Self-numbers 2

本文介绍了一道使用C++解决的程序设计竞赛题目,主要内容包括数组操作、排序算法的应用及位运算技巧。通过该题目,展示了如何利用C++进行高效的数据处理,并给出了一种具体的实现方案。

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#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int D=(1<<16)-1;
int N,K;
int a[5503];
int r[5503];
int d[75503];
bool cmp(int m,int n)
{
	return a[m]<a[n];//用a数组元素大小对r数组排序,好有技巧
}
int get(int x)
{
	int res=x;
	while(x)
	{
		res+=x%10;
		x/=10;
	}
	return res;
}
void solve()
{
	int i,j,k,num,t;
	for(i=0;i<K;i++)
	{
		scanf("%d",&a[i]);
	}
	a[K]=0;//防止越界
	for(i=0;i<K;i++)
		r[i]=i;
	sort(r,r+K,cmp);
	r[K]=K;//防止越界
	memset(d,0,sizeof(d));
	num=k=0;
	for(i=1;i<=N;i++)
	{
		if(!d[i&D])
		{
			++num;
			while(num==a[r[k]])//a[k]可能有多个相等
				a[r[k++]]=i;
		}
		t=get(i);
		if(t<=N)
			d[t&D]=1;//当大于D时开始循环利用
		d[i&D]=0;
	}
	printf("%d\n%d",num,a[0]);
	for(i=1;i<K;i++)
		printf(" %d",a[i]);
  	 	printf("\n");
}
int main()
{
	while(scanf("%d%d",&N,&K)!=EOF)
	{
		solve();
	}	
}


### Linear Complexity Self-Attention Implementation and Optimization Self-attention mechanisms have been pivotal in advancing the capabilities of deep learning models, especially within natural language processing tasks. Traditional self-attention has a quadratic time complexity relative to input length due to its computation involving all pairs of positions in an input sequence[^1]. However, linear complexity self-attention aims at reducing this computational burden. #### Efficient Implementations One approach towards achieving linear complexity involves approximating or restructuring how attentions scores are computed between tokens. For instance, instead of computing full pairwise interactions, one could use locality-sensitive hashing (LSH), which groups similar items into buckets without explicitly comparing every item against each other. This method significantly reduces the number of required comparisons while maintaining performance quality[^3]. Another technique utilizes random projections where high-dimensional vectors representing token embeddings get projected onto lower dimensions through structured matrices like Fastfood transforms. Such transformations preserve distances well enough so that subsequent operations remain effective yet require fewer resources than standard methods do[^4]. ```python import torch from performer_pytorch import PerformerLM model = PerformerLM( num_tokens=20000, dim=512, depth=6, heads=8, causal=True, feature_redraw_interval=1000, generalized_attention=True, kernel_fn='relu' ) text = "The quick brown fox jumps over the lazy dog" tokens = tokenizer.encode(text).ids # assuming you've defined `tokenizer` elsewhere input_tensor = torch.tensor([tokens]) output = model(input_tensor) print(output.shape) # should output something like torch.Size([1, seq_len, vocab_size]) ``` This code snippet demonstrates implementing efficient self-attention via the Performer architecture from PyTorch library, leveraging fast Fourier transform-based kernels for reduced complexity computations during training phases. #### Optimizations Techniques Optimizing these implementations often revolves around exploiting hardware acceleration features such as GPU tensor cores optimized specifically for matrix multiplications involved in attention calculations. Additionally, mixed precision arithmetic can further enhance speed by performing some parts of forward/backward passes using half-precision floating-point numbers when possible without sacrificing much accuracy. Memory efficiency gains come not only from algorithmic improvements but also architectural choices like chunked processing schemes dividing long sequences into smaller manageable chunks processed independently before being recombined later on. These strategies help mitigate memory overhead associated with large-scale transformer architectures operating under constrained environments[^2]. --related questions-- 1. How does Locality-Sensitive Hashing contribute to making self-attention computationally feasible? 2. What role do random projections play in optimizing self-attention algorithms? 3. Can you explain how specific hardware optimizations impact the performance of linear-complexity self-attention models? 4. In what ways might chunked processing improve both runtime and resource utilization compared to traditional approaches?
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