some programs!!

cs101/dh_03_05_perfect_cubes.cpp

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+#include <algorithm>
+#include <iostream>
+#include <vector>
+#include <cmath>
+
+struct PerfectCubeNumber {
+    int num = 0;
+    std::tuple<int, int, int> children;
+
+    constexpr bool operator<(const PerfectCubeNumber& other) const {
+        return std::tie(num, children) < std::tie(other.num, other.children);
+    }
+};
+
+constexpr int MAX_N = 101;
+std::vector<PerfectCubeNumber> perfect_cube_numbers;
+int n;
+
+constexpr int cubes_sum(int a, int b, int c) {
+    return a * a * a + b * b * b + c * c * c;
+}
+
+void init_numbers() {
+    for (int a = 2; a < MAX_N; a++) {
+        for (int b = a; b < MAX_N; b++) {
+            for (int c = b; ; c++) {
+                const int x_cube = cubes_sum(a, b, c);
+                if (x_cube > MAX_N * MAX_N * MAX_N) { break; }
+                for (int x = std::floor(std::cbrt(x_cube)), i = 0; i < 3; x++, i++) {
+                    if (x * x * x == x_cube) {
+                        perfect_cube_numbers.push_back({x, std::tuple(a, b, c)});
+                    }
+                }
+            }
+        }
+    }
+    std::sort(perfect_cube_numbers.begin(), perfect_cube_numbers.end());
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    init_numbers();
+
+    std::cin >> n;
+    for (const auto [num, children] : perfect_cube_numbers) {
+        if (num > n) { break; }
+        auto [a,b,c] = children;
+        std::cout << "Cube = " << num << ", Triple = (" << a << "," << b << "," << c << ")" << std::endl;
+    }
+
+    return 0;
+}

cs101/dh_04_01_fibonacci.cpp

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+#include <iostream>
+#include <array>
+
+constexpr int MAX_N = 21;
+
+// 编译期生成斐波那契数列
+constexpr std::array<int, MAX_N> make_fib() {
+    std::array<int, MAX_N> fib{}; // 零初始化
+    fib[0] = 1;
+    fib[1] = 1;
+    for (int i = 2; i < MAX_N; ++i) {
+        fib[i] = fib[i - 1] + fib[i - 2];
+    }
+    return fib;
+}
+
+static constexpr auto fib = make_fib();
+
+int x;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin >> x;
+    while (std::cin >> x) {
+        std::cout << fib[x - 1] << std::endl;
+    }
+
+    return 0;
+}

cs101/dh_04_04_balloons_init1.py

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+def solve(n: int) -> int:
+    balloons = [i for i in range(1, n + 1)]
+    while True:
+        deleted_amount = 0
+        for x in range(1, n):
+            if len(balloons) <= x * x - deleted_amount - 1 or len(balloons) == 1:
+                break
+            del balloons[x * x - deleted_amount - 1]
+            deleted_amount += 1
+        if len(balloons) == 1:
+            break
+    return balloons[0]
+
+
+if __name__ == '__main__':
+    for n in range(1, 1150):
+        print(n, "->", solve(n))

cs101/sh_04_04_balloons.cpp

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+/*
+ * 本来想打表的，打着打着发现了一些数学规律。具体怎么证明嘛……🤷‍
+ */
+
+#include <iostream>
+#include <cmath>
+
+constexpr size_t MAX_N = 10001;
+
+int get_ans(int n) {
+    const int k = ceil(-0.5 + 0.5 * sqrt(4 * n + 1));
+    const bool extra = k * k < n;
+    const int ans = k * (k - 1) + 1 + k * extra;
+    return ans;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    int n;
+    std::cin >> n;
+    std::cout << get_ans(n) << std::endl;
+
+    return 0;
+}