求助，如何剪枝，如何记忆化搜索？

#include<bits/stdc++.h>
using namespace std;
int n,K,s[100005];
int t1,t2,ans=0,mem[100005];
char c;

void dfs(int shou,int tot,int ceng,int bian){
	if(ceng>n){
		ans=max(ans,tot);
//		cout<<"ans="<<ans<<" tot="<<tot<<'\n';
		return ;
	}
	
	if((n-ceng+1+tot)<ans) return ;
	
	t1=0;
	if(shou==s[ceng]) t1=0;
	else if((shou==0&&s[ceng]==1)||(shou==1&&s[ceng]==2)||(shou==2&&s[ceng]==0)) t1=1;
	dfs(shou,tot+t1,ceng+1,bian);
	
	if(bian<K){
		for(int i=0;i<3;i++){
			t2=0;
			if(shou==s[ceng]) t2=0;
			else if((shou==0&&s[ceng]==1)||(shou==1&&s[ceng]==2)||(shou==2&&s[ceng]==0)) t2=1;
			dfs(i,tot+t2,ceng+1,bian+1);
		}
	}
	return ;
}

int main(){
	ios::sync_with_stdio(0);
	cout.tie(0);
	cin.tie(0);
	cin>>n>>K;
	for(int i=1;i<=n;i++){
		cin>>c;
		if(c=='H') s[i]=0;
		if(c=='S') s[i]=1;
		if(c=='P') s[i]=2;
	}
	for(int i=0;i<=2;i++){
		dfs(i,0,1,0);
	}
	cout<<ans<<'\n';
	return 0;
}