#include <iostream>
int main(void){

char nameOfKid[8];

int noOfLetters;
std::cin >> noOfLetters;
std::cin.ignore( 256, '\n') ;
int cur, temp, steps, newcur;
newcur = 0; cur = 0; steps= 0 ;
for (int i = 0 ; i < noOfLetters; ++i){

        std::cin.getline(nameOfKid, 8);

        temp = static_cast<int>(nameOfKid[0]);

        switch(temp){
            case 65:
            case 80:
            case 79:
            case 82: newcur = 1;
                   break;
            case 66:
            case 77:
            case 83: newcur = 2;
                   break;
            case 68:
            case 71:
            case 74:
            case 75:
            case 84: newcur = 3;
                   break;

        }
        if ((newcur!=cur) && (i!=0)){
        steps = steps + ((newcur>cur) ? (newcur-cur): (cur-newcur));

        }
        cur = newcur;

    }

std::cout << steps;
return 0;
}

You can store first letters with their's corresponding place like that:

int m[256];
m['A'] = m['P'] = m['O'] = m['R'] = 1;
m['B'] = m['M'] = m['S'] = 2;
m['D'] = m['G'] = m['J'] = m['K'] = m['T'] = m['W'] = 3;

#include<bits/stdc++.h>

using namespace std;

int main(){
    map<char,int>mp;
    mp['A'] = 1;
    mp['O'] = 1;
    mp['R'] = 1;
    mp['P'] = 1;

    mp['B'] = 2;
    mp['M'] = 2;
    mp['S'] = 2;

    mp['D'] = 3;
    mp['G'] = 3;
    mp['J'] = 3;
    mp['K'] = 3;
    mp['T'] = 3;
    mp['W'] = 3;

    int n,ans=0,pre=-1;
    string s;
    cin>>n;

    while(n--){
        cin>>s;
        if(pre== -1){
            pre = mp[s[0]];
        }else{
            ans += abs(mp[s[0]] - pre);
            pre = mp[s[0]];
        }
    }
    cout<<ans<<endl;

return  0;
}
i also got WA#3 doing in same way.