计蒜客 2017 ACM-ICPC 亚洲区（南宁赛区）网络赛 L题

Let $S$ 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 $0$.

(2) If is is greater than or equal to $10000$, then its weight is $5$. Furthermore, the real integer value of s_{i}s​i​​ is s_{i}-10000s​i​​−10000 . For example, if s_{i}s​i​​ is $10101$, then is is reset to $101$ and its weight is $5$.

(3) Otherwise, its weight is $1$.

A non-decreasing subsequence of $S$ is a subsequence s_{i1}s​i1​​, s_{i2}s​i2​​, $...$, s_{ik}s​ik​​, with i_{1}i​1​​<i​2​​ ... <i​k​​, such that, for all 1 \leq j1≤j<k, we have s_{ij}s​ij​​<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:

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

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

We guarantee that the length of the sequence does not 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

题意：就是给你一串数字，以输入结束符结束输入，然后在这些数字中，小于零的数字权值为 0，大于等于10000的数字的权值为 5，而且这些数字要减去10000，其余数字的权值为 1 。

题解：这题有点坑，比赛时我就没做到，其实大于10000的数字的权值为 5，可不可以就等于5个权值为1的数字呢。然后这道题就变成时间为nlog（n）的最长上升子序列了。

AC代码：

#include
#include
#include
#include
#include
#include
#define mem(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long LL;
///o(っ。Д。)っ AC万岁!!!!!!!!!!!!!!
const int maxn = 15520200;
int maps[maxn] = {}, dp[maxn] = {};
int bin_searchs(int l, int r, int k)
{
    if(l >= r)
    {
        return l;
    }
    int mid = (l + r + 1) / 2;
    if(dp[mid] > k)
    {
        return bin_searchs(l, mid - 1, k);
    }
    else return bin_searchs(mid, r, k);
}
int main()
{
    int cnt = 0, book;
    while(scanf("%d", &book) != EOF)
    {
        if(book >= 10000)
        {
            book -= 10000;
            for(int i = 1; i <= 5; i++)
            {
                maps[++cnt] = book;
            }
        }
        else if(book < 0)
        {
            continue;
        }
        else maps[++cnt] = book;
    }
    int counter = 1;
    dp[1] = maps[1];
    for(int i = 2; i <= cnt; i++)
    {
        if(maps[i] >= dp[counter])
        {
            dp[++counter] = maps[i];
        }
        else
        {
            int kk = bin_searchs(1, counter, maps[i]);
            if(dp[kk] <= maps[i])
            {
                kk++;
            }
            dp[kk] = maps[i];
            if(kk > counter) counter++;
        }


    }
    printf("%d\n", counter);
    return 0;
}
/*


*/