算法模版 动态规划

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dp 模版，慢慢更新。

动态规划

矩阵加速

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

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
using u128 = unsigned __int128;

constexpr int mod = 1e9 + 7;
struct Matrix {
    vector<vector<i64>> a;
    Matrix() { a.assign(3, vector<i64>(3)); }
    Matrix operator*(const Matrix b) const {
        Matrix res;
        for (int i = 1; i <= 2; i++) {
            for (int j = 1; j <= 2; j++) {
                for (int k = 1; k <= 2; k++) {
                    res.a[i][j] = (res.a[i][j] + a[i][k] * b.a[k][j]) % mod;
                }
            }
        }
        return res;
    }
    void inita() { a[1][1] = a[1][2] = 1; }
    void initb() { a[1][1] = a[2][1] = a[1][2] = 1; }
};

Matrix qpow(Matrix a, i64 b) {
    Matrix res;
    for (int i = 1; i <= 2; i++) {
        res.a[i][i] = 1;
    }
    while (b) {
        if (b % 2 == 1) {
            res = res * a;
        }
        a = a * a;
        b /= 2;
    }
    return res;
}

void solve() {
    i64 n;
    cin >> n;
    if (n <= 2) {
        cout << 1 << "\n";
        return;
    }
    Matrix a, b;
    a.inita(), b.initb();
    a = a * qpow(b, n - 2);
    cout << a.a[1][1] << "\n";
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}

数位 dp

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

int dp[10][2];
int n, m, sz;
int c[10];
int dfs(int pos, bool sta, bool limit) {
    int ans = 0;
    if (pos == sz + 1) {
        return 1;
    }
    if (!limit && dp[pos][sta] != -1) {
        return dp[pos][sta];
    }
    int up = limit ? c[pos] : 9;
    for (int i = 0; i <= up; i++) {
        if (sta && i == 2) {
            continue;
        }
        if (i == 4) {
            continue;
        }
        ans += dfs(pos + 1, i == 6, limit && i == up);
    }
    if (!limit) {
        dp[pos][sta] = ans;
    }
    return ans;
}

void solve() {
    while (true) {
        cin >> n >> m;
        if (n == 0 && m == 0) {
            break;
        }
        for (int i = 0; i < 8; i++) {
            for (int j = 0; j < 2; j++) {
                dp[i][j] = -1;
            }
        }
        string s = to_string(m);
        sz = s.size();
        s = " " + s;
        for (int i = 1; i <= sz; i++) {
            c[i] = s[i] - '0';
        }
        int ans = dfs(1, false, true);
        for (int i = 0; i < 8; i++) {
            for (int j = 0; j < 2; j++) {
                dp[i][j] = -1;
            }
        }
        s = to_string(n - 1);
        sz = s.size();
        s = " " + s;
        for (int i = 1; i <= sz; i++) {
            c[i] = s[i] - '0';
        }
        ans -= dfs(1, false, true);
        cout << ans << "\n";
    }
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t = 1;
    // cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}