string: longest common sequence and longest common substring

1 longest common sequence 

#include <iostream>
#include <assert.h>
using namespace std;

void LCS_LENGTH_1(const char *kArr1, const int kLen1,
				  const char *kArr2, const int kLen2,
				  char **b, int **c)
{
	assert(NULL != kArr1 && NULL != kArr2
			&& kLen1 > 0 && kLen2 > 0
			&& NULL != b && NULL != c);
	for (int i = 0; i <= kLen1; ++i)
		c[i][0] = 0;
	for (int i = 0; i <= kLen2; ++i)
		c[0][i] = 0;
	for (int i = 1; i <=kLen1; ++i)
	{
		for (int j= 1; j <= kLen2; ++j)
		{
			if (kArr1[i-1] == kArr2[j-1])
			{
				c[i][j] = c[i-1][j-1] + 1;
				b[i][j] = '0';
			}
			else if(c[i-1][j] >= c[i][j-1])
			{
				c[i][j] = c[i-1][j];
				b[i][j] = '1';
			}
			else
			{
				c[i][j] = c[i][j-1];
				b[i][j] = '2';
			}
		}
	}
}



void PrintLCS(char **b,const char *arr_1,
			  const int kLen1, const int kLen2)
{
	if (kLen2 <= 1 && kLen1 <= 1)
		return;
	if ('0' == b[kLen1][kLen2])
	{
		PrintLCS(b,arr_1,kLen1-1,kLen2-1);
		cout<<arr_1[kLen1-1]<<" ";
	}
	else if('1' == b[kLen1][kLen2])
	{
		PrintLCS(b,arr_1,kLen1-1,kLen2);
	}
	else
	{
		PrintLCS(b,arr_1,kLen1,kLen2-1);
	}
}
int main()
{
	char arr_1[] = "abcbdab";
	char arr_2[] = "bdcaba";
	char **b = new char*[7+1];
	int **c = new int *[7+1];
	for (int i = 0; i < 7+1; ++i)
	{
		b[i] = new char[6+1];
		c[i] = new int[6+1];
		for (int j = 0; j < 6 + 1; ++j)
		{
			b[i][j] = 'a';
		}
	}
	LCS_LENGTH_1(arr_1,7,arr_2,6,b,c);
	for (int i = 0; i < 7 + 1; ++i)
	{
		for (int j = 0; j < 6 + 1; ++j)
		{
			cout<<c[i][j]<<" ";
		}
		cout<<endl;
	}
	cout<<endl;
	for (int i = 0; i < 7 + 1; ++i)
	{
		for (int j = 0; j < 6 + 1; ++j)
		{
			cout<<b[i][j]<<" ";
		}
		cout<<endl;
	}
	cout<<endl;
	PrintLCS(b,arr_1,7,6);
	cout<<endl;
	return 0;
}

2 longest common substring

/** 
找出两个字符串的最长公共连续子串的长度
** author :liuzhiwei  
** data   :2011-08-16
**/ 
#include "stdio.h"
#include "string.h"
#include "stdlib.h"

int longest_common_substring(char *str1, char *str2)
{
	int i,j,k,len1,len2,max,x,y;
	len1 = strlen(str1);
	len2 = strlen(str2);
	int **c = new int*[len1+1];
	for(i = 0; i < len1+1; i++)
		c[i] = new int[len2+1];
	for(i = 0; i < len1+1; i++)
		c[i][0]=0;        //第0列都初始化为0
	for(j = 0; j < len2+1; j++)
		c[0][j]=0;        //第0行都初始化为0 
	max = -1;
	for(i = 1 ; i < len1+1 ; i++)
	{
		for(j = 1; j < len2+1; j++)
		{
			if(str1[i-1]==str2[j-1])     //只需要跟左上方的c[i-1][j-1]比较就可以了
				c[i][j]=c[i-1][j-1]+1;
			else                         //不连续的时候还要跟左边的c[i][j-1]、上边的c[i-1][j]值比较，这里不需要
				c[i][j]=0;
			if(c[i][j]>max)
			{
				max=c[i][j];
				x=i;
				y=j;
			}
		}
	}

	//输出公共子串
	char s[1000];
	k=max;
	i=x-1,j=y-1;
	s[k--]='\0';
	while(i>=0 && j>=0)
	{
		if(str1[i]==str2[j])
		{
			s[k--]=str1[i];
			i--;
			j--;
		}
		else       //只要有一个不相等，就说明相等的公共字符断了，不连续了
			break;
	}
	printf("最长公共子串为：");
	puts(s);
	for(i = 0; i < len1+1; i++)         //释放动态申请的二维数组
		delete[] c[i];
	delete[] c;
	return max;
}
int main(void)
{
	char str1[1000],str2[1000];
	printf("请输入第一个字符串：");
	gets(str1);
	printf("请输入第二个字符串：");
	gets(str2);
	int len = longest_common_substring(str1, str2);
	printf("最长公共连续子串的长度为：%d\n",len);
	system("pause");
	return 0;
}