CALPOWER - Editorial

Problem statement
Contest source

Author, Editorialist : Dhananjay Raghuwanshi
Tester : Miten Shah

DIFFICULTY:

Simple

PREREQUISITES:

Sorting

PROBLEM:

Given a string S of lowercase english alphabets, we need to find maximum value of the string.
The value of a string S, is defined as ∑ i * (position of i_{th} letter of S in alphabets), for i = 1,2 … length of S. We can transform S in any of the possible rearrangements of this string S.

EXPLANATION:

  • For some index i of the string S it’s contribution in the value of the array is proportional to i * (position of i_{th} letter of S in alphabets) . So to maximise the value of the array we need to maximise the above multiplication. The above product will be maximum if for a lager i, the character at i_{th} position in S comes later in alphabets. So from the above explanation, the rearrangement of string S that will have maximum is the one sorted in non decreasing order.

SOLUTION :

c++ Solution
#include <bits/stdc++.h>
using namespace std;

signed main()
{
    int t;
    cin >> t;
    while (t--)
    {
        int ans = 0, n;
        string s;
        cin >> s;
        n = s.size();
        sort(s.begin(), s.end());
        for (int i = 0; i < n; i++)
            ans += (i + 1) * (s[i] - 'a' + 1);
        cout << ans << endl;
    }
}
C++ Tester's Solution
// created by mtnshh

#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define pb push_back
#define rb pop_back
#define ti tuple<int, int, int>
#define pii pair<int, int>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define mp make_pair
#define mt make_tuple
 
#define rep(i,a,b) for(ll i=a;i<b;i++)
#define repb(i,a,b) for(ll i=a;i>=b;i--)
 
#define err() cout<<"--------------------------"<<endl; 
#define errA(A) for(auto i:A)   cout<<i<<" ";cout<<endl;
#define err1(a) cout<<#a<<" "<<a<<endl
#define err2(a,b) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<endl
#define err3(a,b,c) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<endl
#define err4(a,b,c,d) cout<<#a<<" "<<a<<" "<<#b<<" "<<b<<" "<<#c<<" "<<c<<" "<<#d<<" "<<d<<endl

#define all(A)  A.begin(),A.end()
#define allr(A)    A.rbegin(),A.rend()
#define ft first
#define sd second

#define V vector<ll>
#define S set<ll>
#define VV vector<V>
#define Vpll vector<pll>
 
#define endl "\n"

long long readInt(long long l,long long r,char endd){
    long long x=0;
    int cnt=0;
    int fi=-1;
    bool is_neg=false;
    while(true){
        char g=getchar();
        // char g = getc(fp);
        if(g=='-'){
            assert(fi==-1);
            is_neg=true;
            continue;
        }
        if('0'<=g && g<='9'){
            x*=10;
            x+=g-'0';
            if(cnt==0){
                fi=g-'0';
            }
            cnt++;
            assert(fi!=0 || cnt==1);
            assert(fi!=0 || is_neg==false);
            
            assert(!(cnt>19 || ( cnt==19 && fi>1) ));
        } else if(g==endd){
            if(is_neg){
                x= -x;
            }
            // cerr << x << " " << l << " " << r << endl;
            assert(l<=x && x<=r);
            return x;
        } else {
            assert(false);
        }
    }
}
string readString(int l,int r,char endd){
    string ret="";
    int cnt=0;
    while(true){
        char g=getchar();
        // char g=getc(fp);
        assert(g != -1);
        if(g==endd){
            break;
        }
        cnt++;
        ret+=g;
    }
    assert(l<=cnt && cnt<=r);
    return ret;
}
long long readIntSp(long long l,long long r){
    return readInt(l,r,' ');
}
long long readIntLn(long long l,long long r){
    return readInt(l,r,'\n');
}
string readStringLn(int l,int r){
    return readString(l,r,'\n');
}
string readStringSp(int l,int r){
    return readString(l,r,' ');
}

const int max_q = 1e2;

const ll N = 100005;
const ll INF = 1e12;

void solve(){
    string s = readStringLn(1, max_q);
    sort(all(s));
    ll ans = 0, n = s.length();
    rep(i,0,n){
        ans += (s[i] - 'a' + 1) * (i + 1);
    }
    cout << ans << endl;
}

int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    ll q = readIntLn(1, max_q);
    while(q--){
        solve();
    }
    assert(getchar()==-1);
}