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  • ACM POJ 2533Longest Ordered Subsequence(最长上升子序列,简单DP)

    Longest Ordered Subsequence
    Time Limit: 2000MS Memory Limit: 65536K
    Total Submissions: 19643 Accepted: 8501

    Description

    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
    

    Source

    Northeastern Europe 2002, Far-Eastern Subregion
     
    /*
    POJ2533Longest Ordered Subsequence
    最长上升子序列
    描述:给一队排列整齐的数列ai,找到数列ai中最长上升子序列。
    输入:第一行是数列的元素个数N,第二行是N个整数,范围从0到10,000。(1<=N<=1000)
    输出:包括一个整数,表示最长上升子序列的长度。

    Sample Input
    7
    1 7 3 5 9 4 8

    Sample Output
    4
    */
    /*
    用动态规划做。
    用dp[k]表示以a[k]作为终点的最大上升子序列
    则:
    dp[1] = 1;
    dp[k] = Max (dp[i]:1 <= i < k 且 a[i ]< a[k] 且 k != 1) + 1.
    */
    #include
    <stdio.h>
    #define MAXN 1000
    int dp[MAXN+10],a[MAXN+10];//a数组记录输入的序列
    int main()
    {
    int n,i,j;
    scanf(
    "%d",&n);
    for(i=1;i<=n;i++)
    scanf(
    "%d",&a[i]);
    dp[
    1]=1;
    for(i=2;i<=n;i++)
    {
    int temp=0;
    for(j=1;j<i;j++)
    if(a[i]>a[j])
    if(temp<dp[j])
    temp
    =dp[j];
    dp[i]
    =temp+1;
    }
    int maxlen=0;
    for(i=1;i<=n;i++)
    if(maxlen<dp[i])
    maxlen
    =dp[i];
    printf(
    "%d\n",maxlen);
    return 0;
    }

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  • 原文地址:https://www.cnblogs.com/kuangbin/p/2125951.html
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