HDU 3037 saving beans fzu 2020 combo hit 2813 garden visiting hrbeu combo fzu 1564 combination

Returns the remainder of a combination.

P is not a prime number, P is a prime number

1) P is a prime number.

1. Lucas Theorem
2. M = Mk * P ^ K + MK-1 * P ^ K-1 +... + m1 * P + M0;
3. N = NK * P ^ K + NK-1 * P ^ K-1 +... + N1 * P + N0;
4. C (m, n) = C (MK, NK) * C (MK-1, NK-1) *... * C (M1, N1) * C (M0, N0 );
5. [Topic]
6. Evaluate the value of C (n + m, n) % P.
7. Ensure that p is a prime number.

C (m, n) % P = m! /(N! * (M-N )!) % P

In this case, use the inverse element or extend Euclidean.

2) When P is an arbitrary number

 

hdu 3037

Method 1: # include <stdio. h> # define ll long # define nnum limit 1int num [nnum], X, Y; void Init (INT p) {int I; ll Te; num [0] = 1; for (I = 1; I <= P; I ++) {Te = (LL) I; Te = tE * num [I-1] % P; num [I] = (INT) Te ;}} int modular_exp (int A, int B, int c) {ll res, Te; Res = 1, TE = A % C; while (B) {If (B & 1) {res = res * te % C;} te = tE * te % C; B >>=1 ;} return (INT) res;} int gcd (int A, int B) {if (a <B) {A ^ = B, B ^ = A, a ^ = B;} If (B = 0) {return a;} return gcd (B, A % B );} void extend_gcd (int A, int B) {If (B = 0) {x = 1, y = 0; return;} extend_gcd (B, A % B ); int Tx = x; X = Y, y = TX-A/B * Y;} int C (int A, int B, int p) {If (B>) {return 0;} ll Te; Te = (LL) num [B]; Te = tE * num [A-B] % P; B = (INT) Te; A = num [a]; int d = gcd (a, B); A/= D, B/= D; Te = (LL) A; extend_gcd (B, p); X = (X % P + p) % P; Return (I NT) (Te * x % P);} void solve (ll n, ll M, int p) {ll ans; int A, B; ans = 1; while (N | M) {A = n % P, B = m % P; ans = ans * C (A, B, P) % P; N/= P, m/= P;} printf ("% i64d \ n", ANS);} int main () {# ifndef online_judgefreopen ("t.txt", "r", stdin ); # endifint T, P; ll n, m; while (scanf ("% d", & T )! = EOF) {While (t --) {scanf ("% i64d % i64d % d", & N, & M, & P); Init (P ); solve (n + M, m, p) ;}} return 0 ;}

Method 2:

#include<stdio.h>#define LL long long#define nnum 100001int num[nnum], x, y;void init(int p) {    int i;    LL te;    num[0] = 1;    for (i = 1; i <= p; i++) {        te = (LL) i;        te = te * num[i - 1] % p;        num[i] = (int) te;    }}int modular_exp(int a, int b, int c) {    LL res, te;    res = 1, te = a % c;    while (b) {        if (b & 1) {            res = res * te % c;        }        te = te * te % c;        b >>= 1;    }    return (int) res;}int C(int a, int b, int p) {    if (b > a) {        return 0;    }    LL te;    te = (LL) num[b];    te = te * num[a - b] % p;    b = te;    te = num[a];    return (int) (te * modular_exp(b, p - 2, p) % p);}void solve(LL n, LL m, int p) {    LL ans;    int a, b;    ans = 1;    while (n || m) {        a = n % p, b = m % p;        ans = ans * C(a, b, p) % p;        n /= p, m /= p;    }    printf("%I64d\n", ans);}int main() {#ifndef ONLINE_JUDGE    freopen("t.txt", "r", stdin);#endif    int T, p;    LL n, m;    while (scanf("%d", &T) != EOF) {        while (T--) {            scanf("%I64d %I64d %d", &n, &m, &p);            init(p);            solve(n + m, m, p);        }    }    return 0;} 

fzu 2020

#include<stdio.h>#define LL long longint modular_exp(int a, int b, int c) {LL res, te;te = a % c, res = 1;while (b) {if (b & 1) {res = res * te % c;}te = te * te % c;b >>= 1;}return (int) res;}int C(int n, int m, int p) {if (m > n) {return 0;}int i;LL res, a, b;res = 1, a = 1, b = 1;for (i = 0; i < m; i++) {a = a * (n - i) % p, b = b * (m - i) % p;}res = res * a * modular_exp(b, p - 2, p) % p;return (int) res;}void solve(int n, int m, int p) {LL ans;int a, b;ans = 1;while (n || m) {a = n % p, b = m % p;ans = ans * C(a, b, p) % p;n /= p, m /= p;}printf("%I64d\n", ans);}int main() {#ifndef ONLINE_JUDGEfreopen("t.txt", "r", stdin);#endifint T, m, n, p;while (scanf("%d", &T) != EOF) {while (T--) {scanf("%d %d %d", &n, &m, &p);solve(n, m, p);}}return 0;}

Hit 2813

 

#include<stdio.h>#include<math.h>#include<string.h>#define LL long long#define nmax 200001int prime[nmax], flag[nmax], plen;void init() {memset(flag, -1, sizeof(flag));int i, j;for (i = 2, plen = 0; i < nmax; i++) {if (flag[i]) {prime[plen++] = i;}for (j = 0; (j < plen) && (i * prime[j] < nmax); j++) {flag[i * prime[j]] = 0;if ((i % prime[j]) == 0) {break;}}}}int modular_exp(int a, int b, int c) {LL res, te;res = 1, te = a % c;while (b) {if (b & 1) {res = res * te % c;}te = te * te % c;b >>= 1;}return res;}int getNum(int n, int m) {int res;res = 0;while (n) {res += n / m;n /= m;}return res;}void solve(int a, int b, int c) {int i, te;LL res;for (i = 0, res = 1; (i < plen) && (prime[i] <= a); i++) {te = getNum(a, prime[i]) - getNum(b, prime[i])- getNum(a - b, prime[i]);res = res * modular_exp(prime[i], te, c) % c;}printf("%lld\n", res);}int main() {#ifndef ONLINE_JUDGEfreopen("t.txt", "r", stdin);#endifinit();int t, a, b, c, i;while (scanf("%d", &t) != EOF) {for (i = 1; i <= t; i++) {scanf("%d %d %d", &a, &b, &c);solve(a + b - 2, b - 1, c);}}return 0;}

Number of hrbeu combinations

#include<stdio.h>#include<math.h>#include<string.h>#define LL long long#define nmax 100001int prime[nmax], flag[nmax], plen;void init() {memset(flag, -1, sizeof(flag));int i, j;for (i = 2, plen = 0; i < nmax; i++) {if (flag[i]) {prime[plen++] = i;}for (j = 0; (j < plen) && (i * prime[j] < nmax); j++) {flag[i * prime[j]] = 0;if ((i % prime[j]) == 0) {break;}}}}int modular_exp(int a, int b, int c) {LL res, te;res = 1, te = a % c;while (b) {if (b & 1) {res = res * te % c;}te = te * te % c;b >>= 1;}return res;}int getNum(int n, int m) {int res;res = 0;while (n) {res += n / m;n /= m;}return res;}int getMin(int a, int b) {return (a > b ? b : a);}void solve(int a, int b, int c) {int i, te;LL res;for (i = 0, res = 1; (i < plen) && (prime[i] <= a); i++) {te = getNum(a, prime[i]) - getNum(b, prime[i])- getNum(a - b, prime[i]);res = res * modular_exp(prime[i], te, c) % c;}printf("%lld\n", res);}int main() {#ifndef ONLINE_JUDGEfreopen("t.txt", "r", stdin);#endifinit();int t, a, b, c, i;while (scanf("%d", &t) != EOF) {for (i = 1; i <= t; i++) {scanf("%d %d %d", &a, &b, &c);solve(a + b, getMin(a, b), c);}}return 0;}

Fzu 1564.

#include<stdio.h>#include<string.h>#define nmax 1000001int prime[nmax], flag[nmax], plen, mark;void init() {memset(flag, -1, sizeof(flag));int i, j;for (i = 2, plen = 0; i < nmax; i++) {if (flag[i]) {prime[plen++] = i;}for (j = 0; (j < plen) && (i * prime[j] < nmax); j++) {flag[i * prime[j]] = 0;if (i % prime[j] == 0) {break;}}}}int getNum(int n, int m) {int res;res = 0;while (n) {res += n / m;n /= m;}return res;}/* int getNum(int n, int m) { int res; res = 0; while (n) { res += n % m; n /= m; } return res; } */void solve(int a, int b, int c) {int i, cnt, te;for (i = 0; (i < plen) && (prime[i] <= c); i++) {if (c % prime[i] == 0) {cnt = 0;while (c % prime[i] == 0) {c /= prime[i];cnt++;}te = getNum(a, prime[i]) - getNum(b, prime[i])- getNum(a - b, prime[i]);if (te < cnt) {mark = 1;return;}/*te = -getNum(a, prime[i]) + getNum(b, prime[i]) + getNum(a - b, prime[i]); if (te / (prime[i] - 1) < cnt) { mark = 1; return; }*/}}if (mark && (c > 1)) {te = getNum(a, prime[i]) - getNum(b, prime[i])- getNum(a - b, prime[i]);if (te < cnt) {mark = 1;return;}/*te = -getNum(a, c) + getNum(b, c) + getNum(a - b, c); if (te / (c - 1) < cnt) { mark = 1; return; }*/}}int main() {#ifndef ONLINE_JUDGEfreopen("t.txt", "r", stdin);#endifint t, a, b, c;init();while (scanf("%d", &t) != EOF) {while (t--) {scanf("%d %d %d", &a, &b, &c);mark = 0;solve(a, b, c);if (mark) {puts("No");} else {puts("Yes");}}}return 0;}