppblog.com/Felicia/archive/2007/08/26/30849.htmlFeliciaFeliciaSun, 26 Aug 2007 05:51:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/26/30849.htmlhttp://www.cppblog.com/Felicia/comments/30849.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/26/30849.html#Feedback6http://www.cppblog.com/Felicia/comments/commentRss/30849.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/30849.html 阅读全文

Felicia 2007-08-26 13:51 发表评论

]]>[动态规划]pku 部分动态规划题目列表http://www.cppblog.com/Felicia/archive/2007/08/26/30848.htmlFeliciaFeliciaSun, 26 Aug 2007 03:52:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/26/30848.htmlhttp://www.cppblog.com/Felicia/comments/30848.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/26/30848.html#Feedback3http://www.cppblog.com/Felicia/comments/commentRss/30848.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/30848.html
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Felicia 2007-08-26 11:52 发表评论

]]>[动态规划]pku3345http://www.cppblog.com/Felicia/archive/2007/08/15/30096.htmlFeliciaFeliciaWed, 15 Aug 2007 10:42:00 GMThttp://www.cppblog.com/Felicia/archive/2007/08/15/30096.htmlhttp://www.cppblog.com/Felicia/comments/30096.htmlhttp://www.cppblog.com/Felicia/archive/2007/08/15/30096.html#Feedback0http://www.cppblog.com/Felicia/comments/commentRss/30096.htmlhttp://www.cppblog.com/Felicia/services/trackbacks/30096.html先递归算出子结点的 f 值，然后用背包的方法计算父结点的 f 值。

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Felicia 2007-08-15 18:42 发表评论

]]>