三分查找是二分查找的一個(gè)擴(kuò)展，是基于分治思想的高效查找方法。

三分查找適用于凸函數(shù)或凹函數(shù)，它可以取得當(dāng)前函數(shù)的最大值或最小值。

三分搜索實(shí)現(xiàn)主要是判斷midl 和 midr 值的大小，

模板：

double solve(){} double trisection_search(double left, double right){double midl, midr;while(right - left > 1e-7){midl = (left + right) / 2;midr = (midl + right) / 2;if(solve(midl) >= solve(midr)) right = midr;else left = midl;} }

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例題：http://acm.hdu.edu.cn/showproblem.php?pid=3400

題解：該題很明顯是一道三分搜索的題目，分別搜索ab直線段和bc直線段，同時(shí)進(jìn)行判斷，從而縮小范圍，最后取得最小值。

#include<cstdio> #include<iostream> #include<algorithm> #include<cstring> #include<string> #include<cmath>using namespace std;const double esp = 1e-7; struct Node{double x, y; }a, b, c, d, t1, t2;double p, q, r; double ab, cd;double len(Node a1, Node a2){double x = (a2.x - a1.x) * (a2.x - a1.x);double y = (a2.y - a1.y) * (a2.y - a1.y);double L = sqrt(x + y + esp);return L; } double solve(double cdx){t2.x = c.x + (d.x - c.x) * (cdx / cd);t2.y = c.y + (d.y - c.y) * (cdx / cd);return len(t1, t2) / r + (cd - cdx) / q; }double trisection_search2(double abx){t1.x = a.x + (b.x - a.x) * (abx / ab);t1.y = a.y + (b.y - a.y) * (abx / ab);double left = 0, right = cd; double midl, midr;double ans, tmp1, tmp2;while(right - left > 1e-7){midl = (left + right) / 2;midr = (midl + right) / 2;if((tmp1 = solve(midl)) <= (tmp2 = solve(midr)))right = midr;else left = midl;ans = min(tmp1, tmp2);}return ans + abx / p; }double trisection_search1(double left, double right){double midl, midr;double ans, tmp1, tmp2;while(right - left > 1e-7){midl = (left + right) / 2;midr = (midl + right) / 2;if((tmp1 = trisection_search2(midl)) <= (tmp2 = trisection_search2(midr)))right = midr;else left = midl;ans = min(tmp1, tmp2);}return ans; }int main() {int T;scanf("%d", &T);while(T--){scanf("%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y);scanf("%lf%lf%lf%lf", &c.x, &c.y, &d.x, &d.y);scanf("%lf%lf%lf", &p, &q, &r);ab = len(a, b);cd = len(c, d);double ans = trisection_search1(0, ab);printf("%.2lf\n", ans);}return 0; }

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