HDOJ 1025 DP+二分

本题求最大上升子序列，这个很容易看出来。数据大小是50万，所以不能用O(n^2)的方法来求。因为1000万以上次循环就可能超时。

若用二分来解决，时间复杂度为O(nlogn)。

代码使用了我认为的最经典的二分形式。

 

#include <iostream>
using namespace std;

const int MAXCITYNUM = 500005;
int poorCity[MAXCITYNUM],ans[MAXCITYNUM];

int main ()
{int caseNum = 1,cityNum;
    while (scanf("%d",&cityNum) != -1)
    {
        int richCity;
        for (int i = 1;i <= cityNum;i ++)/* 没说数据按rich city的编号由小到大给出 */
        {
            scanf("%d",&richCity);
            scanf("%d",&poorCity[richCity]);
        }
        ans[1] = poorCity[1];
        int low,high,mid,len = 1;
        for (int i = 2;i <= cityNum;i ++)
        {
            low = 1 , high = len;
            while (low <= high)
            {
                mid = (low + high) / 2;
                if (ans[mid] >= poorCity[i])
                    high = mid - 1;
                else
                    low = mid + 1;
            }
            ans[low] = poorCity[i];
            if (low == (len + 1))
                len ++;
        }
        printf("Case %d:\n",caseNum);
        caseNum ++;
        if (len == 1)/* 注意细节 */
            printf("My king, at most %d road can be built.\n",len);
        else
            printf("My king, at most %d roads can be built.\n",len);
        printf("\n");
    }
    return 0;
}