UV 1356, lga1356

UV 1356, lga1356

Link to the question: Ultraviolet A 1356-Bridge

A number of towers are built on a bridge with a length of B. The distance between the towers cannot exceed D, the height of the tower is H, and the ropes between the towers form a fully equal parabolic curve. The total length of the rope is L. Ask the shortest section of the rope to exit the height of the ground when the least tower is under construction.

Solution: Use greedy ideas to find the number of Towers created at least.
The second height, and then use the integral points to find the length of the rope between the two towers.

C ++ points#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;double f (double a, double x) {    double aa = a * a, xx = x * x;;    return (x * sqrt(aa + xx) + aa * log(fabs(x + sqrt(aa + xx)))) / 2;}double parabola_length (double w, double h) {    double a = 4 * h / (w * w);    double b = 1.0 / (2 * a);    return (f(b, w/2) - f(b, 0)) * 4 * a;}double bsearch (double l, double r, double d, double v) {    while (r - l > 1e-5) {        double mid = (r + l) / 2;        if (parabola_length(d, mid) < v)            l = mid;        else            r = mid;    }    return l;}int main () {    int cas;    scanf("%d", &cas);    for (int kcas = 1; kcas <= cas; kcas++) {        int D, H, B, L;        scanf("%d%d%d%d", &D, &H, &B, &L);        int n = (B + D - 1) / D;        double d = B * 1.0 / n;        double l = L * 1.0 / n;        if (kcas > 1)            printf("\n");        printf("Case %d:\n%.2lf\n", kcas, (double)H - bsearch(0, H, d, l));    }    return 0;}

C ++ Simpson#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;double A;double f (double x) {    return sqrt (1 + 4 * A * A * x * x);}double simpson (double a, double b) {    double c = (a + b) / 2;    return (f(a) + 4*f(c) + f(b)) * (b-a) / 6;}double asr (double a, double b, double eps, double S) {    double c = (a + b) / 2;    double L = simpson(a, c), R = simpson(c, b);    if (fabs(L+R-S) <= eps * 15)        return L + R + (L + R - S) / 15;    return asr(a, c, eps/2, L) + asr(c, b, eps/2, R);}double asr (double a, double b, double eps) {    return asr(a, b, eps, simpson(a, b));}double parabola_length (double w, double h) {    A = 4 * h / (w * w);    return asr(0, w / 2, 1e-5) * 2;}double bsearch (double l, double r, double d, double v) {    while (r - l > 1e-5) {        double mid = (r + l) / 2;        if (parabola_length(d, mid) < v)            l = mid;        else            r = mid;    }    return l;}int main () {    int cas;    scanf("%d", &cas);    for (int kcas = 1; kcas <= cas; kcas++) {        int D, H, B, L;        scanf("%d%d%d%d", &D, &H, &B, &L);        int n = (B + D - 1) / D;        double d = B * 1.0 / n;        double l = L * 1.0 / n;        if (kcas > 1)            printf("\n");        printf("Case %d:\n%.2lf\n", kcas, (double)H - bsearch(0, H, d, l));    }    return 0;}