Submission #109788

#	Time	Username	Problem	Language	Result	Execution time	Memory
109788		qkxwsm	K-th path (IZhO11_kthpath)	C++14	100 / 100	4 ms	640 KiB

kthpath

//clever
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();

struct custom_hash
{
	template<class T>
	unsigned long long operator()(T v) const
	{
		unsigned long long x = v;
		x += FIXED_RANDOM;
		// x += 11400714819323198485ull;
		// x = (x ^ (x >> 30)) * 13787848793156543929ull;
		x = (x ^ (x >> 27)) * 10723151780598845931ull;
		return x ^ (x >> 31);
	}
};

template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;

template<class T>
T randomize(T mod)
{
	return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
	x = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
	{
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		x = x * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		x = -x;
	}
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int buf[20], n = 0;
	while(output)
	{
		buf[n] = ((output % 10));
		output /= 10;
		n++;
	}
	for (n--; n >= 0; n--)
	{
		putchar(buf[n] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
	return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
	if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
	return (b ? gcd(b, a % b) : a);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 69

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;

int N, M;
ll K;
int grid[MAXN][MAXN];
vi xs[MAXN][26];
ll choose[MAXN][MAXN];
ll freq[MAXN][MAXN];
vi ans;

bool valid(int x, int y)
{
	return (0 <= x && x < N && 0 <= y && y < M);
}
ll paths(int x, int y)
{
	return choose[x + y][y];
}

int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	// cout << fixed << setprecision(10);
	// cerr << fixed << setprecision(10);
	// if (fopen("file.in", "r"))
	// {
	// 	freopen ("file.in", "r", stdin);
	// 	freopen ("file.out", "w", stdout);
	// }
	cin >> N >> M;
	FOR(i, 0, N)
	{
		string temps; cin >> temps;
		FOR(j, 0, M)
		{
			grid[i][j] = temps[j] - 'a';
			xs[i + j][grid[i][j]].PB(i);
		}
	}
	cin >> K; K--;
	choose[0][0] = 1;
	FOR(i, 1, N + M + 1)
	{
		choose[i][0] = 1;
		choose[i][i] = 1;
		FOR(j, 1, i)
		{
			choose[i][j] = choose[i - 1][j] + choose[i - 1][j - 1];
		}
	}
	ans.PB(grid[0][0]);
	freq[0][0] = 1;
	FOR(i, 0, N + M - 2)
	{
		FOR(m, 0, 26)
		{
			ll ways = 0;
			FOR(j, 0, N)
			{
				int k = i - j;
				if (k < 0 || k >= M) continue;
				if (valid(j + 1, k) && grid[j + 1][k] == m) ways += freq[j][k] * paths(N - 1 - (j + 1), M - 1 - k);
				if (valid(j, k + 1) && grid[j][k + 1] == m) ways += freq[j][k] * paths(N - 1 - j, M - 1 - (k + 1));
			}
			if (ways <= K)
			{
				K -= ways;
				continue;
			}
			ans.PB(m);
			FOR(j, 0, N)
			{
				int k = i - j;
				if (k < 0 || k >= M) continue;
				if (valid(j + 1, k) && grid[j + 1][k] == m) freq[j + 1][k] += freq[j][k];
				if (valid(j, k + 1) && grid[j][k + 1] == m) freq[j][k + 1] += freq[j][k];
			}
			break;
		}
	}
	for (int x : ans)
	{
		cout << (char) ('a' + x);
	}
	cout << '\n';
	// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/

• Subtask 1: 100 / 100