计蒜客 2017 ACM-ICPC 亚洲区（南宁赛区）网络赛 L题

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Let $S$ be a sequence of integers $s_{1}$ , $s_{2}$ , $. . .$ , $s_{n}$ 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 $s_{i}$ is $s_{i}-10000$ . For example, if $s_{i}$ 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 $s_{i1}$ , $s_{i2}$ , $. . .$ , $s_{ik}$ , with $i_{1}<i_{2}\ ...\ <i_{k}$ , such that, for all $\leq j<k$ , we have $s_{ij}<s_{ij+1}$ .

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 $2*10^{5}$

Input Format

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

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

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 <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <cmath>
#include <vector>
#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;
}
/*

*/

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