Is Bigger Smarter?

Submit Status

Description

Question 1: Is Bigger Smarter?

The Problem

Some people think that the bigger an elephant is, the smarter it is. To disprove this, you want to take the data on a collection of elephants and put as large a subset of this data as possible into a sequence so that the weights are increasing, but the IQ‘s are decreasing.

The input will consist of data for a bunch of elephants, one elephant per line, terminated by the end-of-file. The data for a particular elephant will consist of a pair of integers: the first representing its size in kilograms and the second representing its IQ in hundredths of IQ points. Both integers are between 1 and 10000. The data will contain information for at most 1000 elephants. Two elephants may have the same weight, the same IQ, or even the same weight and IQ.

Say that the numbers on the i-th data line are W[i] and S[i]. 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 an elephant). If these n integers are a[1], a[2],..., a[n] then it must be the case that

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

and

   S[a[1]] > S[a[2]] > ... > S[a[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 IQs 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

题意：大象真的越大越聪明吗，找出体重递增IQ递减的最长大象序列。

分析：很明显的最长递降子序列，先把体重排序，体重一样的按iq递减排，这样就能出来了。

 1 #include<cstdio>
 2 #include<cstdlib>
 3 #include<cstring>
 4 //antiew[i]为编号i个大象的体重排名； ew是体重第i名的大象的编号；w，s是大象的体重，智商；
 5 int w[1005],s[1005],n=0,ew[1005],antiew[1005],loest[1005],p[1005];
 6 //int f[1005][1005];
 7 int cmp(const void* x,const void* y)
 8 {
 9     if(  w[*(int*)x] != w[*(int*)y]  )
10         return w[*(int*)x] - w[*(int*)y];
11     else
12         return s[*(int*)y] - s[*(int*)x] ;
13 }
14
15 void print(int i)
16 {
17     if(i == -1) return;
18     print(p[i]);
19     printf("%d\n",ew[i] + 1);
20     //printf("%d : %d   %d\n",ew[i] + 1,w[ew[i]],s[ew[i]]);
21 }
22
23 int main()
24 {
25     #ifdef LOCAL
26     freopen("..\\data.in","r",stdin);
27     #endif // LOCAL
28     //读入大象的体重w  智商s  共n头大象
29     while(scanf("%d%d",w+n,s+n) == 2)
30         n++;
31     //ew是大象体重增加的
32     for(int i=0;i<n;i++)
33         ew[i] = i;
34     qsort(ew,n,sizeof(int),cmp);
35     for(int i=0;i<n;i++)
36         antiew[ew[i]] = i;
37     memset(p,-1,sizeof(p));
38     memset(loest,0,sizeof(loest));
39
40     loest[0] = 1;
41     for(int i=1;i<n;i++)
42     {
43         //maxl是前i个的大象IQ的严格下降降子序列长度的最大值
44         int maxl=0;
45         for(int j=i-1;j>=0;j--) if( s[ew[i]] < s[ew[j]] && w[ew[i]] > w[ew[j]] && maxl < loest[j] )
46         {
47             maxl = loest[j];
48             p[i] = j;
49         }
50         if(p[i] == -1)
51             loest[i] = 1;
52         else
53             loest[i] = maxl + 1;
54     }
55
56     int maxip=0;
57     for(int i=0;i<n;i++) if(loest[maxip] < loest[i])
58         maxip = i;
59     printf("%d\n",loest[maxip]);
60
61     print(maxip);
62     /*
63     for(int i=0;i<n;i++)
64         printf("编号：%4d  体重：%4d   智商：%4d  体重排名：%4d\n",i + 1,w[i],s[i],antiew[i]+1);
65     for(int i=0;i<n;i++)
66         printf("体重排名：%4d  体重：%4d   智商：%4d  编号：%4d\n",i+1,w[ew[i]],s[ew[i]],ew[i]+1);
67     */
68     return 0;
69 }