1 条题解
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思路与算法
读到行尾/EOF,流式维护最小值、最大值、总和和个数。平均值按总和的绝对值乘1000再除个数,保留商和余数,按最近值、恰好一半时末位取偶的标准浮点输出舍入规则处理,最后补足3位小数及符号。
正确性说明
每次读数更新区间极值与累计和,归纳后即为所有输入的统计量。商是平均值绝对值放大1000后的整数部分,余数与除数的一半比较决定最接近的千分位;正负对称处理保证负数准确。大整数避免输入只声明不超过1000却未声明负数下界时的截断。
复杂度
O(qD)时间、O(D)额外空间,q≤100,D为输入与总和位数;含极值、累计值和十进制格式化初始化。
易错点
输入没有预先给个数,不能把第一个数当n。平均值保留3位,最小最大值仍输出整数;不在每次读入时提前舍入。
参考代码(C++11)
#include <bits/stdc++.h> using namespace std; struct cpp_int { string s; bool neg; cpp_int(long long v = 0) : s(to_string(v)), neg(v < 0) { if (neg) s.erase(s.begin()); } void norm() { auto p = s.find_first_not_of('0'); s = p == string::npos ? "0" : s.substr(p); if (s == "0") neg = false; } static int cmpabs(const cpp_int &a, const cpp_int &b) { if (a.s.size() != b.s.size()) return a.s.size() < b.s.size() ? -1 : 1; return a.s == b.s ? 0 : a.s < b.s ? -1 : 1; } friend bool operator<(const cpp_int &a, const cpp_int &b) { if (a.neg != b.neg) return a.neg; int c = cmpabs(a, b); return a.neg ? c > 0 : c < 0; } friend bool operator==(const cpp_int &a, const cpp_int &b) { return a.neg == b.neg && a.s == b.s; } friend bool operator!=(const cpp_int &a, const cpp_int &b) { return !(a == b); } friend bool operator>(const cpp_int &a, const cpp_int &b) { return b < a; } friend bool operator<=(const cpp_int &a, const cpp_int &b) { return !(b < a); } friend bool operator>=(const cpp_int &a, const cpp_int &b) { return !(a < b); } cpp_int operator-() const { cpp_int r = *this; if (r.s != "0") r.neg = !r.neg; return r; } friend cpp_int operator+(const cpp_int &a, const cpp_int &b) { cpp_int r; r.s.clear(); int carry = 0; if (a.neg == b.neg) { int i = (int)a.s.size() - 1, j = (int)b.s.size() - 1; while (i >= 0 || j >= 0 || carry) { int v = carry + (i >= 0 ? a.s[i--] - '0' : 0) + (j >= 0 ? b.s[j--] - '0' : 0); r.s += char('0' + v % 10); carry = v / 10; } r.neg = a.neg; } else { const cpp_int *x = &a, *y = &b; if (cmpabs(a, b) < 0) swap(x, y); int i = (int)x->s.size() - 1, j = (int)y->s.size() - 1; while (i >= 0) { int v = x->s[i--] - '0' - carry - (j >= 0 ? y->s[j--] - '0' : 0); carry = v < 0; if (carry) v += 10; r.s += char('0' + v); } r.neg = x->neg; } reverse(r.s.begin(), r.s.end()); r.norm(); return r; } friend cpp_int operator-(const cpp_int &a, const cpp_int &b) { return a + (-b); } friend cpp_int operator*(const cpp_int &a, int b) { cpp_int r; r.s.clear(); long long carry = 0; long long z = b; if (z < 0) z = -z; for (int i = (int)a.s.size() - 1; i >= 0; i--) { carry += (a.s[i] - '0') * z; r.s += char('0' + carry % 10); carry /= 10; } while (carry) { r.s += char('0' + carry % 10); carry /= 10; } reverse(r.s.begin(), r.s.end()); r.neg = a.neg ^ (b < 0); r.norm(); return r; } friend cpp_int operator/(const cpp_int &a, int b) { cpp_int r; r.s.clear(); long long rem = 0, z = b; if (z < 0) z = -z; for (char c : a.s) { rem = rem * 10 + c - '0'; r.s += char('0' + rem / z); rem %= z; } r.neg = a.neg ^ (b < 0); r.norm(); return r; } cpp_int &operator+=(const cpp_int &b) { *this = *this + b; return *this; } cpp_int &operator-=(const cpp_int &b) { *this = *this - b; return *this; } cpp_int &operator*=(int b) { *this = *this * b; return *this; } friend istream &operator>>(istream &in, cpp_int &a) { string v; if (in >> v) { a.neg = v[0] == '-'; if (v[0] == '-' || v[0] == '+') v.erase(v.begin()); a.s = v; a.norm(); } return in; } friend ostream &operator<<(ostream &out, const cpp_int &a) { if (a.neg) out << '-'; return out << a.s; } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cpp_int x, sum, mn, mx; int n = 0; while (cin >> x) { if (!n) mn = mx = x; mn = min(mn, x); mx = max(mx, x); sum += x; n++; } bool negative = sum < 0; if (negative) sum = -sum; cpp_int scaled = sum * 1000, q = scaled / n; int rem = 0; for (char c : scaled.s) rem = (rem * 10 + c - '0') % n; if (rem * 2 > n || (rem * 2 == n && (q.s.back() - '0') % 2)) q += 1; string s = q.s; while (s.size() < 4) s = '0' + s; cout << mn << " " << mx << " " << (negative ? "-" : "") << s.substr(0, s.size() - 3) << "." << s.substr(s.size() - 3) << "\n"; }
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