CSU-ACM2017暑期训练8-动态规划初步 D - Longest Ordered Subsequence

D - Longest Ordered Subsequence

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence ( a1, a2, ..., aN) be any sequence ( ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8). Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

7 1 7 3 5 9 4 8

Sample Output

4

​ 状态转移方程

$$f(k) = \left \{ \begin {align} 1 &,& k=1 \\ \max(f(i) 1) &,& 1<i<k ~\&\&~a[i] <p></p> <span class="hljs-preprocessor">#include &lt;iostream&gt;</span> <span class="hljs-preprocessor">#include &lt;cstdio&gt;</span> <span class="hljs-preprocessor">#include &lt;algorithm&gt;</span> <span class="hljs-preprocessor">#include &lt;vector&gt;</span> <span class="hljs-preprocessor">#include &lt;cstring&gt;</span> <span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>; <span class="hljs-keyword">int</span> sample[<span class="hljs-number">1005</span>], dp[<span class="hljs-number">1005</span>]; <span class="hljs-keyword">int</span> main(){ <span class="hljs-preprocessor">#ifdef TEST</span> freopen(<span class="hljs-string">&#34;test.txt&#34;</span>, <span class="hljs-string">&#34;r&#34;</span>, stdin); <span class="hljs-preprocessor">#endif <span class="hljs-comment">// TEST</span></span> <span class="hljs-keyword">int</span> n; <span class="hljs-keyword">while</span>(<span class="hljs-built_in">cin</span> &gt;&gt; n){ <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> i &#61; <span class="hljs-number">0</span>; i &lt; <span class="hljs-number">1005</span>; i&#43;&#43;) dp[i] &#61; <span class="hljs-number">1</span>; <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> i &#61; <span class="hljs-number">0</span>; i &lt; n; i&#43;&#43;) <span class="hljs-built_in">cin</span> &gt;&gt; sample[i]; <span class="hljs-keyword">int</span> res &#61; <span class="hljs-number">1</span>; <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> i &#61; <span class="hljs-number">1</span>; i &lt; n; i&#43;&#43;){ <span class="hljs-keyword">int</span> maxLen &#61; <span class="hljs-number">0</span>, now &#61; sample[i]; <span class="hljs-keyword">for</span>(<span class="hljs-keyword">int</span> j &#61; <span class="hljs-number">0</span>; j &lt; i; j&#43;&#43;){ <span class="hljs-keyword">int</span> temp &#61; sample[j], tLen &#61; dp[j]; <span class="hljs-keyword">if</span>(temp &lt; now && tLen &gt; maxLen) maxLen &#61; tLen; } dp[i]&#43;&#61;maxLen; <span class="hljs-keyword">if</span>(dp[i] &gt; res) res &#61; dp[i]; } <span class="hljs-built_in">cout</span> &lt;&lt; res &lt;&lt; endl; } <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>; } <script></div><div align="center"><script src="https://www.6miu.com/js/artile.js">$$