动态规划--LCS

/*************************************************************
 * file:lcs.c
 * brief:基于动态规划，求两个字符串的最长公共子序列
 * yejing@2015.2.3    1.0      creat
 *************************************************************/
 
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <string.h>

#define MATRIX_MLEN 128

typedef enum{
	DIR_UP,
	DIR_LEFT,
	DIR_UP_LEFT
}DIR_t;

void generate_lcs_matrix(char* str1, int len1, char* str2, int len2, 
						 int lcs_matrix[][MATRIX_MLEN], int dir_matrix[][MATRIX_MLEN]){
	int i = 0, j = 0;
	if(len1 > MATRIX_MLEN || len2 > MATRIX_MLEN)
		assert(0);
	
	for(i = 0; i <= len1; ++i)
		lcs_matrix[i][0] = 0;
	
	for(j = 0; j <= len2; ++j)
		lcs_matrix[0][j] = 0;
		
	for(i = 1; i <= len1; ++i){
		for(j = 1; j <= len2; ++j){
			if(str1[i - 1] == str2[j - 1]){
				lcs_matrix[i][j] = lcs_matrix[i - 1][j - 1] + 1;
				dir_matrix[i][j] = DIR_UP_LEFT;
			}
			else if(lcs_matrix[i - 1][j] >= lcs_matrix[i][j - 1]){
				dir_matrix[i][j] = DIR_UP;
				lcs_matrix[i][j] = lcs_matrix[i - 1][j];
			}
			else{
				dir_matrix[i][j] = DIR_LEFT;
				lcs_matrix[i][j] = lcs_matrix[i][j - 1];
			}
		}
	}
	return;
}

void show_lcs(int dir_matrix[][MATRIX_MLEN], char* str1, int i, int j){
	if(i == 0 || j == 0)
		return;
	
	if(dir_matrix[i][j] == DIR_UP_LEFT){
		show_lcs(dir_matrix, str1, i - 1, j - 1);
		printf("%c ", str1[i - 1]);
	}
	else if(dir_matrix[i][j] == DIR_LEFT){
		show_lcs(dir_matrix, str1, i, j - 1);
	}
	else{
		show_lcs(dir_matrix, str1, i - 1, j);
	}
	
	return;
}

int main(int argc, char* argv[]){
	char* str1 = "aqswdefrgthyjukil";
	char* str2 = "azsxdcfvgbhnjmkl";
	int lcs_matrix[MATRIX_MLEN][MATRIX_MLEN];
	int dir_matrix[MATRIX_MLEN][MATRIX_MLEN];
	
	generate_lcs_matrix(str1, strlen(str1), str2, strlen(str2), lcs_matrix, dir_matrix);
	show_lcs(dir_matrix, str1, strlen(str1), strlen(str2));
	printf("\n");
	
	return 1;
}