#1182604 (C++23) No.3672 Volume 3D

• 問題: No.3672 Volume 3D
• ユーザー: miie
• 提出日時: 2026-09-04 23:14:35
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 163 ms / 2,000 ms
• コード長: 5,955 bytes
• コンパイル時間: 2,152 ms
• コンパイル使用メモリ: 351,516 KB
• 実行使用メモリ: 9,860 KB
• 最終ジャッジ日時: 2026-09-04 23:14:53
• 合計ジャッジ時間: 6,207 ms
• ジャッジサーバーID （参考情報）: judge4_0 / judge2_0

ファイルパターン	結果
sample	AC * 1
other	AC * 20

ソースコード

#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")

// 数値型
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int,int>;
using Pll = pair<ll, ll>;
using Pli = pair<ll, int>;
using Pil = pair<int, ll>;

// vector関連
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
template<typename T>
using vc = vector<T>;
template<typename T>
using vvc = vector<vc<T>>;
template<typename T>
using vvvc = vector<vvc<T>>;
template<typename T>
using vvvvc = vector<vvvc<T>>;

// priority_queue
template<typename T>
using pq = priority_queue<T>;
template<typename T>
using pqg = priority_queue<T, vc<T>, greater<T>>;

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(int i = a; i < (int)(b); i++)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define MIN(vec) *min_element(vec)
#define MAX(vec) *max_element(vec)
#define next_perm(vec) next_permutation((vec).begin(), (vec).end())
#define UNIQUE(vec) vec.erase(unique(vec.begin(), vec.end()), vec.end())
#define el "\n"
#define Yes cout << "Yes" << el
#define No cout << "No" << el
#define YES cout << "YES" << el
#define NO cout << "NO" << el
#define EPS 1e-8
#define Equal(a, b) (fabs((a)-(b)) < EPS) 
#define dbg(x) cerr << #x << "=" << x << el 

// 定数
const string abc = "abcdefghijklmnopqrstuvwxyz";
const string ABC = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};
constexpr int DX8[] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr int DY8[] = {0, 1, 0, -1, 1, -1, 1, -1};

template<typename T1, typename T2>
ostream &operator<< (ostream &os, pair<T1, T2> p) {
    os << "{" << p.first << "," << p.second << "}";
    return os;
}
template<typename T>
ostream &operator<< (ostream &os, vc<T> &vec) {
    int sz = vec.size();
    rep(i, sz){
        os << vec[i] << (i==sz-1?"":" ");
    }
    return os;
}

template<typename T1, typename T2>
istream &operator>> (istream &is, pair<T1, T2> &p) {
    is >> p.first >> p.second;
    return is;
}
template<typename T>
istream &operator>> (istream &is, vc<T> &vec) {
    int sz = vec.size();
    rep(i, sz) { is >> vec[i]; }
    return is;
}
/// @brief aとｂの最大値をaに格納。更新があったかbool値を返す
/// @tparam T1 
/// @tparam T2 
/// @param a 
/// @param b 
/// @return bool
template<typename T1, typename T2>
inline bool chmax(T1 &a, T2 b){
    bool ret = a<b;
    if(ret) a = b;
    return ret;
}

/// @brief aとｂの最小値をaに格納。更新があったかbool値を返す
/// @tparam T1 
/// @tparam T2 
/// @param a 
/// @param b 
/// @return bool
template<typename T1, typename T2>
inline bool chmin(T1 &a, T2 b){
    bool ret = a>b;
    if(ret) {a = b;}
    return ret;
}

inline void YesNo(bool flag){
    if(flag) {Yes;}
    else {No;}
    return;
}

inline void YESNO(bool flag){
    if(flag) {YES;}
    else {NO;}
    return;
}

inline bool outof(ll x, ll xlim){
    return (x<0 || x>=xlim);
}

template<typename T>
inline T sqnorm(T x, T y){
    return x*x+y*y;
}

/// @brief char->int
/// @param c 
/// @return int
inline int ctoi(char c){
    return c-'0';
}

/// @brief xを素因数分解
/// @param x 
/// @return vector<Pli>, 素因数の昇順に {p, cnt}
vector<Pli> prime_fact(ll x){
    vector<Pli> ret;
    for(ll i=2; i*i<=x; i++){
        if(x%i == 0){
            ret.emplace_back(i, 0);
            while(x%i == 0){
                ret.back().second++;
                x /= i;
            }
        }
    }
    if(x != 1) ret.emplace_back(x, 1);
    return ret;
}

/// @brief xの約数列挙
/// @param x 
/// @return vll, 約数の昇順
vll divisor_enum(ll x){
    vector<ll> ret;
    for(ll i=1; i*i<=x; i++){
        if(x%i == 0){
            ret.push_back(x/i);
            ret.push_back(i);
        }
    }
    sort(all(ret));
    UNIQUE(ret);
    return ret;
}

/// @brief 繰り返し二乗法。
/// @tparam T 
/// @param x 
/// @param k 
/// @param op 
/// @param e 
/// @return 
template<typename T>
T pow_t(T x, ll k, T (*op)(T, T), T (*e)()){
    T ret = e();
    while(k){
        if(k&1) ret = op(ret, x);
        x = op(x, x);
        k >>= 1;
    }
    return ret;
}

ll powll(ll x, ll k){
    return pow_t<ll>(x, k, [](ll a, ll b) -> ll{return a*b;}, []() -> ll{return 1;});
}

inline int pop_cnt(ll x) { return __builtin_popcountll(x); }
inline int top_bit(ll x) { return (x==0?-1:63-__builtin_clzll(x));}

void main2();

int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    main2();
}

struct Point {
    double x, y, z;
    Point operator-(const Point &p) {
        return Point{x-p.x, y-p.y, z-p.z};
    }
};
struct Sphere {
    Point c;
    double r;
};

double sqnorm3D(Point p) {
    return p.x*p.x + p.y*p.y + p.z*p.z;
}
double dist(Point p1, Point p2) {
    return sqrt(sqnorm3D(p1 - p2));
}
double sphere_cap_vol(double h, double r) {
    return M_PI*h*h*(3*r - h)/3;
}
double sphere_vol(Sphere s) {
    return M_PI*s.r*s.r*s.r*4/3;
}


double sphere_intersection_vol(Sphere s1, Sphere s2) {
    if(s1.r < s2.r) swap(s1, s2);
    double d = dist(s1.c, s2.c);

    if(d+s2.r <= s1.r+EPS) {
        return sphere_vol(s2);
    }
    if(d-s2.r >= s1.r-EPS) {
        return 0;
    }
    double b = (s1.r*s1.r - s2.r*s2.r - d*d)/(2*d);
    double h1 = s1.r-(d+b), h2 = s2.r + b;
    return sphere_cap_vol(h1, s1.r) + sphere_cap_vol(h2, s2.r);
}

void solve() {
    Sphere s1, s2;
    cin >> s1.c.x >> s1.c.y >> s1.c.z >> s1.r;
    cin >> s2.c.x >> s2.c.y >> s2.c.z >> s2.r;

    cout << fixed << setprecision(16) << sphere_intersection_vol(s1, s2) << el;
}

void main2(){
    int t;
    cin >> t;
    while(t--) {
        solve();
    }
}