Submission #968747

#	Time	Username	Problem	Language	Result	Execution time	Memory
968747		youssef_3breheem	Three Friends (BOI14_friends)	C++17	100 / 100	164 ms	86344 KiB

friends

/** MIT License Copyright (c) 2018 Vasilyev Daniil **/
/**
Solution:
1. It's obvious that T totally depends on S, which means I can determine S by converting U to T.
2. I can convert U to possible T by removing only one letter from any position and check if it's correct.
3. To quickly check if possible T can be done by copying, I can compare first and second half of it.
And to quickly compare first and second half of it, I can use polynomial hashing property that:
hash(S[l : r]) = (hash(S[1 : r]) - hash(S[1 : l - 1]) * (base ^ (r - l + 1)) + mod) % mod.
Since r - l + 1 <= n, then base ^ (r - l + 1) can be precalculated.

5. If strings are equal (hashes are also equal), then I check answer.
If it's empty, then I fill it and calculate its hash.
Else I compare answer's hash and resulting string hash (both are already calculated).
If they differ, then answer is "NO UNIQUE". Otherwise, nothing is changed.

Time complexity: O(n).
**/
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast")
template<typename T> using v = vector<T>;
#define int long long
typedef string str;
typedef vector<int> vint;
#define rep(a, l, r) for(int a = (l); a < (r); a++)
#define pb push_back
#define sz(a) ((int) a.size())
const long long inf = 4611686018427387903; //2^62 - 1
#if 0  //FileIO
const string fileName = "";
ifstream fin ((fileName == "" ? "input.txt"  : fileName + ".in" ));
ofstream fout((fileName == "" ? "output.txt" : fileName + ".out"));
#define get fin>>
#define put fout<<
#else
#define get cin>>
#define put cout<<
#endif
#define eol put endl
void read() {}     template<typename Arg,typename... Args> void read (Arg& arg,Args&... args){get (arg)     ;read(args...) ;}
void print(){}     template<typename Arg,typename... Args> void print(Arg  arg,Args...  args){put (arg)<<" ";print(args...);}
void debug(){eol;} template<typename Arg,typename... Args> void debug(Arg  arg,Args...  args){put (arg)<<" ";debug(args...);}
int getInt(){int a; get a; return a;}
//code goes here
const long long mod1 = 1999998893;
const long long mod2 = 2100003611;
const long long base = 29;
const char startingLetter = 'A'; //starting letter of the alphabet
 
long long hashChar(char c){
    return c - startingLetter + 1;
}
 
pair<long long, long long> hashStr(pair<long long, long long> prevHash, char curChar) {
    return {((prevHash.first * base) % mod1 + hashChar(curChar)) % mod1,
            ((prevHash.second * base) % mod2 + hashChar(curChar)) % mod2};
}
 
const int N = 2e6 + 1;
int powOfBase1[N], powOfBase2[N];
 
void run() {
    int n;
    get n;
    str u;
    get u;
 
    powOfBase1[0] = 1;
    powOfBase2[0] = 1;
    rep(i, 1, n + 1) {
        powOfBase1[i] = (base * powOfBase1[i - 1]) % mod1;
        powOfBase2[i] = (base * powOfBase2[i - 1]) % mod2;
    }
 
    str left = "", right = "";
    rep(i, 0, n / 2 + 1)
        left += u[i];
 
    rep(i, n / 2 + 1, n)
        right += u[i];
 
    str ans = "";
    pair<int, int> ansHsh = {0, 0};
 
    rep(z, 0, 2) {
        v<pair<int, int>> hshLeft, hshRight;
        hshLeft.pb({hashChar(left[0]), hashChar(left[0])});
        rep(i, 1, sz(left)) {
            auto d = hshLeft.back();
            hshLeft.pb(hashStr(d, left[i]));
        }
 
        hshRight.pb({hashChar(right[0]), hashChar(right[0])});
        rep(i, 1, sz(right)) {
            auto d = hshRight.back();
            hshRight.pb(hashStr(d, right[i]));
        }
 
        if (z) {
            //debug(sz(hshRight), right, sz(hshLeft), left);
            rep(i, 1, sz(right)) {
                auto resultHash = hshRight.back();
                int offset = sz(right) - (i + 1);
                resultHash.first =
                ((resultHash.first - (powOfBase1[offset] * hshRight[i].first) % mod1) % mod1 + mod1) % mod1;
 
                if (i)
                    resultHash.first = (resultHash.first + (powOfBase1[offset] * hshRight[i - 1].first) % mod1) % mod1;
 
                resultHash.second =
                ((resultHash.second - (powOfBase2[offset] * hshRight[i].second) % mod2) % mod2 + mod2) % mod2;
 
                if (i)
                    resultHash.second = (resultHash.second + (powOfBase2[offset] * hshRight[i - 1].second) % mod2) % mod2;
 
                if (resultHash == hshLeft.back()) {
                    if (ans == "") {
                        rep(j, 0, sz(right))
                            if (i != j)
                                ans += right[j];
                        for (char j : ans)
                            ansHsh = hashStr(ansHsh, j);
                    } else {
                        if (resultHash != ansHsh) {
                            put "NOT UNIQUE";
                            return;
                        }
                    }
                }
 
            }
        } else {
            rep(i, 0, sz(left)) {
                auto resultHash = hshLeft.back();
                int offset = sz(left) - (i + 1);
                resultHash.first =
                ((resultHash.first - (powOfBase1[offset] * hshLeft[i].first) % mod1) % mod1 + mod1) % mod1;
 
                if (i)
                    resultHash.first = (resultHash.first + (powOfBase1[offset] * hshLeft[i - 1].first) % mod1) % mod1;
 
                resultHash.second =
                ((resultHash.second - (powOfBase2[offset] * hshLeft[i].second) % mod2) % mod2 + mod2) % mod2;
 
                if (i)
                    resultHash.second = (resultHash.second + (powOfBase2[offset] * hshLeft[i - 1].second) % mod2) % mod2;
 
                if (resultHash == hshRight.back()) {
                    if (ans == "") {
                        rep(j, 0, sz(left))
                            if (i != j)
                                ans += left[j];
                        for (char j : ans)
                            ansHsh = hashStr(ansHsh, j);
                    } else {
                        if (resultHash != ansHsh) {
                            put "NOT UNIQUE";
                            return;
                        }
                    }
 
                }
 
            }
        }
 
        if (z)
            break;
 
        right = left.back() + right;
        left.pop_back();
    }
    //debug(ans[0]);
    if (sz(ans) == 0)
        put "NOT POSSIBLE";
    else
        put ans;
}
 
int32_t main() {srand(time(0)); ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); put fixed; put setprecision(15); run(); return 0;}

• Subtask 1: 35 / 35
• Subtask 2: 65 / 65