Bridging signals（最长上升子序列 O（nlogn））

Bridging signals

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 10196		Accepted: 5577

Description

'Oh no, they've done it again', cries the chief designer at the Waferland chip factory. Once more the routing designers have screwed up completely, making the signals on the chip connecting the ports of two functional blocks cross each other all over the place. At this late stage of the process, it is too expensive to redo the routing. Instead, the engineers have to bridge the signals, using the third dimension, so that no two signals cross. However, bridging is a complicated operation, and thus it is desirable to bridge as few signals as possible. The call for a computer program that finds the maximum number of signals which may be connected on the silicon surface without crossing each other, is imminent. Bearing in mind that there may be thousands of signal ports at the boundary of a functional block, the problem asks quite a lot of the programmer. Are you up to the task? 

A typical situation is schematically depicted in figure 1. The ports of the two functional blocks are numbered from 1 to p, from top to bottom. The signal mapping is described by a permutation of the numbers 1 to p in the form of a list of p unique numbers in the range 1 to p, in which the i:th number specifies which port on the right side should be connected to the i:th port on the left side.Two signals cross if and only if the straight lines connecting the two ports of each pair do.

Input

On the first line of the input, there is a single positive integer n, telling the number of test scenarios to follow. Each test scenario begins with a line containing a single positive integer p < 40000, the number of ports on the two functional blocks. Then follow p lines, describing the signal mapping:On the i:th line is the port number of the block on the right side which should be connected to the i:th port of the block on the left side.

Output

For each test scenario, output one line containing the maximum number of signals which may be routed on the silicon surface without crossing each other.

Sample Input

4
6
4
2
6
3
1
5
10
2
3
4
5
6
7
8
9
10
1
8
8
7
6
5
4
3
2
1
9
5
8
9
2
3
1
7
4
6

Sample Output

3
9
1
4

 

       题意：

       给出 T，代表有 T 个 case。后每个 case 首先给出 N（1 ~ 40000），代表有 2 * N 个针头，分成左右两边，后顺序给出 N 个数，代表左边针头编号依次 1 ~ N 连着的就是这个序列右边的针头编号。问最多能找出多少对相互之间不相交的线。

 

       思路：

       最长上升子序列。DP 的写法是 O （n ^ 2）的，TLE 无疑。所以要用 O （n log n）的写法，num 维护每个子序列长度对应的最小值。

       http://blog.csdn.net/dangwenliang/article/details/5728363

 

       AC：

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int num[40005];

int main() {
        int t;
        scanf("%d", &t);

        while (t--) {
                int n, len = 0;
                scanf("%d", &n);

                num[len] = -1;
                while (n--) {
                        int ans;
                        scanf("%d", &ans);

                        if (ans > num[len]) num[++len] = ans;
                        else *lower_bound(num, num + len, ans) = ans;
                }

                printf("%d\n", len);
        }

        return 0;
}