Merge pull request yosupo06#1242 from maspypy/square_sum

問題追加 Represent A Number As Two Square Sum

number_theory/two_square_sum/checker.cpp

@@ -0,0 +1,40 @@
+#include "testlib.h"
+
+#include <vector>
+#include <tuple>
+#include <cassert>
+
+using namespace std;
+using ll = long long;
+
+ll read_ans_cnt(ll N, InStream& stream) {
+  ll n = stream.readInt();
+  vector<pair<ll, ll>> ANS(n);
+  for (int i = 0; i < n; ++i) {
+    ll x = stream.readLong(0LL, 1LL << 30);
+    ll y = stream.readLong(0LL, 1LL << 30);
+    stream.ensure(x * x + y * y == N);
+    ANS[i] = {x, y};
+  }
+  // check distinct
+  sort(ANS.begin(), ANS.end());
+  for (int i = 0; i < n - 1; ++i) stream.ensure(ANS[i] != ANS[i + 1]);
+  return n;
+}
+
+int main(int argc, char* argv[]) {
+  registerTestlibCmd(argc, argv);
+
+  int Q = inf.readInt();
+  for (int q = 0; q < Q; ++q) {
+    ll N = inf.readLong();
+    ll ans_cnt = read_ans_cnt(N, ans);
+    ll ouf_cnt = read_ans_cnt(N, ouf);
+    if (ans_cnt > ouf_cnt) {
+      quitf(_wa, "Not found all solutions. N=%lld, ans_cnt=%lld, ouf_cnt=%lld", N, ans_cnt, ouf_cnt);
+    } else if (ans_cnt < ouf_cnt) {
+      quitf(_fail, "Writer does not find all solutions! N=%lld, ans_cnt=%lld, ouf_cnt=%lld", N, ans_cnt, ouf_cnt);
+    }
+  }
+  quitf(_ok, "OK");
+}

number_theory/two_square_sum/gen/big2.cpp

@@ -0,0 +1,41 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+vector<long long> enum_prime(long long st, long long ed) {
+    if (st == 1) st = 2;
+    vector<bool> is_prime(ed - st + 1, true);
+    for (long long i = 2; i * i <= ed; i++) {
+        for (long long j = (st + i - 1) / i * i; j <= ed; j += i) {
+            is_prime[j - st] = false;
+        }
+    }
+    vector<long long> primes;
+    for (long long i = st; i <= ed; i++) {
+        if (is_prime[i - st]) primes.push_back(i);
+    }
+    return primes;
+}
+
+int main(int, char* argv[]) {
+
+
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    auto primes = enum_prime(1'000'000'000 - 1'000'000, 1'000'000'000);
+    int k = int(primes.size());
+    int q = MAX_Q;
+    vector<long long> a(q);
+    for (int i = 0; i < q; i++) {
+        a[i] = primes[gen.uniform(0, k - 1)] * primes[gen.uniform(0, k - 1)];
+    }
+
+    printf("%d\n", q);
+    for (auto x: a) {
+        printf("%lld\n", x);
+    }
+    return 0;
+}

number_theory/two_square_sum/gen/big_semiprime_random.cpp

@@ -0,0 +1,116 @@
+#include <iostream>
+#include <cmath>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+using ll = long long;
+using ull = unsigned long long;
+template <class T> using V = vector<T>;
+
+// bit op
+int bsf(ull x) { return __builtin_ctzll(x); }
+
+// binary gcd
+ll gcd(ll _a, ll _b) {
+    ull a = abs(_a), b = abs(_b);
+    if (a == 0) return b;
+    if (b == 0) return a;
+    int shift = bsf(a | b);
+    a >>= bsf(a);
+    do {
+        b >>= bsf(b);
+        if (a > b) swap(a, b);
+        b -= a;
+    } while (b);
+    return (a << shift);
+}
+
+template <class T, class U> T pow_mod(T x, U n, T md) {
+    T r = 1 % md;
+    x %= md;
+    while (n) {
+        if (n & 1) r = (r * x) % md;
+        x = (x * x) % md;
+        n >>= 1;
+    }
+    return r;
+}
+
+bool is_prime(ll n) {
+    if (n <= 1) return false;
+    if (n == 2) return true;
+    if (n % 2 == 0) return false;
+    ll d = n - 1;
+    while (d % 2 == 0) d /= 2;
+    for (ll a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
+        if (n <= a) break;
+        ll t = d;
+        ll y = pow_mod<__int128_t>(a, t, n);  // over
+        while (t != n - 1 && y != 1 && y != n - 1) {
+            y = __int128_t(y) * y % n;  // flow
+            t <<= 1;
+        }
+        if (y != n - 1 && t % 2 == 0) {
+            return false;
+        }
+    }
+    return true;
+}
+
+ll pollard_single(ll n) {
+    if (is_prime(n)) return n;
+    if (n % 2 == 0) return 2;
+    ll st = 0;
+    auto f = [&](ll x) { return (__int128_t(x) * x + st) % n; };
+    while (true) {
+        st++;
+        ll x = st, y = f(x);
+        while (true) {
+            ll p = gcd((y - x + n), n);
+            if (p == 0 || p == n) break;
+            if (p != 1) return p;
+            x = f(x);
+            y = f(f(y));
+        }
+    }
+}
+
+V<ll> pollard(ll n) {
+    if (n == 1) return {};
+    ll x = pollard_single(n);
+    if (x == n) return {x};
+    V<ll> le = pollard(x);
+    V<ll> ri = pollard(n / x);
+    le.insert(le.end(), ri.begin(), ri.end());
+    return le;
+}
+
+int main(int, char* argv[]) {
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    int q = MAX_Q;
+    V<ll> a(q);
+    for (int i = 0; i < q; ++i) {
+        while(true) {
+            ll x = gen.uniform(MAX_A - ll(sqrt(MAX_A)), MAX_A);
+            auto v = pollard(x);
+            if (v.size() == 2) {
+                ll p = max(v[0], v[1]);
+                ll q = min(v[0], v[1]);
+                if (p / q < 100) {
+                    a[i] = x;
+                    break;
+                }
+            }
+        }
+    }
+
+    printf("%d\n", q);
+    for (auto x: a) {
+        printf("%lld\n", x);
+    }
+    return 0;
+}

number_theory/two_square_sum/gen/example_00.in

@@ -0,0 +1,12 @@
+11
+0
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10

number_theory/two_square_sum/gen/example_01.in

@@ -0,0 +1,11 @@
+10
+5
+25
+125
+13
+65
+998244353
+1000000007
+1000000009
+536870912
+1073741824

number_theory/two_square_sum/gen/fixed_RNG_buster_00.in

@@ -0,0 +1,2 @@
+1
+124376107291

number_theory/two_square_sum/gen/max.cpp

@@ -0,0 +1,13 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include "../params.h"
+
+int main(int, char **argv) {
+  const long long seed = atoll(argv[1]);
+  printf("%lld\n", MAX_Q);
+  for (int i = 0; i < MAX_Q; ++i) {
+    const long long a = MAX_A - seed * MAX_Q - i;
+    printf("%lld\n", a);
+  }
+  return 0;
+}

number_theory/two_square_sum/gen/num_of_solution_max_00.in

@@ -0,0 +1,101 @@
+100
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