动态规划——LCS

LCS代码实现

#include<iostream>
#include<cstring>
#include<algorithm>
#define maxn 105
using namespace std;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int LCSlength() {
    memset(dp,0,sizeof(dp));
    int alen = strlen(a);
    int blen = strlen(b);
    for(int i=0; i<alen; i++) {
        for(int j=0; j<blen; j++) {
            if(a[i]==b[j]) {
                dp[i][j] = dp[i-1][j-1]+1;
            } else {
                dp[i][j] = max(dp[i-1][j],dp[i][j-1]);
            }
        }
    }
    return dp[alen-1][blen-1];
}
int main() {
    while(~scanf("%s %s",a,b)) {
        int ans = LCSlength();
        printf("%d",ans); 
    }

    return 0;
}

 递归求LSC序列：

#include<iostream>
#include<cstring>
#include<algorithm>
#define maxn 105
using namespace std;
char a[maxn],b[maxn];
int dp[maxn][maxn];
int step[maxn][maxn];
void Print(int i,int j){
    if(i<0 || j<0){
        return;
    }
    if(step[i][j]==1){
        Print(i-1,j-1);
        printf("%c",a[i]); 
    }else if(step[i][j]==2){
        Print(i-1,j);
    }else if(step[i][j]==3){
        Print(i,j-1);
    }
}
void LCS(){
    memset(dp,0,sizeof(dp));
    int alen = strlen(a);
    int blen = strlen(b);
    for(int i=0;i<alen;i++){
        for(int j=0;j<blen;j++){
            if(a[i]==b[j]){
                dp[i][j] = dp[i-1][j-1]+1;
                step[i][j] = 1;
            }else{
                if(dp[i-1][j]>dp[i][j-1]){
                    dp[i][j] = dp[i-1][j];
                    step[i][j] = 2;
                }else{
                    dp[i][j] = dp[i][j-1];
                    step[i][j] = 3;
                }
            }
        }
    }
    cout<<dp[alen-1][blen-1]<<endl;
    Print(alen-1,blen-1);
}
int main() {
    while(~scanf("%s %s",a,b)) {
        LCS();
        
    }

    return 0;
}

非递归LSC序列：