Submission #683304

#	Time	Username	Problem	Language	Result	Execution time	Memory
683304		vovamr	K-th path (IZhO11_kthpath)	C++17	100 / 100	7 ms	572 KiB

kthpath

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) 	(x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }

inline void solve() {
	/*
#ifndef LOCAL
	const string NAME = "kthpath";
	ifstream cin(NAME + ".in");
	ofstream cout(NAME + ".out");
#endif
	*/

	int n, m;
	cin >> n >> m;
	ve<ve<char>> a(n, ve<char>(m));
	for (auto &i : a) for (auto &j : i) cin >> j;

	ve<ve<ll>> dp(n, ve<ll> (m));
	dp[n - 1][m - 1] = 1;

	for (int i = n - 1; ~i; --i) {
		for (int j = m - 1; ~j; --j) {
			if (i + 1 < n) dp[i][j] += dp[i + 1][j];
			if (j + 1 < m) dp[i][j] += dp[i][j + 1];
		}
	}

	ll k;
	cin >> k;

	string result(1, a[0][0]);
	map<string,ve<array<ll,3>>> cand;

	cand[string(1, a[0][0])] = {{1, 0, 0}};

	while (sz(result) < n + m - 1) {
		map<string,ve<array<ll,3>>> cur;

//		cout << "have " << result << " " << sz(result) << " " << k << '\n';

		string S = cand.begin()->fi;
		for (auto &[ways, x, y] : cand.begin()->se) {
//			cout << x << " " << y << " " << ways << endl;
			if (x + 1 < n) {
				cur[S + a[x + 1][y]].pb({ways, x + 1, y});
			}
			if (y + 1 < m) {
				cur[S + a[x][y + 1]].pb({ways, x, y + 1});
			}
		}
//		cout << "built new strings" << endl;

		for (auto &[str, V] : cur) {
			auto vec = V;
			ve<array<ll,3>> c;

//			cout << str << endl;

			sort(all(vec));

			for (int i = 0; i < sz(vec); ++i) {
				if (!sz(c) || mpp(c.back()[1], c.back()[2]) != mpp(vec[i][1], vec[i][2])) c.pb(vec[i]);
				else c.back()[0] += vec[i][0];
			}
			V = c;
		}
//		cout << "erased duplicates -> " << sz(cur) << endl;

		map<string,ve<array<ll,3>>> nw;

		for (auto &[str, vec] : cur) {
			ll tot = 0;
			for (auto &[ways, x, y] : vec) tot += ways * dp[x][y];
			if (k > tot) {
				k -= tot;
			}
			else {
				nw[str] = vec;
				break;
			}
		}

//		cout << "found new" << endl << endl;
//		assert(sz(nw) == 1);

		swap(cand, nw);
		result = cand.begin()->fi;
	}
	cout << result;
}

signed main() {
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	int q = 1; // cin >> q;
	while (q--) solve();
	cerr << fixed << setprecision(3) << "Time execution: " << (double)clock() / CLOCKS_PER_SEC << endl;
}

• Subtask 1: 100 / 100