Codeforces 716A A. Crazy Computer

本文介绍了一个关于在特殊电脑上打字的问题,该电脑会在连续输入间隔超过一定时间后清除所有已输入的内容。文章详细解释了如何计算在一系列输入时间点后屏幕上剩余单词的数量,并通过示例展示了这一过程。

A. Crazy Computer
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
ZS the Coder is coding on a crazy computer. If you don’t type in a word for a c consecutive seconds, everything you typed disappear!

More formally, if you typed a word at second a and then the next word at second b, then if b - a ≤ c, just the new word is appended to other words on the screen. If b - a > c, then everything on the screen disappears and after that the word you have typed appears on the screen.

For example, if c = 5 and you typed words at seconds 1, 3, 8, 14, 19, 20 then at the second 8 there will be 3 words on the screen. After that, everything disappears at the second 13 because nothing was typed. At the seconds 14 and 19 another two words are typed, and finally, at the second 20, one more word is typed, and a total of 3 words remain on the screen.

You’re given the times when ZS the Coder typed the words. Determine how many words remain on the screen after he finished typing everything.

Input
The first line contains two integers n and c (1 ≤ n ≤ 100 000, 1 ≤ c ≤ 109) — the number of words ZS the Coder typed and the crazy computer delay respectively.

The next line contains n integers t1, t2, …, tn (1 ≤ t1 < t2 < … < tn ≤ 109), where ti denotes the second when ZS the Coder typed the i-th word.

Output
Print a single positive integer, the number of words that remain on the screen after all n words was typed, in other words, at the second tn.

Examples
input
6 5
1 3 8 14 19 20
output
3
input
6 1
1 3 5 7 9 10
output
2
Note
The first sample is already explained in the problem statement.

For the second sample, after typing the first word at the second 1, it disappears because the next word is typed at the second 3 and 3 - 1 > 1. Similarly, only 1 word will remain at the second 9. Then, a word is typed at the second 10, so there will be two words on the screen, as the old word won’t disappear because 10 - 9 ≤ 1.

n,c = map(int, raw_input().split())
ans = 1
a = map(int, raw_input().split())
for i in range(1,n):
    if a[i]-a[i-1] <= c:
        ans += 1
    else:
        ans = 1
print ans
### Codeforces 1732A Bestie 题目解析 对于给定的整数数组 \(a\) 和查询次数 \(q\),每次查询给出两个索引 \(l, r\),需要计算子数组 \([l,r]\) 的最大公约数(GCD)。如果 GCD 结果为 1,则返回 "YES";否则返回 "NO"[^4]。 #### 解决方案概述 为了高效解决这个问题,可以预先处理数据以便快速响应多个查询。具体方法如下: - **预处理阶段**:构建辅助结构来存储每一对可能区间的 GCD 值。 - **查询阶段**:利用已有的辅助结构,在常量时间内完成每个查询。 然而,考虑到内存限制以及效率问题,直接保存所有区间的结果并不现实。因此采用更优化的方法——稀疏表(Sparse Table),它允许 O(1) 时间内求任意连续子序列的最大值/最小值/GCD等问题,并且支持静态RMQ(Range Minimum Query)/RANGE_GCD等操作。 #### 实现细节 ##### 构建稀疏表 通过动态规划的方式填充二维表格 `st`,其中 `st[i][j]` 表示从位置 i 开始长度为 \(2^j\) 的子串的最大公约数值。初始化时只需考虑单元素情况即 j=0 的情形,之后逐步扩展至更大的范围直到覆盖整个输入序列。 ```cpp const int MAXN = 2e5 + 5; int st[MAXN][20]; // Sparse table for storing precomputed results. vector<int> nums; void build_sparse_table() { memset(st,-1,sizeof(st)); // Initialize the base case where interval length is one element only. for(int i = 0 ;i < nums.size(); ++i){ st[i][0]=nums[i]; } // Fill up sparse table using previously computed values. for (int j = 1;(1 << j)<=nums.size();++j){ for (int i = 0;i+(1<<j)-1<nums.size();++i){ if(i==0 || st[i][j-1]!=-1 && st[i+(1<<(j-1))][j-1]!=-1) st[i][j]=__gcd(st[i][j-1],st[i+(1<<(j-1))][j-1]); } } } ``` ##### 处理查询请求 当接收到具体的 l 和 r 参数后,可以通过查找对应的 log₂(r-l+1) 来定位合适的跳跃步长 k ,进而组合得到最终答案。 ```cpp string query(int L,int R){ int K=(int)(log2(R-L+1)); return __gcd(st[L][K],st[R-(1<<K)+1][K])==1?"YES":"NO"; } ``` 这种方法能在较短时间内完成大量查询任务的同时保持较低的空间开销,非常适合本题设定下的性能需求。
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