LCS最长公共子串

//
// LCS最长公共自序列问题。动规解法。
#include <iostream>
#include <string.h>
#include <assert.h>
#include <time.h>
using namespace std;


int lcs(const char *str1, const char *str2)
{
	assert(NULL!=str1 && NULL!=str2);
	int Mlen=strlen(str1);
	int Nlen=strlen(str2);
	//1.分配矩阵数组
	int **apn=new int *[Mlen+1];
	int i;
	for (i=0; i<Mlen+1; i++)
	{
		apn[i] = new int[Nlen+1];
	}
	int j;
	for (i=0; i<Mlen+1; i++)
	{
		for (j=0; j<Nlen+1; j++)
		{
			apn[i][j]=0;
		}
	}

	//2.循环	
	for (i=1; i<Mlen+1; i++)
	{
		for (j=1; j<Nlen+1; j++)
		{
			if (str1[i-1] == str2[j-1])
			{
				apn[i][j]=apn[i-1][j-1]+1;
			}
			else
			{
				int t1=apn[i-1][j];
				int t2=apn[i][j-1];
				apn[i][j]=(t1>t2?t1:t2);
			}
		}
	}

	int re=apn[Mlen][Nlen];
	for (i=0;i<Mlen+1;i++)
	{
		for (j=0;j<Nlen+1;j++)
		{
			cout<<apn[i][j]<<" ";
		}
		cout<<endl;
	}
	// 3.销毁矩阵数组
	for (i=0; i<Mlen+1; i++)
	{
		delete []apn[i];
	}
	return re;

}

int main()
{
	
	char str1[]="abcdefghijklp";
	char str2[]="asdhalfnw ";
	char str3[]="acdfg";
	char str4[]="acfdg";
	cout<<str1<<"   and   "<<str2<<": "<<lcs(str1,str2)<<endl;
	cout<<endl;
	cout<<str3<<"   and   "<<str4<<": "<<lcs(str3,str4)<<endl;
	return 0;
}

 

打印其中一个公共子串的版本：

//
// LCS最长公共自序列问题。动规解法。
#include <iostream>
#include <string.h>
#include <assert.h>
#include <time.h>
using namespace std;


int lcs(const char *str1, const char *str2)
{
	assert(NULL!=str1 && NULL!=str2);
	int Mlen=strlen(str1);
	int Nlen=strlen(str2);
	//1.分配矩阵数组
	int **apn=new int *[Mlen+1];
	int **apnf=new int *[Mlen+1];
	int i;
	for (i=0; i<Mlen+1; i++)
	{
		apn[i] = new int[Nlen+1];
		apnf[i] = new int[Nlen+1];
	}
	int j;
	for (i=0; i<Mlen+1; i++)
	{
		for (j=0; j<Nlen+1; j++)
		{
			apn[i][j]=0;
			apnf[i][j]=0;
		}
	}

	//2.循环	
	for (i=1; i<Mlen+1; i++)
	{
		for (j=1; j<Nlen+1; j++)
		{
			if (str1[i-1] == str2[j-1])
			{
				apn[i][j]=apn[i-1][j-1]+1;
				apnf[i][j]=1; // 斜对角方向
			}
			else
			{
				int t1=apn[i-1][j];
				int t2=apn[i][j-1];
				apn[i][j]=(t1>t2?t1:t2);
				if(t1>t2)
					apnf[i][j]=2; // 竖直方向
				else
					apnf[i][j]=3; // 水平方向

			}
		}
	}

	int re=apn[Mlen][Nlen];
	for (i=0;i<Mlen+1;i++)
	{
		for (j=0;j<Nlen+1;j++)
		{
			cout<<apn[i][j]<<" ";
		}
		cout<<endl;
	}
	//3.打印
	i=Mlen;
	j=Nlen;
	while(true)
	{
		if (apnf[i][j]==2 )
		{
			i--;
			continue;
		}else if (apnf[i][j]==3)
		{
			j--;
			continue;
		}else if (apnf[i][j]==1)
		{
			cout<<str1[i-1]<<" ";
			i--;j--;
		}
		if (i==0 || j==0)
		{
			break;
		}
	}
	cout<<endl;
	// 4.销毁矩阵数组
	for (i=0; i<Mlen+1; i++)
	{
		delete []apn[i];
		delete []apnf[i];
	}
	return re;

}

int main()
{
	
	char str1[]="abcdefghijklpn";
	char str2[]="asdhalfnw ";
	char str3[]="acdfg";
	char str4[]="acfdg";
	cout<<str1<<"   and   "<<str2<<": "<<lcs(str1,str2)<<endl;
	cout<<endl;
	cout<<str3<<"   and   "<<str4<<": "<<lcs(str3,str4)<<endl;
	return 0;
}

 

 

参考：

http://blog.youkuaiyun.com/yysdsyl/article/details/4226630