#1040222 (D) No.3031 曲面の向き付け

• 問題: No.3031 曲面の向き付け
• ユーザー: ジュ・ビオレ・グレイス
• 提出日時: 2025-02-01 16:54:45
• 言語: D (dmd 2.109.1)
• 結果: AC
• 実行時間: 335 ms / 2,000 ms
• コード長: 3,579 bytes
• コンパイル時間: 963 ms
• コンパイル使用メモリ: 94,768 KB
• 実行使用メモリ: 61,740 KB
• 最終ジャッジ日時: 2025-02-01 22:01:52
• 合計ジャッジ時間: 7,439 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 29

ソースコード

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import std.algorithm, std.array, std.conv, std.stdio, std.typecons;
class Triangle {
    uint A, B, C;
    Triangle nAB, nBC, nAC;     // the triangles that share the edges
    int orientation;
    this (uint a, uint b, uint c) {
        A = a, B = b, C = c;
        assert(A < B && B < C);
    }
    
    // false if already set
    void set_neighborhood(Triangle n, uint P, uint Q) {
        if      (tuple(P, Q) == tuple(A, B)) {
            nAB = n;
        }
        else if (tuple(P, Q) == tuple(B, C)) {
            nBC = n;
        }
        else if (tuple(P, Q) == tuple(A, C)) {
            nAC = n;
        }
        else assert(0);
    }
    
    // X is A, B or C
    // 1: A->B->C, -1: A->C->B
    uint perm(uint X, int o = 0) {
        if (o == 0) o = this.orientation;
        if (o == 1) {
            if      (X == A) return B;
            else if (X == B) return C;
            else if (X == C) return A;
            else assert(0);
        }
        else if (o == -1) {
            if      (X == B) return A;
            else if (X == C) return B;
            else if (X == A) return C;
            else assert(0);
        }
        else assert(0);
    }
}
class Triangulation {
    Triangle[] triangles;
    bool unorientable = false;
    
    this(uint[][] tri_array) {
        // remove multiple appearance
        bool[Tuple!(uint, uint, uint)] triangle_set;
        foreach (tri3; tri_array) {
            triangle_set[tuple(tri3[0], tri3[1], tri3[2])] = true;
        }
        this.triangles = triangle_set.keys.map!(t => new Triangle(t[0], t[1], t[2])).array;
        
        // set neighborhoods
        Triangle[Tuple!(uint, uint)] edges;
        uint[Tuple!(uint, uint)] edge_appear_times;
        foreach (triangle; triangles) {
            foreach (edge; [tuple(triangle.A, triangle.B), tuple(triangle.B, triangle.C), tuple(triangle.A, triangle.C)]) {
                if (auto neiborhood = edge in edges) {
                    // shared by three triangles
                    if (edge_appear_times[edge] >= 2) {
                        unorientable = true;
                        return;
                    }
                    // set neighborhoods
                    edge_appear_times[edge]++;
                    triangle.set_neighborhood(*neiborhood, edge[0], edge[1]);
                    neiborhood.set_neighborhood(triangle, edge[0], edge[1]);
                }
                else {
                    // set neighborhoods
                    edges[edge] = triangle;
                    edge_appear_times[edge] = 1;
                }
            }
        }
    }
    
    // DFS
    void give_orientation(Triangle triangle, uint P, uint Q) {
        // already set
        if (!triangle || triangle.orientation != 0) return;
        
        triangle.orientation = triangle.perm(P, 1) == Q ? 1 : -1;
        
        // recursively
        if (triangle.perm(triangle.A) == triangle.B)
            give_orientation(triangle.nAB, triangle.B, triangle.A);
        else
            give_orientation(triangle.nAB, triangle.A, triangle.B);
        if (triangle.perm(triangle.B) == triangle.C)
            give_orientation(triangle.nBC, triangle.C, triangle.B);
        else
            give_orientation(triangle.nBC, triangle.B, triangle.C);
        if (triangle.perm(triangle.A) == triangle.C)
            give_orientation(triangle.nAC, triangle.C, triangle.A);
        else
            give_orientation(triangle.nAC, triangle.A, triangle.C);
    }
    
    bool is_orientable() {
        if (unorientable) return false;
        foreach (triangle; triangles) {
            give_orientation(triangle, triangle.A, triangle.B);
        }
        // check
        foreach (triangle; triangles) {
            with (triangle)
            // A -> B -> C -> A
            if (orientation == 1) {
                if ((nAB && nAB.perm(B) != A) || (nBC && nBC.perm(C) != B) || (nAC && nAC.perm(A) != C)) return false;
            }
            // A -> C -> B -> A
            else if (orientation == -1) {
                if ((nAB && nAB.perm(A) != B) || (nBC && nBC.perm(B) != C) || (nAC && nAC.perm(C) != A)) return false;
            }
            else assert (0);
        }
        return true;
    }
}
void main() {
    auto M = readln[0 .. $-1].to!uint;
    uint[][] tris;
    foreach (m; 0 .. M)
        tris ~= readln.split.to!(uint[]);
    auto trig = new Triangulation(tris);
    writeln(trig.is_orientable ? "YES" : "NO");
}
 
 
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