LCS算法

最长公共字串LCS算法的实现

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX 100
#define UPLEFT 1
#define UP 2
#define LEFT 3

char s1[MAX] = {'a','b','c','d','\0'};
int s1len = 4;
char s2[MAX] = {'c','x','b','y','d','z','\0'};
int s2len = 6;
char comm[MAX];
char temp[MAX];
int commlen = 0;
int mx[MAX][MAX];//matrix to store current max common length of two strings
int dir[MAX][MAX];

void init()
{
	int i=0;

	for(i=0;i<s2len;i++)
	{
		if(s2[i] == s1[0])
		{
			mx[0][i] = 1;
			dir[0][i] = UPLEFT;
		}
		else
		{
			mx[0][i] = 0;
			dir[0][i] = LEFT;
		}
	}
	for(i=0;i<s1len;i++)
	{
		if(s1[i] == s2[0])
		{
			mx[i][0] = 1;
			dir[i][0] = UPLEFT;
		}
		else 
		{
			mx[i][0] = 0;
			dir[i][0] = UP;
		}
	}
}

/*void clearDir()
{
	int i=0,j=0;
	for(i=0;i<s1len;i++)
	{
		for(j=0;j<s2len;j++)
		{
			dir[i][j] = 0;
		}
	}
}*/

void buildMx()
{
	int i=0,j=0;
	for(i=1;i<s1len;i++)
	{
		for(j=1;j<s2len;j++)
		{
			if(s1[i] == s2[j])
			{
				mx[i][j] = mx[i-1][j-1] + 1;
				dir[i][j] = UPLEFT;
			}
			else if(mx[i-1][j]>=mx[i][j-1])
			{
				mx[i][j] = mx[i-1][j];
				dir[i][j] = UP;
			}
			else
			{
				mx[i][j] = mx[i][j-1];
				dir[i][j] = LEFT;
			}
		}
	}
}

void getLCS()
{
	int i=s1len-1;
	int j=s2len-1;
	int d; //strore temp direction
	int c = 1;
	int cnt = 0;

	while(i>=0 && j>=0)
	{
		d = dir[i][j];
		switch(d)
		{
			case UP: 
				i = i-1;
				break;
			case LEFT:				
				j = j-1;
				break;
			case UPLEFT:
				temp[cnt] = s1[i];
				i = i-1;
				j = j-1;				
				cnt++;
				break;
			default:
				break;
		}
	}	

	commlen = cnt;
	for(i=0;i<cnt;i++) comm[i] = temp[cnt-i-1];
	comm[cnt] = '\0';
}

void PrintLCS()
{
	int i=0;
	
	printf("s1: %s\n",s1);
	printf("s2: %s\n",s2);
	printf("LCS Length: %d\n", commlen);
	printf("LCS: ");
	/*for(i=0;i<commlen;i++)
	{
		printf("%c",comm[i]);
	}*/
	printf("%s\n",comm);

	
}

int main()
{
	scanf("%s", s1);
	scanf("%s", s2);
	s1len = strlen(s1);
	s2len = strlen(s2);

	init();
	buildMx();
	getLCS();//get the longest common string
	PrintLCS();

	return 0;
}




/*int clearMatrx(int** m)
{
	int i=0, j=0;
	for(i=0;i<s1len;i++)
	{
		for(j=0;j<s2len;j++)
		{
			m[i][j] = 0;
		}
	}
	return 0;
}*/