中位数定理

https://codeforces.com/contest/2149/problem/D

点击查看代码

#include <bits/stdc++.h>
#define int long long
using namespace std;

int f(const vector<int> x){
    if(x.empty())return 0;
    int pos = (int)x.size() / 2;
    int ans = 0;
    for(int i = 0; i < x.size(); i ++){
        ans += abs(abs(pos - i) - abs(x[pos] - x[i]));
        //cout << ans << endl;
    }
    return ans;
}

void solve(){
    int n;
    string s;
    cin >> n >> s;
    //cout << s << endl;
    vector<int> a;
    vector<int> b;
    for(int i = 0; i < n; i ++){
        if(s[i] == 'a')a.push_back(i);
        else b.push_back(i);
    }
    cout << min(f(a),f(b)) << endl;
}

signed main(){
    int t;
    cin >> t;
    while(t --){
        solve();
    }
    return 0;
}

每个a或者到b的坐标,往中间靠是最小代价