From acbf73ce315918d7700d625d23cb4ec88295948c Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Sat, 25 Feb 2023 06:47:19 +0800
Subject: [PATCH] =?UTF-8?q?#1959.=20=E3=80=90cdw-2=E6=A8=A1=E6=8B=9F?=
 =?UTF-8?q?=E9=A2=98T1=E3=80=91=E8=A7=A3=E6=96=B9=E7=A8=8B?=
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https://sjzezoj.com/submission/72541
---
 S2OJ/1959/1959.cpp          | 98 +++++++++++++++++++++++++++++++++++++
 S2OJ/1959/data/chk.cpp      |  3 ++
 S2OJ/1959/data/data1.ans    |  3 ++
 S2OJ/1959/data/data1.in     |  3 ++
 S2OJ/1959/data/data2.ans    |  3 ++
 S2OJ/1959/data/data2.in     |  3 ++
 S2OJ/1959/data/data3.ans    |  3 ++
 S2OJ/1959/data/data3.in     |  3 ++
 S2OJ/1959/data/problem.conf |  3 ++
 9 files changed, 122 insertions(+)
 create mode 100644 S2OJ/1959/1959.cpp
 create mode 100644 S2OJ/1959/data/chk.cpp
 create mode 100644 S2OJ/1959/data/data1.ans
 create mode 100644 S2OJ/1959/data/data1.in
 create mode 100644 S2OJ/1959/data/data2.ans
 create mode 100644 S2OJ/1959/data/data2.in
 create mode 100644 S2OJ/1959/data/data3.ans
 create mode 100644 S2OJ/1959/data/data3.in
 create mode 100644 S2OJ/1959/data/problem.conf

diff --git a/S2OJ/1959/1959.cpp b/S2OJ/1959/1959.cpp
new file mode 100644
index 00000000..edd4a831
--- /dev/null
+++ b/S2OJ/1959/1959.cpp
@@ -0,0 +1,98 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+#include <functional>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+std::vector<std::pair<long long, int>> divide(long long x) {
+    std::vector<std::pair<long long, int>> res;
+
+    for (long long i = 2; i * i <= x; i++) {
+        if (x % i == 0) {
+            int cnt = 0;
+
+            while (x % i == 0) x /= i, cnt++;
+
+            res.emplace_back(i, cnt);
+        }
+    }
+
+    if (x > 1) res.emplace_back(x, 1);
+
+    return res;
+}
+
+void solve() {
+    long long n;
+    bool flag = false;
+
+    cin >> n;
+
+    auto nums = divide(n);
+
+    std::transform(nums.begin(), nums.end(), nums.begin(), [&](const std::pair<long long, int> &o) -> std::pair<long long, int> {
+        return {o.first, o.second << 1};
+    });
+
+    std::function<bool(long long)> check = [&](long long x) -> bool {
+        long long t = x * x - n * n / x;
+
+        if (t % 3) return false;
+
+        long long l = 1, r = x / 2 + 1;
+
+        while (l <= r) {
+            long long mid = (l + r) >> 1;
+
+            if (mid * (x - mid) == t / 3) {
+                cout << x - mid << ' ' << mid << endl;
+
+                return true;
+            }
+
+            if (mid * (x - mid) > t / 3) {
+                r = mid - 1;
+            } else {
+                l = mid + 1;
+            }
+        }
+
+        return false;
+    };
+
+    std::function<void(long long, int)> dfs = [&](long long val, int pos) -> void {
+        if (flag) return;
+
+        if (pos == nums.size()) {
+            if (check(val)) flag = true;
+
+            return;
+        }
+
+        for (int i = 0; i <= nums[pos].second; i++) {
+            dfs(val * std::pow(nums[pos].first, i), pos + 1);
+        }
+    };
+
+    dfs(1, 0);
+
+    if (!flag) cout << "impossible" << endl;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int t;
+
+    cin >> t;
+
+    while (t--) solve();
+
+    return 0;
+}
diff --git a/S2OJ/1959/data/chk.cpp b/S2OJ/1959/data/chk.cpp
new file mode 100644
index 00000000..64e1043a
--- /dev/null
+++ b/S2OJ/1959/data/chk.cpp
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:01f161697ce5735d84215f8768417132ea8dad7fb958059f7054fa4259f32304
+size 524
diff --git a/S2OJ/1959/data/data1.ans b/S2OJ/1959/data/data1.ans
new file mode 100644
index 00000000..ec60e967
--- /dev/null
+++ b/S2OJ/1959/data/data1.ans
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:39255b4ffb00605381b65f1dc7e7d095f98d3d2aeb22182ecb8d4e437351008b
+size 645
diff --git a/S2OJ/1959/data/data1.in b/S2OJ/1959/data/data1.in
new file mode 100644
index 00000000..674f1fa8
--- /dev/null
+++ b/S2OJ/1959/data/data1.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d497d7c8759a0d98c3b036c68d963d47ff6043118419a6b6015a4479d3100374
+size 460
diff --git a/S2OJ/1959/data/data2.ans b/S2OJ/1959/data/data2.ans
new file mode 100644
index 00000000..cb1b58fc
--- /dev/null
+++ b/S2OJ/1959/data/data2.ans
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4aaa5c716e1f9b75a7e474355c3bfb4c96cbaced6c5463d1e260685cab99e3a8
+size 13077
diff --git a/S2OJ/1959/data/data2.in b/S2OJ/1959/data/data2.in
new file mode 100644
index 00000000..adc81d77
--- /dev/null
+++ b/S2OJ/1959/data/data2.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bdf655e80381d2c7cb1d84d3ed43a9bd8c3fcce305712da7c8c3b5efe134994c
+size 9416
diff --git a/S2OJ/1959/data/data3.ans b/S2OJ/1959/data/data3.ans
new file mode 100644
index 00000000..827689fc
--- /dev/null
+++ b/S2OJ/1959/data/data3.ans
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a13120ea71bdb3192cd2853e6a5a9b003adfca44e94e960d2c6bf91a787b961d
+size 65155
diff --git a/S2OJ/1959/data/data3.in b/S2OJ/1959/data/data3.in
new file mode 100644
index 00000000..f778c787
--- /dev/null
+++ b/S2OJ/1959/data/data3.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4ccb79a2bc57b7cd2708b16e5c13e5abcca4c0b994a2fcee8d08fa049c7ddccc
+size 46870
diff --git a/S2OJ/1959/data/problem.conf b/S2OJ/1959/data/problem.conf
new file mode 100644
index 00000000..75548f46
--- /dev/null
+++ b/S2OJ/1959/data/problem.conf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8479cfcc428625f384da715fa765dc2e804cd746879b3058beffd867ed543af9
+size 291