hdu1160 FatMouse's Speed （求最长严格下降子序列路径）

FatMouse's Speed

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

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Total Submission(s): 12507    Accepted Submission(s): 5489

Special Judge

Problem Description

FatMouse believes that the fatter a mouse is, the faster it runs. To disprove this, you want to take the data on a collection of mice and put as large a subset of this data as possible into a sequence so that the weights are increasing, but the speeds are decreasing.

Input

Input contains data for a bunch of mice, one mouse per line, terminated by end of file.

The data for a particular mouse will consist of a pair of integers: the first representing its size in grams and the second representing its speed in centimeters per second. Both integers are between 1 and 10000. The data in each test case will contain information for at most 1000 mice.

Two mice may have the same weight, the same speed, or even the same weight and speed. 

Output

Your program should output a sequence of lines of data; the first line should contain a number n; the remaining n lines should each contain a single positive integer (each one representing a mouse). If these n integers are m[1], m[2],..., m[n] then it must be the case that 

W[m[1]] < W[m[2]] < ... < W[m[n]]

and 

S[m[1]] > S[m[2]] > ... > S[m[n]]

In order for the answer to be correct, n should be as large as possible.
All inequalities are strict: weights must be strictly increasing, and speeds must be strictly decreasing. There may be many correct outputs for a given input, your program only needs to find one. 

Sample Input

6008 1300 6000 2100 500 2000 1000 4000 1100 3000 6000 2000 8000 1400 6000 1200 2000 1900

Sample Output

4 4 5 9 7

Source

​​Zhejiang University Training Contest 2001​​

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解析：子序列要满足：weight递增，但是speed递减，并且有可能多只老鼠的weight相同。

           我这里是是一个O(n^2)的解法，具体思路就不说了，直接看代码吧。

代码：

#include<cstdio>
#include<algorithm>
using namespace std;

const int maxn=1e3;
int last[maxn+10],len[maxn+10];
struct tnode{
  int d,weight,speed;
}p[maxn+10];

bool cmp(tnode a,tnode b)
{
  return a.weight>b.weight;
}

int main()
{
  //freopen("1.in","r",stdin);
  
  int n=1,i,j,k;
  while(scanf("%d%d",&p[n].weight,&p[n].speed)!=EOF)n++;
  len[0]=0,last[1]=0;
  for(i=1;i<n;i++)p[i].d=i,len[i]=1;
  sort(p,p+n,cmp);
  for(i=2;i<n;i++)
    {
    for(k=0,j=1;j<i;j++)
      if(p[j].weight>p[i].weight && 
       p[j].speed<p[i].speed && 
       len[j]>len[k])k=j;
    last[i]=k,len[i]=len[k]+1;
    }
  for(k=1,i=2;i<n;i++)if(len[i]>len[k])k=i;
  printf("%d\n",len[k]);
  while(k)printf("%d\n",p[k].d),k=last[k];
  return 0;
}