HDU 1160 FatMouse's Speed （动态规划最长下降子序列）

Posted 2020-11-10 dyhaohaoxuexi

FatMouse‘s Speed

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 24573    Accepted Submission(s): 10896
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

题目大意与分析

给出一堆鼠标的重量与速度，输出一个最长的序列，满足重量越来越大，速度越来越小。

先将鼠标根据重量从小到大排序，再求最大下降子序列就行了。

#include<bits/stdc++.h>

using namespace std;

typedef struct 
{
    int add;
    int w;
    int s;
}node;
node a[1005];
int dp[1005],anss,i,temp,c[1005],x,y,num,j,n;
bool cmp(node a,node b)
{
    return a.w<b.w;
}

int main()
{
    while(cin>>x>>y)
    {    
        num++;
        a[num].add=num;
        a[num].w=x;
        a[num].s=y;        
    }
    sort(a+1,a+1+num,cmp);
    for(i=1;i<=num;i++)
    {
        dp[i]=1;
        for(j=1;j<i;j++)
        {
            if(a[j].w<a[i].w&&a[j].s>a[i].s)
            dp[i]=max(dp[j]+1,dp[i]);
        }
        if(dp[i]>anss)
        anss=dp[i];
    }
    cout<<anss<<endl;
    temp=anss;
    for(i=num;i>=1;i--)
    {
        if(dp[i]==temp)
        {
            temp--;
            c[temp]=a[i].add;
        }
    }
    for(i=0;i<anss;i++)
    cout<<c[i]<<endl;
   
}