【ZOJ1108】FatMouse's Speed（最长下降子序列）

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=1108

FatMouse's Speed

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Time Limit: 2 Seconds      Memory Limit: 65536 KB      Special Judge

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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 Specification

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 Specification

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

Output for Sample Input

4
4
5
9
7

【题意】

给出每只仓鼠的重量和速度，求序列中重量严格递增速度严格递减的最长序列，并输出该序列的长度及序列，若有多种答案输出一种即可。

【解题思路】

先根据给定要求排个序，此时仓鼠的重量已经是非递减序列，v[i]数组是包含第i只仓鼠在内的最长序列，然后每一次更新dp值的时候说明第i只仓鼠的最长序列已经改变了，所以需要v[i]=v[j]，并且把自己也压入，最后遍历一下v取最长的序列长度即可。

【代码】

#include<bits/stdc++.h>
using namespace std;
struct Node
{
    int weight,speed,num;
}node[1005];
int dp[1005];
vector<int>v[1005],ans;
bool cmp(Node a,Node b)
{
    return (a.weight!=b.weight)?a.weight<b.weight:a.speed>b.speed;
}
int main()
{
    int cnt=1;
    while(~scanf("%d%d",&node[cnt].weight,&node[cnt].speed))
    {
        node[cnt].num=cnt;
        cnt++;
    }
    sort(node,node+cnt,cmp);
    for(int i=1;i<cnt;i++)
    {
        dp[i]=1;
        v[i].push_back(i);
    }
    for(int i=1;i<cnt;i++)
    {
        for(int j=i-1;j>=1;j--)
        {
            if(node[i].weight>node[j].weight && node[i].speed<node[j].speed && dp[i]<dp[j]+1)
            {
                dp[i]=dp[j]+1;
                v[i]=v[j];
                v[i].push_back(i);
            }
        }
    }
    int MAX=0;
    for(int i=1;i<cnt;i++)
    {
        if(MAX<v[i].size())
        {
            MAX=v[i].size();
            ans=v[i];
        }
    }
    printf("%d\n",ans.size());
    for(int i=0;i<ans.size();i++)
        printf("%d\n",node[ans[i]].num);
    return 0;
}