C - 1111gal password

• bottom up dp solution
• Time : O(n)
• Space : O(1)

#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

struct PairHash {inline std::size_t operator()(const std::pair<int,int> & v) const {return v.first*31+v.second;}};

#define MAX_N 1010101
#define INF 987654321
#define EPS 1e-9
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define all3 array<ll,3>
#define all5 array<ll,5>
#define vall5 vector<all5>
#define vll vector<ll>
#define vi vector<int>
#define vs vector<string>
#define usll unordered_set<ll>
#define uspll unordered_set<pll, PairHash>
#define umll unordered_map<ll,ll>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)

ll __gcd(ll x, ll y) { return !y ? x : __gcd(y, x % y); }

using namespace std;

ll solve(ll n) {
    vll dp(10,1);
    dp[0] = 0;
    ll mod = 998244353;
    for(ll i = 1; i < n; i++) {
        vll dpp = dp;
        for(ll j = 1; j <= 9; j++) {
            if(j - 1 >= 1) dpp[j - 1] = (dpp[j - 1] + dp[j]) % mod;
            if(j + 1 <= 9) dpp[j + 1] = (dpp[j + 1] + dp[j]) % mod;
        }
        swap(dpp, dp);
    }
    return accumulate(all(dp), 0ll) % mod;
}

int main() {
    ios_base::sync_with_stdio(0);
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll tc = 1;
    //cin>>tc;
    for(ll i = 1; i <= tc; i++) {
        ll n;
        cin>>n;
        cout<<solve(n)<<endl;
    }
    return 0;
}

• top down dp solution
• Time : O(n)
• Space : O(n)

#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

struct PairHash {inline std::size_t operator()(const std::pair<int,int> & v) const {return v.first*31+v.second;}};

#define MAX_N 1010101
#define INF 987654321
#define EPS 1e-9
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define all3 array<ll,3>
#define all5 array<ll,5>
#define vall5 vector<all5>
#define vll vector<ll>
#define vi vector<int>
#define vs vector<string>
#define usll unordered_set<ll>
#define uspll unordered_set<pll, PairHash>
#define umll unordered_map<ll,ll>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)

ll __gcd(ll x, ll y) { return !y ? x : __gcd(y, x % y); }

using namespace std;

ll dp[10][MAX_N], mod = 998244353;

ll helper(ll x, ll n) {
    if(x == 0 or x > 9) return 0;
    if(n == 0) return 1;
    if(dp[x][n] != -1) return dp[x][n];
    return dp[x][n] = (helper(x - 1, n - 1) + helper(x, n - 1) + helper(x + 1, n - 1)) % mod;
}

ll solve(ll n) {
    memset(dp, -1, sizeof dp);
    ll res = 0;
    for(ll i = 1; i <= 9; i++)
        res = (res + helper(i,n - 1)) % mod;
    return res;
}

int main() {
    ios_base::sync_with_stdio(0);
    ios::sync_with_stdio(0);
    cin.tie(0);
    ll tc = 1;
    //cin>>tc;
    for(ll i = 1; i <= tc; i++) {
        ll n;
        cin>>n;
        cout<<solve(n)<<endl;
    }
    return 0;
}