hdu1025Constructing Roads In JGShining's Kingdom(巧求最长子序列）

最长上升子序列的时间复杂度为O(n2)，此处为500000，上网看了看别人的解题报告，才知道它有两种算法复杂度为O(n*logn)和O(n^2)。前者使用二分查找，后者朴素查找。它的算法大致思路：设置两个a,b数组，a数组存储数据，b数组存储最长不降序序列。此算法关键在于设计二分查找。二分查找关键代码来自http://blog.csdn.net/ice_crazy/article/details/7536332

#include<stdio.h>
int a[500011],dp[500011];
int main()
{
    int n,temp1,temp2,i,k;
    k=0;
    while(scanf("%d",&n)!=-1)
    {
        for(i=1;i<=n;i++)
        {
            scanf("%d%d",&temp1,&temp2);
            a[temp1]=temp2;
        }
        dp[1]=a[1];
        int low,len,high,mid;
        len=1;
        for(i=2;i<=n;i++)
        {
            low=1;
            high=len;
            while(low<=high)
            {
                mid=(low+high)/2;
                if(dp[mid]<a[i])
                    low=mid+1;
                else
                    high=mid-1;
            }
            dp[low]=a[i];
            if(low>len)
                len++;
        }
        k++;
        printf("Case %d:
",k);
        if(len==1)  printf("My king, at most 1 road can be built.
");
        else
            printf("My king, at most %d roads can be built.
",len);
        printf("
");
    }
    return 0;
}