最长公共子序列的一种解决方法

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

const int MAXN=100;

void print_lcs(int i,int j,char *x,int b[][MAXN])
{
    if(i==0||j==0)
    {
        return;
    }
    if(b[i][j]==0)
    {
        print_lcs(i-1,j-1,x,b);
        printf("%c",x[i-1]);
    }
    else
    {
        if(b[i][j]==1)
            print_lcs(i-1,j,x,b);
        else
            print_lcs(i,j-1,x,b);
    }
}
int main()
{
    char s1[MAXN],s2[MAXN];
    int c[MAXN][MAXN],b[MAXN][MAXN];
    int n,m;
    int i,j;
    scanf("%s",s1); n=strlen(s1);
    scanf("%s",s2); m=strlen(s2);
    for(i=0;i<=n+1;i++)
        c[i][0]=0;
    for(j=0;j<=m+1;j++)
        c[0][j]=0;
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=m;j++)
        {
            if(s1[i-1]==s2[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]=-1;
                }
            }
        }
    }
    printf("%d\n",c[n][m]);
    print_lcs(n+1,m+1,s1,b);
}

function LCS(s1,s2)
n=length(s1);
m=length(s2);
C=zeros(100,100);
B=zeros(100,100);
for i=1:n
    for j=1:m
        if (i==1||j==1)
            if(s1(i)==s2(j))
                C(i,j)=1;
            else
                C(i,j)=0;
            end
            continue;
        end
        if(s1(i)==s2(j))
            C(i,j)=C(i-1,j-1)+1;
            B(i,j)=0;
        elseif (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)=-1;
        end
    end
end
fprintf(1,‘%g\n‘,C(n,m))
print_lcs(n,m,s1,B)
fprintf(1,‘\n‘)

function print_lcs(i,j,x,B)
if(i==0||j==0)
    return
end
if(B(i,j)==0)
    print_lcs(i-1,j-1,x,B);
    fprintf(1,‘%s‘,x(i))
end
if(B(i,j)==1)
    print_lcs(i-1,j,x,B);
end
if(B(i,j)==-1)
    print_lcs(i,j-1,x,B);
end
end

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <vector>

using namespace std ;

const int MAXN = 510 ;

int dp[MAXN][MAXN] , prex[MAXN][MAXN] , prey[MAXN][MAXN]  ;
char s1[MAXN] , s2[MAXN] ;
int n , m ;

int main(){
    scanf("%s",s1+1) ; n = strlen(s1+1);
    scanf("%s",s2+1) ; m = strlen(s2+1) ;
    memset(dp,-1,sizeof(dp)) ;
    memset(prex,-1,sizeof(prex)) ;
    memset(prey,-1,sizeof(prey)) ;
    dp[0][0] = 0 ;
    int maxlen = -1 , ansx , ansy ;
    for (int i = 1 ; i <= n ; i++)
        for (int j = 1 ; j <= m ; j++){
            if (s1[i] != s2[j]) continue ;
            for (int px = 0 ; px < i ; px++)
                for (int py = 0 ; py < j ; py++){
                    if (s1[px] == s2[py] && dp[px][py] + 1 > dp[i][j]){
                        dp[i][j] = dp[px][py] + 1 ;
                        prex[i][j] = px ;
                        prey[i][j] = py ;
                    }
            }
        if (dp[i][j] > maxlen){
            maxlen = dp[i][j] ;
            ansx = i ;
            ansy = j ;
        }
    }
    printf("Length = %d\n" , dp[ansx][ansy]) ;
    vector<char> result ;
    while (ansx != 0 && ansy != 0){
        result.push_back(s1[ansx]) ;
        int tempx = prex[ansx][ansy] ;
        int tempy = prey[ansx][ansy] ;
        ansx = tempx ; ansy = tempy ;
    }
    for (int i = (int)result.size() - 1 ; i >= 0 ; i--)
        printf("%c",result[i]);
    printf("\n");
    return 0 ;
}