CSES-Solutions/Dynamic Programming/TwoSets2.cpp at main · Avuvos/CSES-Solutions · GitHub

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//Two Sets II - https://cses.fi/problemset/task/1093

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int MOD = 1e9 + 7;
const ll INF = 1e18;

template<class T>
constexpr T power(T a, ll b) {
    T res = 1;
    while (b > 0) {
        if (b & 1) {
            res *= a;
        }
        a *= a;
        b >>= 1;
    }
    return res;
}
template<int P>
struct MInt {
    int x;
    constexpr MInt() : x{} {}
    constexpr MInt(ll x) : x{norm(x % P)} {}

    constexpr int norm(int z) const {
        if (z < 0) {
            z += P;
        }
        if (z >= P) {
            z -= P;
        }
        return z;
    }
    constexpr int val() const {
        return x;
    }
    explicit constexpr operator int() const {
        return x;
    }
    constexpr MInt operator-() const {
        MInt res;
        res.x = norm(P - x);
        return res;
    }
    constexpr MInt inv() const {
        assert(x != 0);
        return power(*this, P - 2);
    }
    constexpr MInt &operator*=(MInt rhs) {
        x = 1LL * x * rhs.x % P;
        return *this;
    }
    constexpr MInt &operator+=(MInt rhs) {
        x = norm(x + rhs.x);
        return *this;
    }
    constexpr MInt &operator-=(MInt rhs) {
        x = norm(x - rhs.x);
        return *this;
    }
    constexpr MInt &operator/=(MInt rhs) {
        return *this *= rhs.inv();
    }
    friend constexpr MInt operator*(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res *= rhs;
        return res;
    }
    friend constexpr MInt operator+(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res += rhs;
        return res;
    }
    friend constexpr MInt operator-(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res -= rhs;
        return res;
    }
    friend constexpr MInt operator/(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res /= rhs;
        return res;
    }
    friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
        ll v;
        is >> v;
        a = MInt(v);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
        return os << a.val();
    }
    friend constexpr bool operator==(MInt lhs, MInt rhs) {
        return lhs.val() == rhs.val();
    }
    friend constexpr bool operator!=(MInt lhs, MInt rhs) {
        return lhs.val() != rhs.val();
    }
};

template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
constexpr int P = MOD;
using Mint = MInt<P>;

void solve() {
    int n;
    cin >> n;
    int s = n * (n + 1) / 2;
    vector<vector<Mint>> dp(n + 2, vector<Mint>(2*s + 2, -1));
    auto dfs = [&](auto dfs, int cur, int sum) -> Mint {
        if (cur == n + 1) {
            return sum == 0;
        }
        if (dp[cur][s + sum] != -1) {
            return dp[cur][s + sum];
        }
        return dp[cur][s + sum] = dfs(dfs, cur + 1, sum - cur) + dfs(dfs, cur + 1, sum + cur);
    };
    cout << dfs(dfs, 1, 0) / 2 << endl;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int T = 1;
//    cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}