DP算法

某国为了防御敌国的导弹袭击,发展出一种导弹拦截系统.但是这种导弹拦截系统有一个缺陷:虽然它的第一发炮弹能够到达任意的高度,但是以后每一发炮弹都不能超过前一发的高度.某天,雷达捕捉到敌国的导弹来袭.由于该系统还在试用阶段,所以只有一套系统,因此有可能不能拦截所有的导弹.
怎么办呢?多搞几套系统呗!你说说倒蛮容易,成本呢?成本是个大问题啊.所以俺就到这里来求救了,请帮助计算一下最少需要多少套拦截系统. 

输入若干组数据.每组数据包括:导弹总个数(正整数),导弹依此飞来的高度(雷达给出的高度数据是不大于30000的正整数,用空格分隔)

对应每组数据输出拦截所有导弹最少要配备多少套这种导弹拦截系统. 

     
     

      
       8 389 207 155 300 299 170 158 65 
     
     

     
     

      
       2 

      
      解答1：

      
      

       
       

        
        

         
         [cpp] 
         
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#include<stdio.h>  
int main()  
{  
    int a[10001],b[10001]={0};  
    int n,i,k,j;  
    while(scanf("%d",&n)!=EOF)  
    {k=0;  
            b[0]=0;  
        for(i=0;i<n;i++)  
        scanf("%d",&a[i]);  
        for(i=0;i<n;i++)  
        {  
                for(j=0;j<=k;j++)  //总体思路是一个个接入，一个个与前面递减序列最小值相比较，  
                //如果比之小，替换再接入，如果比所有的都大，则再加入一个 递减序列   
                {  
                if(a[i]<b[j])  
                {  
                b[j]=a[i];  
                break;  
                }  
                else if(j==k)  
                {  
                b[++k]=a[i];  
                break;  
                }  
                  
                }  
        }  
        printf("%d\n",k+1);  
    }  
    return 0;  
      
      
     
     

A subsequence of a given sequence is the given sequence with some elements (possible none) left out. Given a sequence X = <x1, x2, ..., xm> another sequence Z = <z1, z2, ..., zk> is a subsequence of X if there exists a strictly increasing sequence <i1, i2, ..., ik> of indices of X such that for all j = 1,2,...,k, xij = zj. For example, Z = <a, b, f, c> is a subsequence of X = <a, b, c, f, b, c> with index sequence <1, 2, 4, 6>. Given two sequences X and Y the problem is to find the length of the maximum-length common subsequence of X and Y. 
The program input is from a text file. Each data set in the file contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct. For each set of data the program prints on the standard output the length of the maximum-length common subsequence from the beginning of a separate line. 

     
     

      
       abcfbc abfcab
programming contest 
abcd mnp 
     
     

     
     

      
       4
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