LCS(最长公共子序列)

DFS：

#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
using namespace std;

const int maxn = 1000 + 10;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int main(){
    while(scanf("%s %s",a,b) != EOF){   
    int n = strlen(a);
    int m = strlen(b);
    for(int i = 0;i<n;i++){
        for(int j = 0;j<m;j++){
            if(a[i] == b[j]){
                if(dp[i][j] + 1 > max(dp[i+1][j],dp[i][j+1]))//用dp[i+1][j+1]来记录a前i个和b前j个 
                {
                    dp[i+1][j+1] = dp[i][j] + 1;
                }
                else dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1]);
            } 
            else 
                dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1]);
        }
    }
    printf("%d\n",dp[n][m]);

    }


}

DFS加路径：

#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<stack> 
using namespace std;

const int maxn = 1000 + 10;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int n,m;
void lcs(){
    for(int i = 0;i<n;i++){
        for(int j = 0;j<m;j++){
            if(a[i] == b[j]){
//              if(dp[i][j] + 1 > max(dp[i+1][j],dp[i][j+1]))////用dp[i+1][j+1]来记录a前i个和b前j个 
//              {
//                  dp[i+1][j+1] = dp[i][j] + 1;
//              }
//              else dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1]);
                dp[i+1][j+1] = dp[i][j] + 1;
            } 
            else 
                dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1]);
        }
    }   
}

stack<char> road;
int main(){
    scanf("%s %s",a,b);
    n = strlen(a),m = strlen(b);
    lcs();
    int ii = n,jj = m;
    while(dp[ii][jj]){

        if(dp[ii][jj] == dp[ii][jj-1]) jj--;
        else if(dp[ii][jj] == dp[ii-1][jj]) ii--;
        else{
            ii--,jj--;
            road.push(a[ii]);//ii-1记录的是 a[ii]
            //ii--,jj--;
        }
    }

    while(!road.empty()){
        printf("%c",road.top());
        road.pop();
    }
    return 0;
}

DFS记录路径2：

#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<stack> 
using namespace std;

const int maxn = 1000 + 10;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int n,m;
int road[maxn][maxn]; 
void lcs(){
    for(int i = 0;i<n;i++){
        for(int j = 0;j<m;j++){
            if(a[i] == b[j]){
//              if(dp[i][j] + 1 > max(dp[i+1][j],dp[i][j+1]))////用dp[i+1][j+1]来记录a前i个和b前j个 
//              {
//                  dp[i+1][j+1] = dp[i][j] + 1;
//              }
//              else dp[i+1][j+1] = max(dp[i+1][j],dp[i][j+1]);
                dp[i+1][j+1] = dp[i][j] + 1;
                road[i+1][j+1] = 1;
            } 

            else {
                if(dp[i+1][j] > dp[i][j+1]){
                    road[i+1][j+1] = 2;
                    dp[i+1][j+1] = dp[i+1][j];
                } 
                else{
                    road[i+1][j+1] = 3;
                    dp[i+1][j+1] = dp[i][j+1];
                } 
            }
        }
    }   
}

stack<char> ro;
char vis[maxn];
int main(){
    scanf("%s %s",a,b);
    n = strlen(a),m = strlen(b);
    lcs();
    int ii = n,jj = m;
    memset(road,0,sizeof(road));
//  int i = 0;
    while(dp[ii][jj]){

        if(road[ii][jj] == 3) jj--;
        else if(road[ii][jj] == 2) ii--;
        else{
            ii--,jj--;
            ro.push(a[ii]);//ii-1记录的是 a[ii]
            //ii--,jj--;
        }
    }

    while(!ro.empty()){
        printf("%c",ro.top());
        ro.pop();
    }

    return 0;
}