loigiai

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c_cpp
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#include <iostream>
#include <algorithm>
#include <iomanip>

// Structure to store material data
struct Material {
    double x; // x coordinate
    double mass; // mass
};

// Function to calculate gravitational force
double gravitationalForce(double m1, double m2, double d) {
    
    return 6.67430e-11 * m1 * m2 / (d * d);
}

// Function to check if force from left side is greater than, less than or equal to force from right side
int compareForces(Material materials[], int n, double mid) {
    double left_force = 0.0;
    double right_force = 0.0;

    // Calculate total mass
    double total_mass = 0.0;
    for (int i = 0; i < n; ++i) {
        total_mass += materials[i].mass;
    }

    // Calculate force from left side
    for (int i = 0; i < n; ++i) {
        double d = mid - materials[i].x;
        if (d > 0) {
            left_force += gravitationalForce(materials[i].mass, total_mass - materials[i].mass, d);
        }
    }

    // Calculate force from right side
    for (int i = 0; i < n; ++i) {
        double d = materials[i].x - mid;
        if (d > 0) {
            right_force += gravitationalForce(materials[i].mass, total_mass - materials[i].mass, d);
        }
    }

    // Compare forces
    if (left_force > right_force) {
        return 1; // Left force is greater
    } else if (left_force < right_force) {
        return -1; // Right force is greater
    } else {
        return 0; // Forces are equal
    }
}

// Function to find balance point using binary search
double findBalancePoint(Material materials[], int n) {
    double left = materials[0].x;
    double right = materials[n - 1].x;

    while (right - left > 1e-9) {
        double mid = (left + right) / 2.0;
        int cmp = compareForces(materials, n, mid);

        if (cmp == 0) {
            return mid;
        } else if (cmp < 0) {
            left = mid;
        } else {
            right = mid;
        }
    }

    return (left + right) / 2.0;
}

int main() {
	freopen("Text.txt","r",stdin);

    for (int case_num = 1; case_num <= 10; ++case_num) {
        int n;
        std::cin >> n;
        Material* materials = new Material[n];

        // Read x coordinates and masses
        for (int i = 0; i < n; ++i) {
            std::cin >> materials[i].x;
        }
        for (int i = 0; i < n; ++i) {
            std::cin >> materials[i].mass;
        }

        // Sort materials by x coordinate
        std::sort(materials, materials + n, [](const Material& a, const Material& b) {
            return a.x < b.x;
        });

        // Find balance point
        double balance_point = findBalancePoint(materials, n);

        // Output result
        std::cout << "#" << case_num << " ";
        std::cout << std::fixed << std::setprecision(10) << balance_point << std::endl;

        // Free allocated memory
        delete[] materials;
    }

    return 0;
}
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