nk_ladders.cpp

#include <bits/stdc++.h>

using namespace std;

#define F              first
#define S              second
#define pb             push_back
#define si             set <int>
#define vi             vector <int>
#define pii            pair <int, int>
#define vpi            vector <pii>
#define vpp            vector <pair<int, pii>>
#define mii            map <int, int>
#define mpi            map <pii, int>
#define spi            set <pii>
#define endl           "\n"
#define sz(x)          ((int) x.size())
#define all(p)         p.begin(), p.end()
#define double         long double
#define que_max        priority_queue <int>
#define que_min        priority_queue <int, vi, greater<int>>
#define bug(...)       __f (#__VA_ARGS__, __VA_ARGS__)
#define print(a)       for(auto x : a) cout << x << " "; cout << endl
#define print1(a)      for(auto x : a) cout << x.F << " " << x.S << endl
#define print2(a,x,y)  for(int i = x; i < y; i++) cout<< a[i]<< " "; cout << endl

inline int power(int a, int b)
{
	int x = 1;
	while (b)
	{
		if (b & 1) x *= a;
		a *= a;
		b >>= 1;
	}
	return x;
}

template <typename Arg1>
void __f (const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << endl; }
template <typename Arg1, typename... Args>
void __f (const char* names, Arg1&& arg1, Args&&... args)
{
	const char* comma = strchr (names + 1, ',');
	cout.write (names, comma - names) << " : " << arg1 << " | "; __f (comma + 1, args...);
}

const int N = 200005;

int nk_ladders_recursive(int n, int k) {
	if (n == 0 || n == 1) {
		return 1;
	}

	if (n < 0) {
		return 0;
	}

	int count = 0;
	for (int i = n - 1; i >= n - k && i >= 0; i--) {
		count += nk_ladders_recursive(i, k);
	}
	return count;
}


int nk_ladders_topdown(int n, int k, int *memory) {
	if (memory[n])
		return memory[n];

	int count = 0;
	for (int i = n - 1; i >= n - k && i >= 0; i--) {
		if (memory[i])
			count += memory[i];
		else {
			memory[i] = nk_ladders_topdown(i, k, memory);
			count += memory[i];
		}
	}
	return memory[n] = count;
}

int nk_ladders_bottomup(int n, int k) {
	int support_arr[k] = {1, 1, 2};

	for (int j = 2; j < n; j++) {
		int count = 0;
		for (int i = 0; i < k; i++) {
			count += support_arr[i];
			support_arr[i] = support_arr[i + 1];
		}
		support_arr[k - 1] = count;
	}
	return support_arr[k - 1];
}

void solve() {
	int n, k;
	cin >> n >> k;
	
	int memory[n + 1] = {1, 1, 0};

	cout << nk_ladders_recursive(n, k);
}

int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

#ifndef ONLINE_JUDGE
	freopen("input.txt",  "r",  stdin);
	freopen("output.txt", "w", stdout);
#endif

	clock_t z = clock();

	int t = 1;
	// cin >> t;
	while (t--) solve();

	cerr << "Run Time : " << ((double)(clock() - z) / CLOCKS_PER_SEC);

	return 0;
}