hdu 1025 Constructing Roads In JGShining's Kingdom

本题明白题意以后，就可以看出是让求最长上升子序列，但是不知道最长上升子序列的算法，用了很多YY的方法去做，最后还是超时，

因为普通算法时间复杂度为O(n*2)，去搜了题解，学习了一下，感觉不错，拿出来分享一下。

#include <stdio.h>
#include <string.h>

#define N 500005
int map[N], dp[N];

int main ()
{
    int x, y, n, i, j = 0;
    
    while (scanf ("%d", &n) != EOF)
    {
        for (i=0; i<n; i++)
        {
            scanf ("%d %d", &x, &y);
            map[x] = y;
        }
        
        memset (dp, 0, sizeof(dp));
        
        dp[1] = map[1];
        
        int low, up, mid, len = 1;
        for (i=2; i<=n; i++)
        {
            low = 1;
            up = len;
            
            while (low <= up)
            {
                mid = (low + up) / 2;
                if (dp[mid] > map[i])
                    up = mid - 1;
                else
                    low = mid + 1;
            }
            
            dp[low] = map[i];
            if (low > len)
                len ++;
        }
        if (len == 1)
            printf ("Case %d:
My king, at most 1 road can be built.

", ++j);
        else
            printf ("Case %d:
My king, at most %d roads can be built.

", ++j, len);
    }
    
    return 0;
}