#1959. 【cdw-2模拟题T1】解方程

https://sjzezoj.com/submission/72541

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;
+}