题目意思

题目规定的还是比较正统的BST,那么就左右子树差值不超过给定的第二个数字,高度为第一个数字

解题思路

直接动态规划是最简单的解法:
我们想想假设待求得状态为,代表高度为i的所求节点个数
那么就有代表着高度为得左右子树所求节点个数之和再加上根节点
最终就有左子数为满二叉树,右子树为满足题目高度只差不超过m的二叉树,减掉即可!注意别取到负数的下标了

#pragma GCC target("avx,sse2,sse3,sse4,popcnt")
#pragma GCC optimize("O2,O3,Ofast,inline,unroll-all-loops,-ffast-math")
#include <bits/stdc++.h>
using namespace std;
#define js ios::sync_with_stdio(false);cin.tie(0); cout.tie(0)
#define all(__vv__) (__vv__).begin(), (__vv__).end()
#define endl "\n"
#define pai pair<int, int>
#define mk(__x__,__y__) make_pair(__x__,__y__)
typedef long long ll; typedef unsigned long long ull; typedef long double ld;
const int MOD = 1e9 + 7;
const ll INF = 0x3f3f3f3f;
inline ll read() { ll s = 0, w = 1; char ch = getchar(); for (; !isdigit(ch); ch = getchar()) if (ch == '-') w = -1; for (; isdigit(ch); ch = getchar())    s = (s << 1) + (s << 3) + (ch ^ 48); return s * w; }
inline void write(ll x) { if (!x) { putchar('0'); return; } char F[40]; ll tmp = x > 0 ? x : -x; if (x < 0)putchar('-');    int cnt = 0;    while (tmp > 0) { F[cnt++] = tmp % 10 + '0';        tmp /= 10; }    while (cnt > 0)putchar(F[--cnt]); }
inline ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; }
ll qpow(ll a, ll b) { ll ans = 1;    while (b) { if (b & 1)    ans *= a;        b >>= 1;        a *= a; }    return ans; }    ll qpow(ll a, ll b, ll mod) { ll ans = 1; while (b) { if (b & 1)(ans *= a) %= mod; b >>= 1; (a *= a) %= mod; }return ans % mod; }
inline int lowbit(int x) { return x & (-x); }

const int N = 1e5 + 7;
ll dp[100];

int main() {
    int n = read(), m = read();
    dp[1] = 1;
    for (int i = 2; i <= n; ++i)
        dp[i] = dp[i - 1] + dp[max(i - m - 1, 0)] + 1;
    ll ans = 1ll << n - 1;
    ans -= dp[n - m - 1];
    cout << ans - 1 << endl;
    return 0;
}