oj.uz

Submission #746261

# Submission time Handle Problem Language Result Execution time Memory
746261 2023-05-22T04:31:29 Z GrindMachine Vještica (COCI16_vjestica) C++17
160 / 160
 100 ms 1108 KB 
// Om Namah Shivaya

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a, b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a, b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

refs:
edi
some codes from https://github.com/mostafa-saad/MyCompetitiveProgramming/blob/master/Olympiad/COCI/COCI-16-vjestica.txt


permute strings in any way
find min possible size of trie

n <= 16, bitmask dp intended

when we have set of strings, optimal to create a chain with all common letters that appear in all strings
after removing all common chars, the trie has to branch into >= 2 subtrees

we will always break into 2 subtrees
this also accounts for > 2 subtrees case
because if there are no common chars in the strings that go to a subtree, then it will further break into some more subtrees

so lets do bitmask dp

dp(mask) = dp(sub) + dp(mask^sub) - common(mask)
iterate over all sub for a given mask and take min

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

void solve(int test_case)
{
    ll n; cin >> n;
    vector<vector<ll>> cnt(n,vector<ll>(26));

    rep(i,n){
        string s; cin >> s;
        trav(ch,s) cnt[i][ch-'a']++;
    }

    auto common = [&](ll mask){
        vector<ll> mn_cnt(26,inf2);
        rep(i,n){
            if(mask & (1 << i)){
                rep(j,26){
                    amin(mn_cnt[j], cnt[i][j]);
                }
            }
        }

        ll res = 0;
        rep(j,26) res += mn_cnt[j];

        return res;
    };

    vector<ll> dp(1<<n, inf2);
    dp[0] = 0;

    rep1(mask,(1<<n)-1){
        if(setbits(mask) == 1){
            ll bit = __lg(mask);
            dp[mask] = 0;
            rep(j,26){
                dp[mask] += cnt[bit][j];
            } 

            conts;
        }

        ll common_val = common(mask);
    
        for(int sub = mask; sub; sub = (sub-1) & mask){
            ll val = dp[sub] + dp[mask^sub] - common_val;
            amin(dp[mask],val);
        }
    }

    ll ans = dp[(1<<n)-1] + 1; // +1 for root of trie
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Subtask #1
160.0 / 160.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 316 KB Output is correct
4 Correct 88 ms 852 KB Output is correct
5 Correct 87 ms 852 KB Output is correct
6 Correct 89 ms 1108 KB Output is correct
7 Correct 100 ms 1104 KB Output is correct
8 Correct 89 ms 1108 KB Output is correct
9 Correct 91 ms 1100 KB Output is correct
10 Correct 89 ms 1108 KB Output is correct