ZOJ1986 Bridging Signals onlogn复杂度求LIS

Bridging Signals
Time Limit: 2 Seconds      Memory Limit: 65536 KB

'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?



Figure 1. To the left: The two blocks' ports and their signal mapping (4, 2, 6, 3, 1, 5). To the right: At most three signals may be routed on the silicon surface without crossing each
other. The dashed signals must be bridged.
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 ith number specifies which port on the right side should be connected to the ith 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 ith line is the port number of the block on the right side which should be connected to the ith 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

Source: Northwestern Europe 2003

题意：题意是说去掉几根线后，使得剩下不相交的线数量最多，问剩下最多的线的条数

思路：对于右边而言，不交叉就意味着序号是严格递增的，那么严格递增的最大数量是多少？这样想的话可以转化成求LIS，即最长上升子序列。然后看一看数据范围，发现最大只能承受onlogn的复杂度，于是可以使用二分。

#include <iostream>
#include <stdio.h>
#include <string>
#include <cstring>
#include <algorithm>

using namespace std;

int a[40009];
int b[40009];

int find(int len,int x)
{
int i=1,j=len;

while(i<=j)
{
int mid=(i+j)/2;
if(b[mid]>x)
j=mid-1;
else
i=mid+1;
}
return i;
}

int main()
{
int T,n;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);

int j=1;
b[1]=a[1];

for(int i=2;i<=n;i++)
{
if(b[j]<a[i])
b[++j]=a[i];
else
{
int k=find(j,a[i]);//求出第一个大于a[i]的数字，然后用a[i]去替换掉
b[k]=a[i];
}
}

printf("%d\n",j);

}
return 0;
}