The Heaviest Non-decreasing Subsequence Problem（2017南宁网络赛）

Let $S$ be a sequence of integers s1s_{1}s​1​​,s2s_{2}s​2​​,$...$,sns_{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 sis_{i}s​i​​ is si−10000s_{i}-10000. For example, if sis_{i}s​i​​ is 1010110101, then is is reset to 101101and its weight is 55.

(3) Otherwise, its weight is 11.

A non-decreasing subsequence of $S$ is a subsequence si1s_{i1}​​,si2s_{i2}​​,$...$,siks_{ik}​​, with i1<i2 ... <iki_{1}<i_{2}\ ...\ <i_{k}i​1​​<i​2​​ ... <i​k​​, such that, for all 1≤j<k1 \leq j<k, we have sij<sij+1 s_{ij}<s_{ij+1​​<s​ij+1​​.

A heaviest non-decreasing subsequence of $S$ 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:

8080757737393937373737310101101019797−1-1−1-1114114−1-11011310113118118

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 $14$ in this example.

We guarantee that the length of the sequence does not exceed2∗1052*10^{5}。​​

Input Format

A list of integers separated by blanks:s1s_{1}s​1​​,s2s_{2}s​2​​,$...$,sns_{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

//题意：给定一个数组，现规定，里面的数值为负的话，它的weight是0，若大于等于0且小于10000的话，其weight为1，若大于等于10000，它的weight为5，且它的值是原来的值减10000。求这个数组的子串中weight和的最大值。

//思路：开一个新数组，遍历给定的数组，值为负的直接舍去，若值是小于10000的非负数，就依次存到一个新数组，若值大于10000，将这个值减去10000后，放入新数组中，放5次，因为它的weught=5，然后就得到一个新数组，求这个新数组的非递减最长子序列的长度即可。

#include <iostream>#include <cstdio>#include <string>#include <cstring>#include <cmath>#include <vector>#include <queue>#include <algorithm>using namespace std;const int MAX=2e5+100;int num[MAX];int a[MAX];int dp[MAX];int cnt;int bsearch(int len,int x){    int l=0,r=len-1;    while(l<=r)    {        int mid=(l+r)/2;        if(x>=dp[mid-1]&&x<dp[mid])return mid;        else if(x<dp[mid-1])r=mid-1;        else l=mid+1;    }    return l;}//最长非递减子序列int LIS(){    dp[0]=a[0];    int len=1;    int j;    for(int i=1; i<cnt; i++)    {        if(a[i]<dp[0])j=0;        else if(a[i]>=dp[len-1])j=len++;        else j=bsearch(len,a[i]);        dp[j]=a[i];    }    return len;}int main(){    memset(num,0,sizeof(num));    memset(dp,0,sizeof(dp));    memset(a,0,sizeof(a));    int nn=0;    while(scanf("%d",&num[nn])!=EOF)    {        nn++;    }    cnt=0;    for(int i=0;i<nn;i++)    {        if(num[i]<0)            continue;        if(num[i]>=10000)        {            num[i]-=10000;            for(int j=0;j<5;j++)            {                a[cnt++]=num[i];            }        }        else        {            a[cnt++]=num[i];        }    }    int ans=LIS();    printf("%d\n",ans);    return 0;}