C++博客-C++研究-随笔分类-Algorithm

求有序序列公共部分(集合交集的O(n)复杂度求法)

小龙哥 — Tue, 15 Jan 2008 13:12:00 GMT

摘要: 假定两个有序序列，扫描至多一遍求出其公共部分，复杂度O(n),但中间跳跃前进，实战复杂度在O(n)以下，应用环境为搜索引擎在对文档特征向量相似度的判定部分，对于10万维以上的数据，效率还可以~ 阅读全文

小龙哥 2008-01-15 21:12 发表评论

精炼循环右移

小龙哥 — Tue, 15 May 2007 02:03:00 GMT

摘要: 精炼循环右移在对内存与CPU要求高的移动设备中尤为重要，如：求描超长型整数，浮点数，游戏中循环选关，卡牌数字处理等。本文为循环右移的常用解法做了总结，并对相关算法做了简洁描述。阅读全文

小龙哥 2007-05-15 10:03 发表评论

Some algorithms about judging a prime .

小龙哥 — Wed, 18 Apr 2007 19:05:00 GMT

1.GRIDDLE METHOD (ALSO CALLED SIFT METHOD)

When I was a student in Bachelor phrase , a teacher has tought me a method called griddle method , it's principle is:

if a number can be devided by another number(except 1) , it isn't a prime , so , we set the non-prime at zero. after all number [In fact , half of the range checked is OK ]test finished , We simply output the NON-ZERO number , it 's the prime table in the RANGE.

E.G
Define the Range from 1-100;

/********************************************************************
created: 2007/04/19
created: 19:4:2007 3:00
filename: C:\testvc6\TestStll\TestStll.cpp
file path: C:\testvc6\TestStll
file base: TestStll
file ext: cpp
author: Chang xinglong(King.C)
purpose: Print Prime Table in RANGE(1-100)
*********************************************************************/

The Code Here :

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;

void InitArray(int A[] ,int len)
{
    for (int i=0;i<len;i++)
    {
        A[i]=i+1;
    }
}

void OutputPrime(int A[] ,int len)
{
  for (int i=2;i<len;i++)
  {
      for (int j=2;i*j<=len;j++)
      {
          A[i*j-1]=0;
          cout<<i<<","<<j<<","<<i*j<<endl;
      }

  }
  for (i=0;i<len;i++)
  {
      if (A[i]!=0)
      {
          cout<<A[i]<<" ";
      }

  }
  cout<<endl;
}
// Main Method [4/19/2007 Changxinglong (King.C)]
int main(int argc, char* argv[])
{
    int A[100];
    InitArray(A,100);
    OutputPrime(A,100);
    return 1;
}

2.THE DIRECT METHOD

E.G

/********************************************************************
created: 2007/04/19
created: 19:4:2007 3:00
filename: C:\testvc6\TestStll\TestStll.cpp
file path: C:\testvc6\TestStll
file base: TestStll
file ext: cpp
author: Chang xinglong(King.C)
purpose: Prime ?
*********************************************************************/

Here is the Kernel Function(Quote : STL TURORIAL REFERRENCE):

1//predicate, which returns whether an integer is a prime number
2bool isPrime (int number)
3{
4//ignore negative sign
5number = abs(number);
6// 0 and 1 are prime numbers
7if (number == 0 || number == 1) {
8return true;
9}
10//find divisor that divides without a remainder
11int divisor;
12for (divisor = number/2; number%divisor != 0; --divisor) {
13;
14}
15//if no divisor greater than 1 is found, it is a prime number
16return divisor == 1;
17}

In Main Function , traverse the given range judge every number use the above function:

int main(int argc , char * argv[])
{
  int A[100];
  InitArray(A,100);
  for(int i=0;i<100;i++)
    if(isPrime(A[i]))
       cout<<A[i]<<endl;
}

3. Extention
Further , if there is a given List or Vector and it's filled with data , how can you find the prime number in the data effiectly ?
STL Algorithm can help you indeed. After the step two , we can write a few code to implement the function:

int main()
{
list<int> coll;
//insert elements from 1 to 100
for (int i=1; i<=100; ++i) {
coll.push_back(i);
}
//search for prime number
list<int>::iterator pos;
pos = find_if (coll.begin(), coll.end(), //range
isPrime); //predicate
if (pos != coll.end()) {
//found
cout << *pos << " is first prime number found" << endl;
}
else {
//not found
cout << "no prime number found" << endl;
}
}

小龙哥 2007-04-19 03:05 发表评论

How can you efficeny judge whether the num is primer?

小龙哥 — Wed, 18 Apr 2007 18:39:00 GMT

A friend ask me 'How can you efficeny judge whether the num is primer? '

There is a easy way to do it , the follow code isn't written by me but a classic method

E.G quote from STL tutorial reference

#include <iostream>
#include <list>
#include <algorithm>
#include <cstdlib> //for abs()
using namespace std;
//predicate, which returns whether an integer is a prime number
bool isPrime (int number)
{
//ignore negative sign
number = abs(number);
// 0 and 1 are prime numbers
if (number == 0 || number == 1) {
return true;
}
//find divisor that divides without a remainder
int divisor;
for (divisor = number/2; number%divisor != 0; --divisor) {
;
}
//if no divisor greater than 1 is found, it is a prime number
return divisor == 1;
}

小龙哥 2007-04-19 02:39 发表评论