Uddered But Not Herd

#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <unordered_map>
#include <iomanip>
#include <regex>
#include <numeric>
using namespace std;
#define pii pair<int , int>
#define FAST ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
const int MAX = 100005;

string s;
int arr[26];
int used = 0;
int consecutive[20][20];
int dp[(1 << 20)];

int main() {
    //freopen("talent.in", "r", stdin);
    //freopen("talent.out", "w", stdout);
    FAST;
    cin >> s;
    for(int i = 0; i < 26; i++){
        arr[i] = -1;
    }
    for(int i = 0; i < s.size(); i++) {
        if(i == 0){
            arr[s[0] - 'a'] = used;
            used++;
        }
        int nxt = i + 1;
        if (nxt >= s.size()) {
            continue;
        }
        if (arr[s[nxt] - 'a'] == -1) {
            arr[s[nxt] - 'a'] = used;
            used++;
        }
        consecutive[arr[s[i] - 'a']][arr[s[nxt] - 'a']]++;
    }
    memset(dp, 2e9, sizeof dp);
    dp[0] = 0;
    for(int state = 1; state < (1 << 20); state++){
        dp[state] = 2e9;
        for(int cur_char = 0; cur_char < 20; cur_char++){
            if(!(state & (1 << cur_char))){
                continue;
            }
            int val = dp[state ^ (1 << cur_char)];
            for(int added_char = 0; added_char < 20; added_char++){
                if(!(state & (1 << added_char))){
                    continue;
                }
                val += consecutive[cur_char][added_char];
            }
            dp[state] = min(dp[state], val);
        }
    }
    cout << dp[(1 << 20) - 1] + 1<< "\n";

}