Submission #1135950

---

Source Code Expand

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

import std.stdio, std.range, std.conv, std.algorithm;
import std.math;
// import dcomp.foundation;
// import dcomp.scanner;
// import dcomp.array;
// import dcomp.algorithm;

// import dcomp.twosat;
import core.bitop : bsr;

immutable INF = 10^^9 + 10^^7;

int n;
int[] pos;

//md より大きくは出来ない
bool solve(int md) {
    int[2][] v;
    foreach (int i, d; pos) {
        v ~= [d, i];
    }
    v = v.sort!((l, r) => cmp(l[], r[]) == -1).array;
    int m = v.length.to!int;
    int lg = m.bsr;
    if ((2^^lg) < m) lg++;
    m = 1<<lg;

    int getI(int i, int x) {
        return binSearch!(idx => cmp(v[idx][], [x, i].fixed[]) != -1)(-1, v.length.to!int);
    }

    auto sat = TwoSat(2*n + 2*m);
    foreach (i; 0..n) {
        // exactly 1 true
        sat.addCond(2*i, true, 2*i+1, true);
        sat.addCond(2*i, false, 2*i+1, false);
    }
    //make segtree
    foreach (i; 1..m) {
        sat.addCond(2*n+2*i, false, 2*n+i, true);
        sat.addCond(2*n+2*i+1, false, 2*n+i, true);
    }

    void query(int a, int b, int i, int l = 0, int r = m, int k = 1) {
        if (b <= l || r <= a) return;
        if (a <= l && r <= b) {
            sat.addCond(i, false, 2*n+k, false);
            return;
        }
        int md = (l+r)/2;
        query(a, b, i, l, md, 2*k);
        query(a, b, i, md, r, 2*k+1);
    }
    foreach (int i, x; pos) {
        int idx = getI(i, x);
        query(getI(-1, x-md), idx, i);
        query(idx+1, getI(INF, x+md), i);
        sat.addCond(i, false, 2*n + m + idx, true);
    }
    return sat.exec() == false;
}

int main() {
    auto sc = new Scanner(stdin);
    sc.read(n);
    pos = new int[2*n];
    pos.each!((ref x) => sc.read(x));
    writeln(binSearch!(md => solve(md))(-1, INF));
    return 0;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/twosat.d */
// module dcomp.twosat;

// import dcomp.graph.scc;
// import dcomp.array;

struct TwoSat {
    bool[] res;

    struct Edge {int to;}
    import std.array;
//    Edge[][] g;
    FastAppender!(Edge[])[] g;

    // add ((a == aExp) || (b == bExp))
    void addCond(int a, bool aExp, int b, bool bExp) {
        void addEdge(int l, int r) {
            g[l] ~= Edge(r);
        }
        addEdge(2*a+(aExp?0:1), 2*b+(bExp?1:0));
        addEdge(2*b+(bExp?0:1), 2*a+(aExp?1:0));
    }
    bool exec() {
        import std.algorithm : map;
        import std.conv : to;
        int n = res.length.to!int;
        auto sccInfo = scc(g.map!(v => v.data).array);
        for (int i = 0; i < n; i++) {
            if (sccInfo.id[2*i] == sccInfo.id[2*i+1]) return false;
            res[i] = sccInfo.id[2*i] < sccInfo.id[2*i+1];
        }
        return true;
    }
    this(int n) {
        res = new bool[n];
        g = new FastAppender!(Edge[])[](2*n);
    }
}

unittest {
    import std.algorithm, std.conv, std.stdio, std.range;
    import std.random;
    import std.typecons;
    import std.datetime;

    struct E {int to;}

    writeln("TwoSat Random10000");
    void f() {
        int n = uniform(1, 50);
        int m = uniform(1, 100);
        auto ans = new bool[n];
        auto sat = TwoSat(n);
        ans.each!((ref x) => x = uniform(0, 2) == 1);
        struct N {int i; bool expect;}
        N[2][] conds;
        foreach (i; 0..m) {
            int x = uniform(0, n);
            int y = uniform(0, n);
            while (true) {
                bool f = uniform(0, 2) == 1;
                bool g = uniform(0, 2) == 1;
                if (ans[x] != f && ans[y] != g) continue;
                sat.addCond(x, f, y, g);
                conds ~= [N(x, f), N(y, g)];
                break;
            }
        }
        assert(sat.exec());
        auto res = sat.res;
        foreach (cond; conds) {
            int x = cond[0].i;
            bool f = cond[0].expect;
            int y = cond[1].i;
            bool g = cond[1].expect;
            assert(res[x] == f || res[y] == g);
        }
    }
    auto ti = benchmark!(f)(10000);
    writeln(ti[0].msecs, "ms");
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/graph/scc.d */
// module dcomp.graph.scc;

struct SCC {
    int[] id; // vertex id -> scc id
    int[][] groups; // scc id -> scc vertexs
    int count; // scc count
    this(int n) {
        id = new int[n];
    }
}

// import dcomp.array;

SCC scc(T)(T g) {
    import std.array : appender;
    import std.range;
    import std.algorithm : each, map;
    import std.conv : to;
    int n = g.length.to!int;
    //make reverse graph
    struct Edge {int to;}
    FastAppender!(Edge[])[] rg_buf = new FastAppender!(Edge[])[](n);
    g.each!((i, v) => v.each!(e => rg_buf[e.to] ~= Edge(i.to!int)));
    auto rg = rg_buf.map!(v => v.data).array;

    auto sccInfo = SCC(n);
    with (sccInfo) {
        auto used = new bool[n];

        //make backorder list
        auto vs = appender!(int[])();
        void dfs(int v) {
            used[v] = true;
            foreach (e; g[v]) {
                if (used[e.to]) continue;
                dfs(e.to);
            }
            vs ~= v;
        }
        foreach (i; 0..n) {
            if (used[i]) continue;
            dfs(i);
        }

        used[] = false;        
        count = 0;
        auto buf = appender!(int[])();
        void rdfs(int v) {
            used[v] = true;
            id[v] = count;
            buf ~= v;
            foreach (e; rg[v]) {
                if (used[e.to]) continue;
                rdfs(e.to);
            }
        }
        foreach_reverse (i; vs.data) {
            if (used[i]) continue;
            rdfs(i);
            groups ~= buf.data().dup;
            buf.clear();
            count++;
        }
    }
    return sccInfo;
}

unittest {
    import std.algorithm, std.conv, std.stdio, std.range;
    import std.random;
    import std.typecons;
    import std.datetime;

    struct E {int to;}

    writeln("SCC Random1000");
    void f() {
        int n = uniform(1, 50);
        int p = uniform(1, 50);
        E[][] g = new E[][n];
        bool[][] naive = new bool[][](n, n);
        foreach (i; 0..n) {
            foreach (j; 0..n) {
                if (i == j) continue;
                if (uniform(0, 100) < p) {
                    g[i] ~= E(j);
                    naive[i][j] = true;
                }
            }
        }

        auto sccInfo = scc(g);

        foreach (k; 0..n) {
            foreach (i; 0..n) {
                foreach (j; 0..n) {
                    naive[i][j] |= naive[i][k] && naive[k][j];
                }
            }
        }

        foreach (i; 0..n) {
            foreach (j; i+1..n) {
                bool same = sccInfo.id[i] == sccInfo.id[j];
                if (same) {
                    assert(naive[i][j] && naive[j][i]);
                } else {
                    assert(!naive[i][j] || !naive[j][i]);                    
                    if (sccInfo.id[i] < sccInfo.id[j]) {
                        assert(!naive[j][i]);
                    } else {
                        assert(!naive[i][j]);
                    }
                }
            }
        }
    }
    auto ti = benchmark!(f)(1000);
    writeln(ti[0].msecs, "ms");
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/algorithm.d */
// module dcomp.algorithm;

import std.range.primitives;
import std.traits : isFloatingPoint, isIntegral;

//[0,0,0,...,1,1,1]で、初めて1となる場所を探す。pred(l) == 0, pred(r) == 1と仮定
T binSearch(alias pred, T)(T l, T r) if (isIntegral!T) {
    while (r-l > 1) {
        T md = (l+r)/2;
        if (!pred(md)) l = md;
        else r = md;
    }
    return r;
}

T binSearch(alias pred, T)(T l, T r, int cnt = 60) if (isFloatingPoint!T) {
    foreach (i; 0..cnt) {
        T md = (l+r)/2;
        if (!pred(md)) l = md;
        else r = md;
    }
    return r;
}

Rotator!Range rotator(Range)(Range r) {
    return Rotator!Range(r);
}

struct Rotator(Range)
if (isForwardRange!Range && hasLength!Range) {
    size_t cnt;
    Range start, now;
    this(Range r) {
        cnt = 0;
        start = r.save;
        now = r.save;
    }
    this(this) {
        start = start.save;
        now = now.save;
    }
    @property bool empty() {
        return now.empty;
    }
    @property auto front() {
        assert(!now.empty);
        import std.range : take, chain;
        return chain(now, start.take(cnt));
    }
    @property Rotator!Range save() {
        return this;
    }
    void popFront() {
        cnt++;
        now.popFront;
    }
}


E minimum(alias pred = "a < b", Range, E = ElementType!Range)(Range range, E seed)
if (isInputRange!Range && !isInfinite!Range) {
    import std.algorithm, std.functional;
    return reduce!((a, b) => binaryFun!pred(a, b) ? a : b)(seed, range);
}

ElementType!Range minimum(alias pred = "a < b", Range)(Range range) {
    assert(!range.empty, "range must not empty");
    auto e = range.front; range.popFront;
    return minimum!pred(range, e);
}

E maximum(alias pred = "a < b", Range, E = ElementType!Range)(Range range, E seed)
if (isInputRange!Range && !isInfinite!Range) {
    import std.algorithm, std.functional;
    return reduce!((a, b) => binaryFun!pred(a, b) ? b : a)(seed, range);
}

ElementType!Range maximum(alias pred = "a < b", Range)(Range range) {
    assert(!range.empty, "range must not empty");
    auto e = range.front; range.popFront;
    return maximum!pred(range, e);
}

unittest {
    assert(minimum([2, 1, 3]) == 1);
    assert(minimum!"a > b"([2, 1, 3]) == 3);
    assert(minimum([2, 1, 3], -1) == -1);
    assert(minimum!"a > b"([2, 1, 3], 100) == 100);

    assert(maximum([2, 1, 3]) == 3);
    assert(maximum!"a > b"([2, 1, 3]) == 1);
    assert(maximum([2, 1, 3], 100) == 100);
    assert(maximum!"a > b"([2, 1, 3], -1) == -1);
}

bool[ElementType!Range] toMap(Range)(Range r) {
    import std.algorithm : each;
    bool[ElementType!Range] res;
    r.each!(a => res[a] = true);
    return res;
}
/* 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;
    }
    string[] buf;
    private bool succ() {
        while (!buf.length) {
            if (f.eof) return false;
            buf = f.readln.split;
        }
        return true;
    }
    private bool readSingle(T)(ref T x) {
        if (!succ()) return false;
        static if (isArray!T) {
            alias E = ElementType!T;
            static if (isSomeChar!E) {
                //string or char[10] etc
                x = buf.front;
                buf.popFront;
            } else {
                static if (isStaticArray!T) {
                    //static
                    assert(buf.length == T.length);
                }
                x = buf.map!(to!E).array;
                buf.length = 0;                
            }
        } else {
            x = buf.front.to!T;
            buf.popFront;            
        }
        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]));
}
/* 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);
    }
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/array.d */
// module dcomp.array;

T[N] fixed(T, int N)(T[N] a) {return a;}

//this is not reference type!(please attention to copy)
struct FastAppender(A) {
    import std.algorithm : max;
    import std.range.primitives : ElementEncodingType;
    import core.stdc.string : memcpy;

    private alias T = ElementEncodingType!A;
    private T* _data;
    private size_t len, cap;

    void reserve(size_t nlen) {
        import core.memory : GC;
        if (nlen <= cap) return;
        
        void* nx = GC.malloc(nlen * T.sizeof);            

        cap = nlen;
        if (len) memcpy(nx, _data, len * T.sizeof);
        _data = cast(T*)(nx);
    }
    void opOpAssign(string op : "~")(T item) {
        if (len == cap) {
            reserve(max(4, cap*2));
        }
        _data[len++] = item;
    }
    void clear() {
        len = 0;
    }    
    T[] data() {
        return (_data) ? _data[0..len] : null;
    }
}

unittest {
    import std.stdio, std.algorithm;
    auto u = FastAppender!(int[])();
    u ~= 4; u ~= 5;
    assert(equal(u.data, [4, 5]));
}

Submission Info

Judge Result