hdu 1160 FatMouse's Speed（最大上升子序列+路径输出）

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 13006000 2100500 20001000 40001100 30006000 20008000 14006000 12002000 1900

Sample Output

44597

原题的样例输出有点问题，正确的应该是4 4 5 9 8，以为自己写的不对，找了好长时间debug，后来用网上的代码ac了，发现原来是样例数据错了。

题解：先把数据排序（先按照体重从小到大排序，体重相同的再按照速度从大到小排序），这样题目就转换成了求最大上升子序列并输出路径。

注意要认真理解体会，其实并不复杂。

#include <iostream>#include <memory.h>#include <algorithm>#include <stdio.h>#define NUM 1010#define INF 0x3f3f3f3fusing namespace std;int flag;  //最大上升子序列的最末尾元素下标int dp[NUM];//dp[i]代表以第i个数据结尾的最大上升子序列的序列长度int path[NUM];//path[i]用来存储以第i个元素结尾的最大上升子序列的前驱标号int re[NUM];//用来存储最大上升子序列的下标，记得要倒序输出struct Mouse{    int w;//重量    int s;//速度    int index;//记录数据初始顺序}m[NUM];int cmp(Mouse a,Mouse b){    if(a.w==b.w)        return a.s>b.s;    return a.w<b.w;}int main(){    int num=1;    while(cin>>m[num].w>>m[num].s)    {        m[num].index=num;        num++;    }    num--;    sort(m+1,m+1+num,cmp);    memset(dp,0,sizeof(dp));    memset(path,0,sizeof(path));    dp[1]=1;    for(int i=2;i<=num;i++)    {        for(int j=1;j<i;j++)        {            if(m[j].w<m[i].w&&m[j].s>m[i].s)            {                if(dp[i]<dp[j])                {                    dp[i]=dp[j];                    path[i]=j;                }            }        }        dp[i]++;    }    int Max=-1;    for(int j=1; j<=num; j++)    {        if(Max<dp[j])        {            Max=dp[j];            flag=j;        }    }    cout<<Max<<endl;    cout<<"flag:"<<flag<<endl;    for(int i=1;i<=num;i++)    {        printf("path[%d]:%d   m[%d]:%d\n",i,path[i],i,m[i].index);    }    int e=0;    while(flag)  //将标号存入re数组    {        re[e++]=flag;        flag=path[flag];    }    while(e)  //倒序输出    {       e--;       cout<<m[re[e]].index<<endl;    }}