uva 10668 - Expanding Rods(二分)

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题目链接：uva 10668 - Expanding Rods

题目大意：有一根长度为L的木棍被固住两端，现在为它加热，木棍受热增长L‘=(1+nC)∗L长度变长，形成弧形。求木棍中心的偏离高度。

解题思路：因为L′形成圆弧形，所以二分圆心角，判断即可。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>using namespace std;
const double pi = 4 * atan(1.0);double parabola_length (double w, double x) {double r = w / sin(x/2);return x * r;
}double bsearch (double l, double r, double v, double w) {for (int i = 0; i < 100; i++) {double mid = l + (r - l) / 2;if (parabola_length(w, mid) < v)l = mid;elser = mid;}return r;
}double solve (double w, double x) {return (1 - cos(x/2)) * w / sin(x/2);
}int main () {double L, l, n, c;while (scanf("%lf%lf%lf", &L, &n, &c) == 3) {if (L < 0 && n < 0 && c < 0)break;l = (1 + n * c) * L;printf("%.3lf\n", solve(L/2, bsearch(0, pi, l, L/2)));}return 0;
}

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