v1.2.3:添加和修复和若干内容

lr580 · lr580 · commit 30d3bb78f294 · 2025-03-05T00:30:36.000+08:00
diff --git a/code/ex_euler.py b/code/ex_euler.py
@@ -0,0 +1,8 @@
+# https://oj.socoding.cn/p/2117
+p, phi, f, fp = 998244353, 998244352, [1, 1], [1, 1]
+for i in range(2, 5001):
+    f.append((f[-1] * i) % p)
+    fp.append((fp[-1] * i) % phi)
+for _ in range(int(input())):
+    n = int(input())
+    print(pow(f[n], fp[n], p))
diff --git a/code/p4718_pollard_rho.cpp b/code/p4718_pollard_rho.cpp
@@ -0,0 +1,152 @@
+#include <iostream>
+#include <algorithm>
+#include <random>
+#include <chrono>
+
+#define int long long
+
+using namespace std;
+
+typedef long long ll;
+
+auto seed = chrono::system_clock::now().time_since_epoch().count();
+mt19937 gen(seed);
+    
+uniform_int_distribution<long long> dis(1, (long long)1e18);
+
+ll qpow(ll a, ll b, ll mod)
+{
+    ll r = 1;
+    
+    for (; b; b >>= 1)
+    {
+        if (b & 1)
+            r = (__int128)r * a % mod;
+        a = (__int128)a * a % mod;
+    }
+    
+    return r;
+}
+
+bool miller_rabin(ll p, ll k = 30) // 判断素数
+{
+    if (p < 2) return false;
+    if (p == 2) return true;
+    if (p == 3) return true;
+    
+    ll d = p - 1, r = 0;
+    while (!(d & 1)) ++r, d >>= 1; // 将d处理为奇数
+    
+    while(k--) // k次随机运算提高准确率
+    {
+        ll a = dis(gen) % (p - 2) + 2;
+        ll x = qpow(a, d, p);
+        
+        if (x == 1 || x == p - 1) continue;
+        
+        for (ll i = 0; i < r - 1; ++i)
+        {
+            x = (__int128)x * x % p;
+            
+			if (x == p - 1) break;
+        }
+        
+        if (x != p - 1) return false;
+    }
+    
+    return true;
+}
+
+ll pollard_rho(ll x)
+{
+    ll c = dis(gen) % (x - 1) + 1;
+    
+    for (ll goal = 1, s = 0, t; true; goal <<= 1, s = t)
+    {
+    	ll val = 1;
+    	
+        for (ll step = 1; step <= goal; ++step)
+        {
+            t = ((__int128)t * t + c) % x; //随机数生成器
+            val = ((__int128)val * abs(t - s)) % x;
+            
+            if (step % 127 == 0)
+            {
+                ll d = __gcd(val, x);
+                if (d > 1) return d;
+            }
+        }
+        
+        ll d = __gcd(val, x);
+        if (d > 1) return d;
+    }
+}
+
+ll get_maxi_prime_factor(ll x)
+{
+    if (x < 2) return 0;
+    
+    if (miller_rabin(x)) return x;
+    
+    ll p = x;
+    while (p >= x) p = pollard_rho(x); //直到找到平凡
+    while (x % p == 0) x /= p;
+    
+    return max(get_maxi_prime_factor(x), get_maxi_prime_factor(p)); //返回最大质因子
+}
+
+signed main()
+{
+	ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
+    
+	ll t, n;
+    
+    cin >> t;
+    while (t--)
+    {
+        cin >> n;
+        
+        ll mx = get_maxi_prime_factor(n);
+        
+        if (mx == n) cout << "Prime\n";
+        else cout << mx << '\n';
+    }
+    
+    return 0;
+}
+
+/* 因式分解：
+void get_prime_factors(ll base, ll index, map<ll, ll>& cnt_prime_fac)
+{
+    if (base < 2) return;
+    
+    if (miller_rabin(base))
+    {
+        cnt_prime_fac[base]+=index;
+        
+        return;
+    }
+    
+    ll new_fac= base, multimes = 0;
+    while (new_fac >= base) new_fac = pollard_rho(base); //直到找到平凡
+    while (base % new_fac == 0) base /= new_fac, multimes++;
+    
+    get_prime_factors(base, index, cnt_prime_fac);
+	get_prime_factors(new_fac, index * multimes, cnt_prime_fac);
+    
+    return;
+}
+
+signed main()
+{
+	ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
+    
+	map<ll,ll> prime_factors;
+	get_prime_factors(27, 2, prime_factors);
+	
+	for(auto x:prime_factors) cout<<x.first<<':'<<x.second<<'\n';
+    
+    return 0;
+}
+
+*/
diff --git a/code/p4718_pollard_rho_old.cpp b/code/p4718_pollard_rho_old.cpp
@@ -0,0 +1,108 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+ll qpow(ll a, ll b, ll p)
+{
+    ll r = 1;
+    for (; b; b >>= 1)
+    {
+        if (b & 1)
+            r = (__int128)r * a % p;
+        a = (__int128)a * a % p;
+    }
+    return r;
+}
+bool millerRabin(ll p)
+{ // 判断素数
+    if (p < 2)
+        return 0;
+    if (p == 2)
+        return 1;
+    if (p == 3)
+        return 1;
+    ll d = p - 1, r = 0;
+    while (!(d & 1))
+        ++r, d >>= 1; // 将d处理为奇数
+    for (ll k = 0; k < 10; ++k)
+    {
+        ll a = rand() % (p - 2) + 2;
+        ll x = qpow(a, d, p);
+        if (x == 1 || x == p - 1)
+            continue;
+        for (int i = 0; i < r - 1; ++i)
+        {
+            x = (__int128)x * x % p;
+            if (x == p - 1)
+                break;
+        }
+        if (x != p - 1)
+            return 0;
+    }
+    return 1;
+}
+ll pollard_rho(ll x)
+{
+    ll s = 0, t = 0, c = (ll)rand() % (x - 1) + 1;
+    ll step = 0, goal = 1, val = 1;
+    for (goal = 1;; goal <<= 1, s = t, val = 1)
+    {
+        for (step = 1; step <= goal; ++step)
+        {
+            t = ((__int128)t * t + c) % x; //随机数生成器
+            val = ((__int128)val * abs(t - s)) % x;
+            if (step % 127 == 0)
+            {
+                ll d = __gcd(val, x);
+                if (d > 1)
+                    return d;
+            }
+        }
+        ll d = __gcd(val, x);
+        if (d > 1)
+            return d;
+    }
+}
+ll mx;
+void fac(ll x)
+{
+    if (x <= mx || x < 2)
+        return;
+    if (millerRabin(x))
+    {
+        mx = max(mx, x); //最大质因子
+        return;
+    }
+    ll p = x;
+    while (p >= x) //直到找到平凡
+    {
+        p = pollard_rho(x);
+    }
+    while (x % p == 0)
+    {
+        x /= p;
+    }
+    fac(x), fac(p); // x*p=raw x
+}
+signed main()
+{
+    ll t, n;
+    cin.tie(0)->ios::sync_with_stdio(false);
+    cin >> t;
+    while (t--)
+    {
+        srand(time(0));
+        cin >> n;
+        mx = 0;
+        fac(n);
+        if (mx == n)
+        {
+            cout << "Prime\n";
+        }
+        else
+        {
+            cout << mx << '\n';
+        }
+    }
+    return 0;
+}
