POJ 1631 Bridging signals（优化的最长子序列）

Bridging signals

Time Limit: 1000MS
Memory Limit: 10000KTotal Submissions: 14420
Accepted: 7804

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

4642631510234567891018876543219589231746

Sample Output

3914

Source

Northwestern Europe 2003

题目大意：

第一个数T，代表有T组数据

接着输入N，表示有N个桥梁

接着第 i 行表示左边第 i 个端口连着的右边的端口

求最多可以搭建多少个不相交的桥梁

解题思路

这是一道求最长上升子序列的题目，因为数据规模有40000，所以要用到 nlogn 的解法

AC代码

#include<iostream>  #include<cstdio>  #include<algorithm>  #include<cstring>  #define N 44444  using namespace std;    int f[N];  int main()  {      int T;      scanf("%d",&T);      while(T--)      {          int n,c=0;          scanf("%d",&n);          for(int i=1;i<=n;i++)          {              int t;              scanf("%d",&t);              if(i==1) f[++c]=t;              else              {                  if(t>f[c]) f[++c]=t;                  else                  {                      int pos=lower_bound(f+1,f+c,t)-f;//二分找到数组中比t大的第一个元素的的地址。                      f[pos]=t;                  }              }          }          printf("%d\n",c);      }      return 0;  }