## 三分法查找(ternary search) 概念

https://www.geeksforgeeks.org/ternary-search/

## 方法一

$m1=l+(r-l)/3$
$m2=r-(r-l)/3$

## 方法二

$m1=(l+r)/2$
$m2=(m1+r)/2$

## UVa-1476 Error Curves

https://onlinejudge.org/external/14/1476.pdf

## 完整代码

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125  /* =========================================================== * @Name: UVa-1476 Error Curves * @Author: Shawn * @create Time: 2020/5/23 20:02:29 * @url: https://onlinejudge.org/external/14/1476.pdf * @Description: =========================================================== */ #ifdef ONLINE_JUDGE #define NDEBUG //ban assert when submit to online judge #endif #include using namespace std; using ll = long long; const double eps = 1e-10; struct coefficient //系数 { int a, b, c; }; //二次方程式 double f(double x, vector & coefficients, int n) { //int n=coefficients.size(); double ret = coefficients[0].a * x * x + coefficients[0].b * x + coefficients[0].c; for (int i = 1; i <= n - 1; ++i) ret = max(ret, coefficients[i].a * x * x + coefficients[i].b * x + coefficients[i].c); return ret; } //三分搜索 //https://yuihuang.com/ternary-search/ //https://blog.csdn.net/u011787119/article/details/44598871 double ternary_search(double left, double right, vector & coefficients, int n) { double midL, midR, ans; while (right - left > eps) { midL = (left + right) / 2.0; midR = (midL + right) / 2.0; double fL = f(midL, coefficients, n); double fR = f(midR, coefficients, n); //如果是求最大值的话这里判>=即可 //如果是求最小值的话这里判<=即可 if (fL <= fR) right = midR; else left = midL; ans = fL; } return ans; } //三分搜索2 //https://cp-algorithms.com/num_methods/ternary_search.html //https://www.geeksforgeeks.org/ternary-search/ double ternary_search2(double left, double right, vector & coefficients, int n) { double midL, midR, ans; while (right - left > eps) { midL = left + (right - left) / 3.0; midR = right - (right - left) / 3.0; double fL = f(midL, coefficients, n); double fR = f(midR, coefficients, n); //如果是求最大值的话这里判>=即可 //如果是求最小值的话这里判<=即可 if (fL <= fR) right = midR; else left = midL; ans = fL; } return ans; } void solve() { cout << fixed << std::setprecision(4); int T; cin >> T; while (T--) { int n; cin >> n; vector coefficients; //输入的系数 int size1 = n; while (size1--) { coefficient coe; cin >> coe.a >> coe.b >> coe.c; coefficients.push_back(coe); } double ans = ternary_search2(0.0, 1000.0, coefficients, n); cout << ans << "\n"; } } int main() { ios_base::sync_with_stdio(false); std::cin.tie(NULL); std::cout.tie(NULL); #ifndef ONLINE_JUDGE freopen("UVa1476_ErrorCurves.in", "r", stdin); //freopen("UVa1476_ErrorCurves.out", "w", stdout); #endif solve(); cout.flush(); return 0; } 

## 练习

• UVa-1476 Error Curves
• UVa-12197 Trick or Treat
• CF-1355E Restorer Distance
• CF-939E Maximize!
• 782B The Meeting Place Cannot Be Changed
• 578C Weakness and Poorness (三分+dp，double精度不够，long double才行)