Submission #1220291

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Source Code Expand

/+ dub.sdl:
    name "A"
    dependency "dcomp" version=">=0.6.0"
+/

import std.stdio, std.algorithm, std.range, std.conv;
import std.typecons, std.math;
// import dcomp.foundation, dcomp.scanner;
// import dcomp.datastructure.unionfind;

int n;
double[2][] p;
double[] a;

double[] costs;

double calc(int f) {
    alias Q = Tuple!(double, int, int);
    Q[] edges;
    foreach (i; 0..n) {
        foreach (j; i+1..n) {
            if (!(f & (1<<i))) continue;
            if (!(f & (1<<j))) continue;
            double u = 0;
            u += (p[i][0]-p[j][0])*(p[i][0]-p[j][0]);
            u += (p[i][1]-p[j][1])*(p[i][1]-p[j][1]);
            edges ~= Q(sqrt(u), i, j);
        }
    }
    edges.sort!"a[0]<b[0]";
    auto uf = UnionFind(n);
    double ans = 0;
    foreach (e; edges) {
        if (uf.same(e[1], e[2])) continue;
        ans += e[0];
        uf.merge(e[1], e[2]);
    }
    double sm = 0;
    int co = 0;
    foreach (i; 0..n) {
        if (f & (1<<i)) {
            co++;
            sm += a[i];
        }
    }
    return max(0.0, (sm-ans))/co;
}
int main() {
    auto sc = new Scanner(stdin);
    sc.read(n);
    p = new double[2][n];
    a = new double[n];
    foreach (i; 0..n) {
        sc.read(p[i][0], p[i][1], a[i]);
    }
    costs = new double[1<<n];
    iota(1, 1<<n).each!(i => costs[i] = calc(i));
//    writeln(costs);

    auto dp = new double[1<<n];
    foreach (i; 1..(1<<n)) {
        dp[i] = costs[i];
        for (auto j = 0; j < i; j = ((j|~i)+1)&i) {
            if (j == 0) continue;
            dp[i] = max(dp[i], min(dp[j], costs[i^j]));
        }
    }
    writefln("%.20f", dp[(1<<n)-1]);
    return 0;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/foundation.d */
// module dcomp.foundation;
//fold(for old compiler)
static if (__VERSION__ <= 2070) {
    template fold(fun...) if (fun.length >= 1) {
        auto fold(R, S...)(R r, S seed) {
            import std.algorithm : reduce;
            static if (S.length < 2) {
                return reduce!fun(seed, r);
            } else {
                import std.typecons : tuple;
                return reduce!fun(tuple(seed), r);
            }
        }
    }
    unittest {
        import std.stdio;
        auto l = [1, 2, 3, 4, 5];
        assert(l.fold!"a+b"(10) == 25);
    }
}
version (X86) static if (__VERSION__ < 2071) {
    int bsf(ulong v) {
        foreach (i; 0..64) {
            if (v & (1UL << i)) return i;
        }
        return -1;
    }
    int bsr(ulong v) {
        foreach_reverse (i; 0..64) {
            if (v & (1UL << i)) return i;
        }
        return -1;   
    }
    int popcnt(ulong v) {
        int c = 0;
        foreach (i; 0..64) {
            if (v & (1UL << i)) c++;
        }
        return c;
    }
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/scanner.d */
// module dcomp.scanner;

class Scanner {
    import std.stdio : File;
    import std.conv : to;
    import std.range : front, popFront, array, ElementType;
    import std.array : split;
    import std.traits : isSomeChar, isStaticArray, isArray; 
    import std.algorithm : map;
    File f;
    this(File f) {
        this.f = f;
    }
    char[512] lineBuf;
    char[] line;
    private bool succ() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (true) {
            while (!line.empty && line.front.isWhite) {
                line.popFront;
            }
            if (!line.empty) break;
            if (f.eof) return false;
            line = lineBuf[];
            f.readln(line);
        }
        return true;
    }

    private bool readSingle(T)(ref T x) {
        import std.algorithm : findSplitBefore;
        import std.string : strip;
        import std.conv : parse;
        if (!succ()) return false;
        static if (isArray!T) {
            alias E = ElementType!T;
            static if (isSomeChar!E) {
                //string or char[10] etc
                //todo optimize
                auto r = line.findSplitBefore(" ");
                x = r[0].strip.dup;
                line = r[1];
            } else {
                auto buf = line.split.map!(to!E).array;
                static if (isStaticArray!T) {
                    //static
                    assert(buf.length == T.length);
                }
                x = buf;
                line.length = 0;
            }
        } else {
            x = line.parse!T;
        }
        return true;
    }
    int read(T, Args...)(ref T x, auto ref Args args) {
        if (!readSingle(x)) return 0;
        static if (args.length == 0) {
            return 1;
        } else {
            return 1 + read(args);
        }
    }
}



unittest {
    import std.path : buildPath;
    import std.file : tempDir;
    import std.algorithm : equal;
    import std.stdio : File;
    string fileName = buildPath(tempDir, "kyuridenanmaida.txt");
    auto fout = File(fileName, "w");
    fout.writeln("1 2 3");
    fout.writeln("ab cde");
    fout.writeln("1.0 1.0 2.0");
    fout.close;
    Scanner sc = new Scanner(File(fileName, "r"));
    int a;
    int[2] b;
    char[2] c;
    string d;
    double e;
    double[] f;
    sc.read(a, b, c, d, e, f);
    assert(a == 1);
    assert(equal(b[], [2, 3]));
    assert(equal(c[], "ab"));
    assert(equal(d, "cde"));
    assert(e == 1.0);
    assert(equal(f, [1.0, 2.0]));
}

unittest {
    import std.path : buildPath;
    import std.file : tempDir;
    import std.algorithm : equal;
    import std.stdio : File, writeln;
    import std.datetime;
    string fileName = buildPath(tempDir, "kyuridenanmaida.txt");
    auto fout = File(fileName, "w");
    foreach (i; 0..1_000_000) {
        fout.writeln(3*i, " ", 3*i+1, " ", 3*i+2);
    }
    fout.close;
    writeln("Scanner Speed Test(3*1,000,000 int)");
    StopWatch sw;
    sw.start;
    Scanner sc = new Scanner(File(fileName, "r"));
    foreach (i; 0..500_000) {
        int a, b, c;
        sc.read(a, b, c);
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    foreach (i; 500_000..700_000) {
        int[3] d;
        sc.read(d);
        int a = d[0], b = d[1], c = d[2];
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    foreach (i; 700_000..1_000_000) {
        int[] d;
        sc.read(d);
        assert(d.length == 3);
        int a = d[0], b = d[1], c = d[2];
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    writeln(sw.peek.msecs, "ms");
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/datastructure/unionfind.d */
// module dcomp.datastructure.unionfind;

struct UnionFind {
    import std.algorithm : map, swap, each;
    import std.range : iota, array;
    int[] id; // group id
    int[][] groups; // group list
    int count; // group count
    this(int n) {
        id = iota(n).array;
        groups = iota(n).map!(a => [a]).array;
        count = n;
    }
    void merge(int a, int b) {
        if (same(a, b)) return;
        count--;
        int x = id[a], y = id[b];
        if (groups[x].length < groups[y].length) swap(x, y);
        groups[y].each!(a => id[a] = x);
        groups[x] ~= groups[y];
        groups[y] = [];
    }
    int[] group(int i) {
        return groups[id[i]];
    }
    bool same(int a, int b) {
        return id[a] == id[b];
    }
}

unittest {
    import std.algorithm : equal, sort;
    auto uf = UnionFind(5);
    assert(!uf.same(1, 3));
    assert(uf.same(0, 0));

    uf.merge(3, 2);
    uf.merge(1, 1);
    uf.merge(4, 2);
    uf.merge(4, 3);

    assert(uf.count == 3);
    assert(uf.id[2] == uf.id[3]);
    assert(uf.id[2] == uf.id[4]);
    assert(equal(uf.group(0), [0]));
    assert(equal(uf.group(1), [1]));
    assert(equal(sort(uf.group(2)), [2, 3, 4]));
}

unittest {
    import std.datetime, std.stdio, std.range;
    // speed check
    writeln("UnionFind Speed Test");
    StopWatch sw;
    sw.start;
    UnionFind uf;
    // line
    uf = UnionFind(1_000_000);
    foreach (i; 1..1_000_000) {
        uf.merge(i-1, i);
    }
    // line(reverse)
    uf = UnionFind(1_000_000);
    foreach_reverse (i; 1..1_000_000) {
        uf.merge(i-1, i);
    }
    // binary tree
    uf = UnionFind(1_000_000);
    foreach (lg; 1..20) {
        int len = 1<<lg;
        foreach (i; iota(0, 1_000_000-len/2, len)) {
            uf.merge(i, i+len/2);
        }
    }
    sw.stop;
    writeln(sw.peek.msecs, "ms");
}

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