LG 推出锐龙版 gram 笔记本，续航可达 24 小时（lg2021款gram笔记本）

25-04-28 1

本篇文章给大家谈谈LG推出锐龙版gram笔记本，续航可达24小时，以及lg2021款gram笔记本的知识点，同时本文还将给你拓展17-正交矩阵和Gram-Schmidt正交化、AllOurN-gram

本篇文章给大家谈谈LG 推出锐龙版 gram 笔记本，续航可达 24 小时，以及lg2021款gram笔记本的知识点，同时本文还将给你拓展17 - 正交矩阵和 Gram-Schmidt 正交化、All Our N-gram are Belong to You、cbow与skip-gram、Codeforces 977B Two-gram（stl之string掉进坑）等相关知识，希望对各位有所帮助，不要忘了收藏本站喔。

本文目录一览：

LG 推出锐龙版 gram 笔记本，续航可达 24 小时（lg2021款gram笔记本）
17 - 正交矩阵和 Gram-Schmidt 正交化
All Our N-gram are Belong to You
cbow与skip-gram
Codeforces 977B Two-gram（stl之string掉进坑）

LG 推出锐龙版 gram 笔记本，续航可达 24 小时（lg2021款gram笔记本）

小编 7 月 21 日消息，据日媒 PC Watch 消息，LG 将在 7 月下旬在日本推出 AMD 锐龙版的 gram 笔记本，包含 14 和 16 英寸型号。

据报道，锐龙版的 gram 笔记本将可选 R7 5825U 和 R5 5625U，采用 16:10 的 IPS 显示屏。14 英寸型号薄约 16mm，实现了最长 24 小时的续航，16 英寸型号实现了最多 22.5 小时的续航时间。

价格方面，14 英寸型号售价 186000 日元（约 9095.4 元人民币）起。

小编了解到，LG gram 2022 款 16/17 英寸笔记本已在中国上市，均搭载 12 代酷睿 P 系列处理器，首发价 9599 元起。

目前，LG 暂未在国内公布锐龙版的 gram 笔记本发布时间。

17 - 正交矩阵和 Gram-Schmidt 正交化

一、视频链接

　1）正交矩阵

　　定义：如果一个矩阵，其转置与自身的乘积等于单位向量，那么该矩阵就是正交矩阵，该矩阵一般用 Q 来表示，即 $Q^TQ=QQ^T=I$，也就是 $Q^T=Q^{-1}$，即转置 = 逆

　　注意：正交矩阵一定是方阵，我们来举例一个正交矩阵

$Q=\left|cosθ−sinθsinθcosθ

\right|$

$Q^{T}=\left|cosθsinθ−sinθcosθ

\right|$

　　性质：有了上面正交矩阵的定义，微秒可以得到几个正交矩阵的性质

　　　a）正交矩阵的行列式 $|Q|=1$ 或者 $|Q|=-1$，即行列式等于 1 或者 - 1，这个好推导，根据上面的定义，可知正交矩阵的行列式的平方与单位矩阵的行列式（为 1）的平方相等

　　　b）$Q^T=Q^{-1}$，并且也正交

　　　c）如果矩阵 $P$ 正交，那么矩阵 $PQ$ 也正交

　2）预备知识

　　a）正交向量：两个向量正交意味着两个向量的夹角是 90°

All Our N-gram are Belong to You

Google 的超大 5 元语言模型

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《Beautiful Data》第 14 章，讲得是 Google 的超大 5 元语言模型

对此模型有兴趣的读者可以查阅，下文

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Google Research Blog 上的文章《Official Google Research Blog: All Our N-gram are Belong to You》

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Posted by Alex Franz and Thorsten Brants, Google Machine Translation Team

Here at Google Research we have been using word n-gram models for a variety of R&D projects, such as statistical machine translation, speech recognition, spelling correction, entity detection, information extraction, and others. While such models have usually been estimated from training corpora containing at most a few billion words, we have been harnessing the vast power of Google''s datacenters and distributed processing infrastructure to process larger and larger training corpora. We found that there''s no data like more data, and scaled up the size of our data by one order of magnitude, and then another, and then one more - resulting in a training corpus of one trillion words from public Web pages.

We believe that the entire research community can benefit from access to such massive amounts of data. It will advance the state of the art, it will focus research in the promising direction of large-scale, data-driven approaches, and it will allow all research groups, no matter how large or small their computing resources, to play together. That''s why we decided to share this enormous dataset with everyone. We processed 1,024,908,267,229 words of running text and are publishing the counts for all 1,176,470,663 five-word sequences that appear at least 40 times. There are 13,588,391 unique words, after discarding words that appear less than 200 times.

Watch for an announcement at the Linguistics Data Consortium ( LDC), who will be distributing it soon, and then order your set of 6 DVDs. And let us hear from you - we''re excited to hear what you will do with the data, and we''re always interested in feedback about this dataset, or other potential datasets that might be useful for the research community.

Update (22 Sept. 2006): The LDC now has the data available in their catalog. The counts are as follows:

File sizes: approx. 24 GB compressed (gzip''ed) text files

Number of tokens:    1,024,908,267,229
Number of sentences:    95,119,665,584
Number of unigrams:         13,588,391
Number of bigrams:         314,843,401
Number of trigrams:        977,069,902
Number of fourgrams:     1,313,818,354
Number of fivegrams:     1,176,470,663

The following is an example of the 3-gram data contained this corpus:

ceramics collectables collectibles 55
ceramics collectables fine 130
ceramics collected by 52
ceramics collectible pottery 50
ceramics collectibles cooking 45
ceramics collection , 144
ceramics collection . 247
ceramics collection </S> 120
ceramics collection and 43
ceramics collection at 52
ceramics collection is 68
ceramics collection of 76
ceramics collection | 59
ceramics collections , 66
ceramics collections . 60
ceramics combined with 46
ceramics come from 69
ceramics comes from 660
ceramics community , 109
ceramics community . 212
ceramics community for 61
ceramics companies . 53
ceramics companies consultants 173
ceramics company ! 4432
ceramics company , 133
ceramics company . 92
ceramics company </S> 41
ceramics company facing 145
ceramics company in 181
ceramics company started 137
ceramics company that 87
ceramics component ( 76
ceramics composed of 85
ceramics composites ferrites 56
ceramics composition as 41
ceramics computer graphics 51
ceramics computer imaging 52
ceramics consist of 92

The following is an example of the 4-gram data in this corpus:

serve as the incoming 92
serve as the incubator 99
serve as the independent 794
serve as the index 223
serve as the indication 72
serve as the indicator 120
serve as the indicators 45
serve as the indispensable 111
serve as the indispensible 40
serve as the individual 234
serve as the industrial 52
serve as the industry 607
serve as the info 42
serve as the informal 102
serve as the information 838
serve as the informational 41
serve as the infrastructure 500
serve as the initial 5331
serve as the initiating 125
serve as the initiation 63
serve as the initiator 81
serve as the injector 56
serve as the inlet 41
serve as the inner 87
serve as the input 1323
serve as the inputs 189
serve as the insertion 49
serve as the insourced 67
serve as the inspection 43
serve as the inspector 66
serve as the inspiration 1390
serve as the installation 136
serve as the institute 187
serve as the institution 279
serve as the institutional 461
serve as the instructional 173
serve as the instructor 286
serve as the instructors 161
serve as the instrument 614
serve as the instruments 193
serve as the insurance 52
serve as the insurer 82
serve as the intake 70
serve as the integral 68

cbow与skip-gram

场景：上次回答word2vec相关的问题，回答的是先验概率和后验概率，没有回答到关键点。

词袋模型（Bag of Words, BOW）与词向量（Word Embedding）模型

词袋模型就是将句子分词，然后对每个词进行编码，常见的有one-hot、TF-IDF、Huffman编码，假设词与词之间没有先后关系。
词向量模型是用词向量在空间坐标中定位，然后计算cos距离可以判断词于词之间的相似性。

先验概率和后验概率

先验概率和后验证概率是基于词向量模型。首先一段话由五个词组成： A B C D E 对C来说：先验概率指ABDE出现后C出现的概率，即P(C|A,B,D,E) 可以将C用ABDE出现的概率来表示 Vector(C) = [P(C|A), P(C|B), P(C|D), P(C|E) ] 后验概率指C出现后ABDE出现的概率：即P(A|C),P(B|C),P(D|C),P(E|C)

n-gram

先验概率和后验概率已经知道了，但是一个句子很长，对每个词进行概率计算会很麻烦，于是有了n-gram模型。该模型基于这样一种假设，第N个词的出现只与前面N-1个词相关，而与其它任何词都不相关，整句的概率就是各个词出现概率的乘积。一般情况下我们只计算一个单词前后各两个词的概率，即n取2, 计算n-2,.n-1,n+1,n+2的概率。如果n=3，计算效果会更好；n=4，计算量会变得很大。

cbow

cbow输入是某一个特征词的上下文相关的词对应的词向量，而输出就是这特定的一个词的词向量，即先验概率。训练的过程如下图所示，主要有输入层(input)，映射层(projection)和输出层(output)三个阶段。

skip-gram

Skip-Gram模型和CBOW的思路是反着来的，即输入是特定的一个词的词向量，而输出是特定词对应的上下文词向量，即后验概率。训练流程如下：

word2vec中的Negative Sampling概述

传统网络训练词向量的网络：

word2vec训练方法和传统的神经网络有所区别，主要解决的是softmax计算量太大的问题，采用Hierarchical Softmax和Negative Sampling模型。 word2vec中cbow,skip-gram都是基于huffman树然后进行训练，左子树为1右子树为0，同时约定左子树权重不小于右子树。构建的Huffman树如下：其中，根节点的词向量对应我们的投影后的词向量，而所有叶子节点就类似于之前神经网络softmax输出层的神经元，叶子节点的个数就是词汇表的大小。在霍夫曼树中，隐藏层到输出层的softmax映射不是一下子完成的，而是沿着霍夫曼树一步步完成的，因此这种softmax取名为"Hierarchical Softmax"。

因为时间有限，暂时总结这些，下一次详细看一下word2vec中的实现。

参考： word2vec原理(一) CBOW与Skip-Gram模型基础 word2vec原理(二) 基于Hierarchical Softmax的模型自己动手写word2vec (四):CBOW和skip-gram模型

Codeforces 977B Two-gram（stl之string掉进坑）

Two-gram is an ordered pair (i.e. string of length two) of capital Latin letters. For example, "AZ", "AA", "ZA" — three distinct two-grams.

You are given a string ss consisting of nn capital Latin letters. Your task is to find any two-gram contained in the given string as a substring(i.e. two consecutive characters of the string) maximal number of times. For example, for string ss = "BBAABBBA" the answer is two-gram "BB", which contained in ss three times. In other words, find any most frequent two-gram.

Note that occurrences of the two-gram can overlap with each other.

Input

The first line of the input contains integer number nn (2≤n≤1002≤n≤100) — the length of string ss. The second line of the input contains the string ss consisting of nn capital Latin letters.

Output

Print the only line containing exactly two capital Latin letters — any two-gram contained in the given string ss as a substring (i.e. two consecutive characters of the string) maximal number of times.

Examples

input

Copy

7
ABACABA

output

Copy

AB

input

Copy

5
ZZZAA

output

Copy

ZZ

Note

In the first example "BA" is also valid answer.

In the second example the only two-gram "ZZ" can be printed because it contained in the string "ZZZAA" two times.

思路：用map<string, int>维护一个最大值输出即可

坑点：string的加法为string = string + char* ，不是string = char* + char* 或者char + char！

反正第一个加号前面必须得是string！

然后就是学一下map的一些操作了，注意map迭代器表示key和value的方式

代码：

#include<cstdio>
#include<iostream>
#include<string>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<set>
#include<map>
typedef long long ll;
using namespace std;
const int maxn = 100000 + 100;

int main(){
    map<string, int> m;
    int n;
    scanf("%d", &n);
    getchar();
    string s;
    cin >> s ;
    //int len = s.length();
    string ans;
    int maxx = 0;
    for(int i = 0; i < n-1; i++){
    	string ss;
    	ss =ss+ s[i] + s[i+1];
    	//cout << ss<<endl;
    	if(!m.count(ss))m[ss] = 0;
    	m[ss]++;
    	//if(m[ss] > )
	}
	map<string, int>::iterator it;
	map<string, int>::iterator itt;

	for( it = m.begin(); it != m.end(); it++){
		if(it->second > maxx){
			itt = it;
			maxx = it->second;
			//cout << it->second << endl;
		}
	}
	cout <<itt->first;
    return 0;
}

我们今天的关于LG 推出锐龙版 gram 笔记本，续航可达 24 小时和lg2021款gram笔记本的分享就到这里，谢谢您的阅读，如果想了解更多关于17 - 正交矩阵和 Gram-Schmidt 正交化、All Our N-gram are Belong to You、cbow与skip-gram、Codeforces 977B Two-gram（stl之string掉进坑）的相关信息，可以在本站进行搜索。

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