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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#616320#8023. The Journey of Geor Autumntkt0506TL 139ms39752kbC++141.4kb2024-10-06 01:44:172024-10-06 01:44:17

Judging History

This is the latest submission verdict.

  • [2024-10-06 01:44:17]
  • Judged
  • Verdict: TL
  • Time: 139ms
  • Memory: 39752kb
  • [2024-10-06 01:44:17]
  • Submitted

answer

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

typedef long long ll;
const ll MOD = 998244353; // bruh

ll pow(ll x, ll y){
    ll res = 1;
    x = x%MOD;

    while(y > 0){
        if(y&1) res = (res*x)%MOD;
        y = y >> 1;
        x = (x*x)%MOD;
    }
    return res;
}

ll inv(ll x){
    return pow(x, MOD-2);
}

vector<ll> fact{1}, invfact{1};

ll C(ll n, ll r){
    if(n < r) return 0;
    return ((fact[n]*invfact[r])%MOD*invfact[n-r])%MOD;
}

void precompute(ll n){
    for(ll i = fact.size(); i<=n; i++){
        fact.push_back((fact.back()*i)%MOD);
        invfact.push_back(inv(fact.back()));
    }
}

int main(){
    ll n, k;
    cin >> n >> k;
    precompute(n);

    vector<ll>dp(n+1,0), sum(n+1,0);
    dp[0] = sum[0] = 1;

    for(ll i=1; i<=n; i++){
        dp[i] = sum[i-1];
        if(i>k)dp[i] = (dp[i]-sum[i-k-1]+MOD)%MOD;
        dp[i] *= fact[i-1];
        dp[i] %= MOD;
        sum[i] = (sum[i-1]+(dp[i]*invfact[i])%MOD)%MOD;
    }

    cout << dp[n];
}

/*

let dp[i] = valid permutation with len i 
we can only place 1 on [1,k], assume we place on pos j
[1,j-1] can place any element 
permutation = (i-1)C(j-1) * (j-1)! 

for remain [j,n] part, it is actually a sub-problem
permutation = dp[i-j]

for(int j=0; j<=min(i,k); j++){
    dp[i] = dp[i-j]*(i-1)C(j-1)*(j-1)! 
}

dp[i-j]*(i-1)C(j-1)*(j-1)! 
= dp[i-j]*(i-1)!/(i-j)!
= (i-1)! *dp[i-j]/(i-j)!
prefix sum store


*/

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3524kb

input:

1 1

output:

1

result:

ok "1"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3580kb

input:

1 2

output:

1

result:

ok "1"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3460kb

input:

1 3

output:

1

result:

ok "1"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3748kb

input:

1 4

output:

1

result:

ok "1"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3520kb

input:

2 1

output:

1

result:

ok "1"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3756kb

input:

2 2

output:

2

result:

ok "2"

Test #7:

score: 0
Accepted
time: 0ms
memory: 3716kb

input:

2 3

output:

2

result:

ok "2"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3580kb

input:

2 4

output:

2

result:

ok "2"

Test #9:

score: 0
Accepted
time: 0ms
memory: 3580kb

input:

3 1

output:

1

result:

ok "1"

Test #10:

score: 0
Accepted
time: 0ms
memory: 3780kb

input:

3 2

output:

4

result:

ok "4"

Test #11:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

3 3

output:

6

result:

ok "6"

Test #12:

score: 0
Accepted
time: 0ms
memory: 3580kb

input:

3 4

output:

6

result:

ok "6"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

4 1

output:

1

result:

ok "1"

Test #14:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

4 2

output:

10

result:

ok "10"

Test #15:

score: 0
Accepted
time: 0ms
memory: 3448kb

input:

4 3

output:

18

result:

ok "18"

Test #16:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

4 4

output:

24

result:

ok "24"

Test #17:

score: 0
Accepted
time: 0ms
memory: 3576kb

input:

99 50

output:

955866606

result:

ok "955866606"

Test #18:

score: 0
Accepted
time: 0ms
memory: 3592kb

input:

99 70

output:

296999003

result:

ok "296999003"

Test #19:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

1034 998

output:

637688669

result:

ok "637688669"

Test #20:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

1099 997

output:

712935289

result:

ok "712935289"

Test #21:

score: 0
Accepted
time: 2ms
memory: 3908kb

input:

10314 998

output:

224695890

result:

ok "224695890"

Test #22:

score: 0
Accepted
time: 2ms
memory: 3844kb

input:

10929 9974

output:

160291286

result:

ok "160291286"

Test #23:

score: 0
Accepted
time: 15ms
memory: 6488kb

input:

103124 99448

output:

695932649

result:

ok "695932649"

Test #24:

score: 0
Accepted
time: 16ms
memory: 6780kb

input:

109139 9937

output:

268916696

result:

ok "268916696"

Test #25:

score: 0
Accepted
time: 135ms
memory: 35380kb

input:

1031234 99238

output:

441457721

result:

ok "441457721"

Test #26:

score: 0
Accepted
time: 139ms
memory: 39752kb

input:

1091239 991237

output:

61047495

result:

ok "61047495"

Test #27:

score: -100
Time Limit Exceeded

input:

10000000 9982443

output:


result: