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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#810029#9782. NonZero PrefSuf SumsAfterlife#AC ✓25ms12484kbC++203.1kb2024-12-11 19:13:592024-12-11 19:14:05

Judging History

你现在查看的是最新测评结果

  • [2024-12-11 19:14:05]
  • 评测
  • 测评结果:AC
  • 用时:25ms
  • 内存:12484kb
  • [2024-12-11 19:13:59]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
int n , m , mod ;
int fpow(int a,int b) {
    int ans = 1;
    while(b) {
        if(b & 1) ans = 1LL * ans * a %mod;
        a = 1LL * a * a % mod ; b >>= 1;
    }
    return ans;
}
int t[105] , rt[105];
int C(int a,int b) {
    return 1LL * t[a] * rt[b] % mod * rt[a - b] % mod;
}
const int D = 1e4 ;
// int f[20005] , g[20005];
int calc() {
    vector<int> f(20005) , g(20005) ;
    f[D] = 1;
    for(int i = 1;i <= n;i++) {
        for(int j = -i*m ; j <= i *m;j++) {
            f[D + j] = (f[D + j] + f[D + j - 1]) % mod;
        }
        for(auto &x : g) x = 0;
        for(int j = -i * m ; j <= i * m ; j++) {
            g[D + j] = (f[D + min(i*m , j + m)] - f[max(0 , D + j - m - 1)] + mod) % mod;
        }
        for(int j = -i*m ; j <= i*m;j++) f[D + j] = g[D + j] ;
    }
    return f[D];
}

int f[105][105][105] , g[105][105][105];

int calcm(int mx) { //// max <= mx
    // vector<vector<int> > f(n + 1 , vector<int>(n + 1)) ;
    // vector<vector<int> > g(n + 1 , vector<int>(n + 1)) ;
    f[mx][0][0] = 1;
    for(int i = 0;i <= n;i++) g[mx][0][i] = 1;
    for(int i = 1;i <= n;i++) {
        for(int j = 0 ; j <= n ; j++) {
            if(j <= mx) f[mx][i][j] = g[mx][i - 1][j];
            else f[mx][i][j] = (g[mx][i - 1][j] - g[mx][i - 1][j - mx - 1] + mod) % mod;
            f[mx][i][j] = (f[mx][i][j] - f[mx][i - 1][j] + mod) % mod;
        }

        g[mx][i][0] = f[mx][i][0];
        for(int j = 1;j <= n;j++) {
            g[mx][i][j] = (f[mx][i][j] + g[mx][i][j - 1]) % mod;
        }
    }

    int ans = 0;
    for(int neg = 1 ; neg < n ; neg++) {
        // printf("neg %d : %d : %d\n" , neg , g[n - neg][neg - 1] - g[n-neg][min(neg-1 , max(0,lm-1))]  , (g[n - neg][neg - 1] - g[n-neg][min(neg-1 , max(0,lm-1))]  ) * C(n , neg)) ;
        // printf("B %d : %d\n" , min(neg - 1 , max(0 , lm - 1)) , lm) ;
        for(int zero = 0 ; zero + neg < n ; zero++) {

            // int lm = (n - zero - 1) / 2;
            int lm = neg - mx - 1;

            int tk = (g[mx][n - neg - zero][neg - 1] - g[mx][n-neg - zero][min(neg-1 , max(0,lm-1))] + mod) % mod;
            int pre = (g[mx - 1][n - neg - zero][neg - 1] - g[mx - 1][n-neg - zero][min(neg-1 , max(0,lm-1))] + mod) % mod;
            tk = (tk - pre + mod) % mod;

            ans = (ans + 1LL * tk * C(n , neg) % mod * C(n-neg , zero)) % mod;
            
        }
    }
    ans = ans*2 % mod;
    return ans;
}
int main() {
    cin >> n >> m >> mod ;
    t[0] = rt[0] = 1;
    for(int i = 1;i <= n;i++) {
        t[i] = 1LL * t[i - 1] * i % mod;
        rt[i] = fpow(t[i] , mod - 2) ;
    }
    int ans = fpow(m*2 + 1 , n) ;
    ans = (ans - calc() + mod) % mod; /// case1

    ans = (ans - 1LL * (m*2) * n + mod) % mod; // case2
    

    vector<int> sol(m + 1);
    for(int mx = 1 ; mx <= m ; mx++) {
        sol[mx] = calcm(mx) ;
        // printf("%d %d\n",mx,sol[mx]) ;
    }
    for(int i = 1;i <= m;i++) {
        // int s = (sol[i] - sol[i - 1] + mod) % mod;
        int s=sol[i];
        ans = (ans - 1LL * s * (m/i) % mod + mod) % mod;
    }
    cout << ans << '\n' ;
}

Details

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Test #1:

score: 100
Accepted
time: 1ms
memory: 6004kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #2:

score: 0
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time: 6ms
memory: 10908kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #3:

score: 0
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time: 1ms
memory: 5936kb

input:

2 1 998244353

output:

2

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ok single line: '2'

Test #4:

score: 0
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time: 0ms
memory: 9992kb

input:

69 42 696969697

output:

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result:

ok single line: '378553557'

Test #5:

score: 0
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time: 8ms
memory: 10900kb

input:

61 75 677323601

output:

34613998

result:

ok single line: '34613998'

Test #6:

score: 0
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time: 0ms
memory: 6064kb

input:

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output:

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Test #7:

score: 0
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memory: 5864kb

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output:

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score: 0
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memory: 5892kb

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output:

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Test #9:

score: 0
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time: 2ms
memory: 6000kb

input:

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output:

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Test #10:

score: 0
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time: 1ms
memory: 6008kb

input:

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output:

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Test #11:

score: 0
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time: 1ms
memory: 5768kb

input:

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output:

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score: 0
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time: 1ms
memory: 6020kb

input:

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Test #13:

score: 0
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time: 4ms
memory: 12388kb

input:

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output:

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score: 0
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memory: 5692kb

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score: 0
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memory: 7824kb

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score: 0
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memory: 12104kb

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output:

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Test #17:

score: 0
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time: 1ms
memory: 5672kb

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output:

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memory: 5780kb

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time: 1ms
memory: 6012kb

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memory: 7940kb

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memory: 10076kb

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output:

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Test #22:

score: 0
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time: 1ms
memory: 5988kb

input:

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output:

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Test #23:

score: 0
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time: 2ms
memory: 10332kb

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Test #24:

score: 0
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memory: 5792kb

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score: 0
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memory: 5748kb

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output:

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memory: 6024kb

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Test #31:

score: 0
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memory: 10080kb

input:

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output:

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result:

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Test #32:

score: 0
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time: 1ms
memory: 5708kb

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output:

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Test #33:

score: 0
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memory: 7904kb

input:

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Test #34:

score: 0
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memory: 6016kb

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Test #36:

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Test #37:

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Test #39:

score: 0
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memory: 5784kb

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score: 0
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memory: 5732kb

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score: 0
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score: 0
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memory: 5720kb

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memory: 5804kb

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score: 0
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memory: 7804kb

input:

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score: 0
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memory: 7880kb

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score: 0
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memory: 6188kb

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Test #48:

score: 0
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time: 3ms
memory: 7932kb

input:

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output:

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Test #49:

score: 0
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time: 1ms
memory: 7860kb

input:

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output:

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result:

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Test #50:

score: 0
Accepted
time: 25ms
memory: 12484kb

input:

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output:

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result:

ok single line: '313377809'

Extra Test:

score: 0
Extra Test Passed