2017 ACM-ICPC 亚洲区（南宁赛区）网络赛 The Heaviest Non-decreasing Subsequence Problem 最长不下降序列

Let SS be
a sequence of integers s_{1}s​1​​, s_{2}s​2​​, ......, s_{n}s​n​​ Each
integer is is associated with a weight by the following rules:
(1) If is is negative, then its weight is 00.

(2) If is is greater than or equal to 1000010000,
then its weight is 55.
Furthermore, the real integer value of s_{i}s​i​​ is s_{i}-10000s​i​​−10000 .
For example, if s_{i}s​i​​ is 1010110101,
then is is reset to 101101 and
its weight is 55.

(3) Otherwise, its weight is 11.

A non-decreasing subsequence of SS is
a subsequence s_{i1}s​i1​​, s_{i2}s​i2​​, ......, s_{ik}s​ik​​,
with i_{1}<i_{2}\
...\ <i_{k}i​1​​<i​2​​ ... <i​k​​,
such that, for all 1
\leq j<k1≤j<k,
we have s_{ij}<s_{ij+1}s​ij​​<s​ij+1​​.

A heaviest non-decreasing subsequence of SS is
a non-decreasing subsequence with the maximum sum of weights.

Write a program that reads a sequence of integers, and outputs the weight of its

heaviest non-decreasing subsequence. For example, given the following sequence:

8080 7575 7373 9393 7373 7373 1010110101 9797 -1−1 -1−1 114114 -1−1 1011310113 118118

The heaviest non-decreasing subsequence of the sequence is <73,
73, 73, 101, 113, 118><73,73,73,101,113,118> with
the total weight being 1+1+1+5+5+1
= 141+1+1+5+5+1=14.
Therefore, your program should output 1414 in
this example.

We guarantee that the length of the sequence does not exceed 2*10^{5}2∗10​5​​

Input Format

A list of integers separated by blanks:s_{1}s​1​​, s_{2}s​2​​,......,s_{n}s​n​​

Output Format

A positive integer that is the weight of the heaviest non-decreasing subsequence.

样例输入

80 75 73 93 73 73 10101 97 -1 -1 114 -1 10113 118

样例输出

14

    题目是说找出一个值最大的序列，而这个序列的值的定义方式是对于负数，值为0。对于正数，如果小于10000，那么值就是1，否则为5。另外，如果大于10000，那么这个数要减去10000才是他真正在数列中的数（比如10101，在数列中也将其视为101）。然后将其排列出一个最长的序列，要求这个序列的值最大，且序列为不下降的序列。

    处理的时候，对于负数，因为没有值，所以直接舍去不读入就可以了。对于正数，如果小于10000就正常读入，如果大于10000的话，先将这个数减去10000存入，因为这个数的值为5，所以再复制4次，存入这个数5次进去，这样就相当于处理了权值为5的问题，然后读入完之后求出最长不下降子序列就可以了。、

    （PS：这个题输入是一组数据，比赛的时候我当成多组数据写了，然后写了很多getchar判断空格回车结束，结果TLE了两发改成一组数据才A了....）

    下面AC代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[1000005];
int b[1000005],c[1000005];

int fin(int *t,int len,int n)
{
int left=0,right=len,mid=(left+right)/2;
while(left<=right)
{
if(n>=t[mid])
left=mid+1;
else if(n<t[mid])
right=mid-1;
else
return mid;
mid=(left+right)/2;
}
return left;
}

int main()
{
int n;
int i,j;
int k;
int m;
int t;
int len;
char g;
i=0;
while(scanf("%d",&m)!=EOF)
{
a[i]=m;
if(a[i]<0)
{
i--;
}
else if(a[i]>10000)
{
a[i]-=10000;
k=a[i];
for(j=1;j<=4;j++)
{
i++;
a[i]=k;
}
}
i++;
}
n=i;
/*for(i=0;i<n;i++)
{
cout<<"a["<<i<<"] = "<<a[i]<<endl;
}*/
b[0]=1;
c[0]=-1;
c[1]=a[0];
len=1;
for(i=1;i<n;i++)
{
j=fin(c,len,a[i]);
c[j]=a[i];
if(j>len)
len=j;
}
cout<<len<<endl;
return 0;
}