计蒜客 The Heaviest Non-decreasing Subsequence Problem（最大权值和非递减子序列）

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

题目来源

2017
ACM-ICPC 亚洲区（南宁赛区）网络赛

先把数值转换，然后把weight转换为连续出现次数，套用最长非递减子序列模板。

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<math.h>
using namespace std;
const int maxn=1000010;
int data[maxn];
int maxv[maxn];
int BinaryResearch(int x,int len)
{
int mid,low=1,high=len;
while(low<=high)
{
mid=(low+high)>>1;
if(maxv[mid]<=x)
{
low=mid+1;
}
else high=mid-1;
}
return low;
}
int lis(int n)
{
int i,len=1;
maxv[1]=data[0];
for(i=1;i<n;i++)
{
if(data[i]>=maxv[len])
{
maxv[++len]=data[i];
}
else
{
int pos=BinaryResearch(data[i],len);
maxv[pos]=data[i];
}
}
return len;
}
int main()
{
memset(data,0,sizeof(data));
memset(maxv,0,sizeof(maxv));
int len=0;
int x;
while(scanf("%d",&x)!=EOF)
{
if(x<0)continue;
else if(x>=10000)
{
x=x-10000;
data[len++]=x;
data[len++]=x;
data[len++]=x;
data[len++]=x;
data[len++]=x;
}
else
{
data[len++]=x;
}
}
printf("%d\n",lis(len));
}