From d8602188165b9de352c2c1d7c562c9289bc3ec84 Mon Sep 17 00:00:00 2001 From: TooYoungTooSimp <6648049+TooYoungTooSimp@users.noreply.github.com> Date: Fri, 17 Feb 2017 10:48:08 +0800 Subject: [PATCH] 1/2 Section 3 --- 省选准备/assets/day3/Eratosthenes.cpp | 6 ++ 省选准备/assets/day3/exgcd.cpp | 2 + 省选准备/assets/day3/poj2689.cpp | 49 ++++++++++ 省选准备/assets/day3/poj3090.cpp | 22 +++++ 省选准备/assets/day3/poj3421.cpp | 30 ++++++ 省选准备/省选基础算法.pdf | Bin 225471 -> 325591 bytes 省选准备/省选基础算法.tex | 129 +++++++++++++++++++++++++- 7 files changed, 235 insertions(+), 3 deletions(-) create mode 100644 省选准备/assets/day3/Eratosthenes.cpp create mode 100644 省选准备/assets/day3/exgcd.cpp create mode 100644 省选准备/assets/day3/poj2689.cpp create mode 100644 省选准备/assets/day3/poj3090.cpp create mode 100644 省选准备/assets/day3/poj3421.cpp diff --git a/省选准备/assets/day3/Eratosthenes.cpp b/省选准备/assets/day3/Eratosthenes.cpp new file mode 100644 index 0000000..0c3d8ed --- /dev/null +++ b/省选准备/assets/day3/Eratosthenes.cpp @@ -0,0 +1,6 @@ +fill(isprime, true); +for (int i = 2; i < n; i++) + if (isprime[i]) + for (int j = i * i; j < n; j += i) + isprime[i] = false; + diff --git a/省选准备/assets/day3/exgcd.cpp b/省选准备/assets/day3/exgcd.cpp new file mode 100644 index 0000000..816c320 --- /dev/null +++ b/省选准备/assets/day3/exgcd.cpp @@ -0,0 +1,2 @@ +void exgcd(int64 a, int64 b, int64 &x, int64 &y) +{ b == 0 ? (x = 1, y = 0) : (exgcd(b, a % b, y, x), y -= x * (a / b)); } \ No newline at end of file diff --git a/省选准备/assets/day3/poj2689.cpp b/省选准备/assets/day3/poj2689.cpp new file mode 100644 index 0000000..cd7dacc --- /dev/null +++ b/省选准备/assets/day3/poj2689.cpp @@ -0,0 +1,49 @@ +#include +#include +#include +int prime_count; +int prime[5140]; +bool f[1000010]; +bool notprime[50010]; +int main() +{ + for (int i = 2; i < 50010; i++) + if (!notprime[i]) + for (long long j = 1ll * i * i; j < 50010; j += i) + notprime[j] = true; + for (int i = 2; i < 50010; i++) + if (!notprime[i]) + prime[prime_count++] = i; + int l, r; + while (~scanf("%d%d", &l, &r)) + { + l = l == 1 ? 2 : l; + memset(f, 0, sizeof(f)); + for (int i = 0, a, b; i < prime_count; i++) + { + a = (l - 1) / prime[i] + 1; + b = r / prime[i]; + for (int j = a; j <= b; j++) + if (j > 1) + f[j * prime[i] - l] = true; + } + int mx = -1, mn = 0x3f3f3f3f, x1 = 0, x2 = 0, y1 = 0, y2 = 0; + for (int i = 0, p = -1; i <= r - l; i++) + if (!f[i]) + { + if (~p) + { + if (mx < i - p) + mx = i - p, x1 = p + l, y1 = i + l; + if (mn > i - p) + mn = i - p, x2 = p + l, y2 = i + l; + } + p = i; + } + if (mx == -1) + puts("There are no adjacent primes."); + else + printf("%d,%d are closest, %d,%d are most distant.\n", x2, y2, x1, y1); + } + return 0; +} \ No newline at end of file diff --git a/省选准备/assets/day3/poj3090.cpp b/省选准备/assets/day3/poj3090.cpp new file mode 100644 index 0000000..9194f0f --- /dev/null +++ b/省选准备/assets/day3/poj3090.cpp @@ -0,0 +1,22 @@ +#include +const int maxn = 1010; +int phi[maxn], sum[maxn]; +int main() +{ + phi[1] = 1; + for (int i = 2; i <= 1005; i++) if (!phi[i]) + for (int j = i; j <= 1005; j += i) + { + if (!phi[j]) phi[j] = j; + phi[j] = phi[j] / i * (i - 1); + } + for (int i = 1; i <= 1005; i++) sum[i] = sum[i - 1] + phi[i]; + int T, x; + scanf("%d", &T); + for (int i = 1; i <= T; i++) + { + scanf("%d", &x); + printf("%d %d %d\n", i, x, sum[x] << 1 | 1); + } + return 0; +} diff --git a/省选准备/assets/day3/poj3421.cpp b/省选准备/assets/day3/poj3421.cpp new file mode 100644 index 0000000..40d43f7 --- /dev/null +++ b/省选准备/assets/day3/poj3421.cpp @@ -0,0 +1,30 @@ +#include +int f[1 << 12 | 1]; +long long _f(int x) +{ + long long ans = 1; + for (int i = x; i; i--) ans *= i; + return ans; +} +int main() +{ + int x; + while (~scanf("%d", &x)) + { + int _x = x, t = 0; + for (int i = 2; i * i <= _x; i++) + { + f[t] = 0; + while (_x % i == 0) + _x /= i, f[t]++; + t++; + } + if (_x != 1) f[t++] = 1; + int sum = 0; + for (int i = 0; i < t; i++) sum += f[i]; + long long fac = _f(sum); + for (int i = 0; i < t; i++) fac /= _f(f[i]); + printf("%d %lld\n", sum, fac); + } + return 0; +} \ No newline at end of file diff --git a/省选准备/省选基础算法.pdf b/省选准备/省选基础算法.pdf index e94914e33da2a7cb329835aa577a148db3cbf030..4e12a83044997f3f5d613abd0e74954eef63308f 100644 GIT binary patch literal 325591 zcma&NQ;=vulW^O%ZQHipecHBd+qP}nwrv}yZQK8uhs{+fgqSS+%ob<*F=F 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c\bmod{b}$,即为求$ax+my=b$的解。记$d=gcd(a,m)$,先使用拓展欧几里得求$ax+my=b$,如果$d\nmid b$则无解,否则$\mod m$意义下的解有$d$个,可以通过对其中某个解不断地加$\frac{m}{d}$得到。(这$d$个解的形式为$x_0+\frac{m}{d}t,\;t\in\mathbb{Z}$,其中$x_0$是已知的一个解) +\paragraph{中国剩余定理} + 若$m_1,m_2,m_3,\ldots,m_r$是两两互素的正整数,则同余方程组 + \begin{equation} + \left\{ + \begin{aligned} + & x\equiv a_1\pmod{m_1}\\ + & x\equiv a_2\pmod{m_2}\\ + & x\equiv a_3\pmod{m_3}\\ + & \cdots\\ + & x\equiv a_r\pmod{m_r}\\ + \end{aligned} + \right. + \end{equation} + 有$\mod M=\prod\limits_1^r m$的唯一解,即为中国剩余定理。\\ + 若$n=pq$且$gcd(p,q)=1$,那么$x\mod p,x\mod q$的值确定后,$x\mod n$的值也会随之确定。 +\subparagraph{算法说明} + $$M_i=\prod\limits_{j\ne i}m_j\to gcd(M_i,m_i)=1\Rightarrow \exists p_i,q_i,\,M_ip_i+m_iq_i=1$$ + $$(e_i=M_i p_i)\equiv int(j==i)\pmod{m_i} \to \sum\limits_1^r e_i a_i\mod{\sum\limits_1^r m_i}\mbox{是方程的最小非负整数解}$$ \end{document} \ No newline at end of file