think about it, how can we differentiate the case which takes zero digit with the valid case which take at least one digit?

306c.cc

#include <string>
#include <iostream>
using namespace std;
string s;
int n;
int dp[100][8];
int solve(int p, int num){
	if(p==n){
		return dp[p][num] = (num==0);
	}
	if(dp[p][num]!=-1) return dp[p][num];	

	int t = (num*10)+(s[p]-'0');
	//take digit at position p or not
	int a = solve(p+1, t%8);
	int b = solve(p+1, num);
	return dp[p][num] = max(a,b);  
}

int main(){
	cin>>s;
	n = s.size();
	memset(dp, -1, sizeof dp);
	if(solve(0,0)==0) cout<<"NO\n";  
	else{
		for(int i=0;i<n;++i){
			if(dp[i][0]==1){
				return cout<<"YES\n", 0;
			}
		}
	}
	cout<<"NO\n"; 
	return 0;
}