Problem:
ペンキの色

問題

情報オリンピックの宣伝のために,長方形のベニヤ板にペンキを塗り看板を制作したい.ベニヤ板には色を塗りたくないところにあらかじめ何枚かの長方形のマスキングテープが貼られている.そこでマスキングテープで区切られた領域ごとに別々の色を使いペンキを塗ることにした.例えば,図 5-1 の場合は 5 色のペンキを使う.

入力としてマスキングテープを貼る位置が与えられた時,使うペンキの色の数を求めるプログラムを作成せよ.ただし,ベニヤ板全体がマスキングテープで覆われることはなく,全てのマスキングテープの辺はベニヤ板のいずれかの辺に平行である.

入力

入力は複数のデータセットからなる．各データセットは以下の形式で与えられる．

1 行目にはベニヤ板の幅 w (1 ≤ w ≤ 1000000 となる整数) と高さ h (1 ≤ h ≤ 1000000 となる整数) がこの順に空白区切りで書かれている.

2 行目にはマスキングテープの数 n (1 ≤ n ≤ 1000 となる整数) が書かれている.
続く 3 行目以降の 2 + i 行目 (1 ≤ i ≤ n) には,i 番目に貼るマスキングテープの左下の座標 (x1 , y1 ) と,右上の座標 (x2 , y2 ) が x1 , y1 , x2 , y2 (0 ≤ x1 < x2 ≤ w, 0 ≤ y1 < y2 ≤ h となる整数) の順に空白区切りで書かれている.

ただし,ベニヤ板の左下の角の座標は (0, 0) で右上の角の座標は (w, h) である. 採点用データのうち, 配点の 30% 分は w ≤ 100, h ≤ 100, n ≤ 100 を満たす.

h, w がともに 0 のとき入力の終了を示す. データセットの数は 20 を超えない．

出力

データセットごとに使うペンキの色数を１行に出力する.

入出力例

次の例は図 5-1 の場合である.

入力例

15 6
10
1 4 5 6
2 1 4 5
1 0 5 1
6 1 7 5
7 5 9 6
7 0 9 2
9 1 10 5
11 0 14 1
12 1 13 5
11 5 14 6
0 0

出力例

5

上記問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。

Solution in JAVA (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

/**
 * @author baito
 */

public class Main
{
    static StringBuilder sb = new StringBuilder();
    static FastScanner sc = new FastScanner(System.in);
    static int INF = 12345678;
    static long LINF = 123456789123456789L;
    static long MINF = -123456789123456789L;
    static long MOD = 1000000007;
    static int[] y4 = {0, 1, 0, -1};
    static int[] x4 = {1, 0, -1, 0};
    static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
    static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
    static long[] F;//factorial
    static boolean[] isPrime;
    static int[] primes;
    static char[][] map;

    static int N, H, W;
    static int[] A;


    public static void main(String[] args)
    {
        while (true)
        {
            W = sc.nextInt();
            H = sc.nextInt();
            if ((H | W) == 0) break;
            N = sc.nextInt();
            int[] x1 = new int[N];
            int[] x2 = new int[N];
            int[] y1 = new int[N];
            int[] y2 = new int[N];
            for (int i = 0; i < N; i++)
            {
                x1[i] = sc.nextInt();
                y1[i] = sc.nextInt();
                x2[i] = sc.nextInt();
                y2[i] = sc.nextInt();
            }
            W = compress(x1, x2, W);
            H = compress(y1, y2, H);
            boolean[][] pa = new boolean[H][W];
            for (int i = 0; i < N; i++)
            {
                for (int h = y1[i]; h < y2[i]; h++)
                {
                    for (int w = x1[i]; w < x2[i]; w++)
                    {
                        pa[h][w] = true;
                    }
                }
            }
            print(pa);

            //深さ優先探索で塗りつぶす
            long ans = 0;
            for (int h = 0; h < H; h++)
            {
                for (int w = 0; w < W; w++)
                {
                    if (pa[h][w]) continue;
                    pa[h][w] = true;
                    ans++;
                    ArrayDeque<int[]> que = new ArrayDeque<>();
                    que.push(new int[]{w, h});
                    while (!que.isEmpty())
                    {
                        int[] xy = que.pop();
                        int x = xy[0];
                        int y = xy[1];
                        for (int i = 0; i < 4; i++)
                        {
                            int nx = x + x4[i];
                            int ny = y + y4[i];
                            if (nx >= 0 && ny >= 0 && nx < W && ny < H && !pa[ny][nx])
                            {
                                pa[ny][nx] = true;
                                que.push(new int[]{nx, ny});
                                print(pa);
                            }
                        }
                    }

                }
            }
            System.out.println(ans);
        }
    }

    public static void print(boolean[][] pa)
    {
        System.out.println("");
        for (int h = 0; h < H; h++)
        {
            for (int w = 0; w < W; w++)
            {
                if (pa[h][w]) System.out.print('#');
                else System.out.print(".");
            }
            System.out.println("");
        }
    }

    //座標を圧縮し、長さを返す
    public static int compress(int[] x1, int[] x2, int w)
    {
        int n = x1.length;
        TreeSet<Integer> set = new TreeSet<>();
        for (int i = 0; i < n; i++)
        {
            set.add(x1[i]);
            set.add(x2[i]);
        }
        int nw = set.size();
        Integer[] x = set.toArray(new Integer[nw]);
        for (int i = 0; i < n; i++)
        {
            x1[i] = Arrays.binarySearch(x, x1[i]);
            x2[i] = Arrays.binarySearch(x, x2[i]);
        }
        return nw - 1; // | | | | の区切りがある時、長さは3
    }

    public static long toLong(int[] ar)
    {
        long res = 0;
        for (int i : ar)
        {
            res *= 10;
            res += i;
        }
        return res;
    }

    public static int toInt(int[] ar)
    {
        int res = 0;
        for (int i : ar)
        {
            res *= 10;
            res += i;
        }
        return res;
    }

    //k個の次の組み合わせをビットで返す 大きさに上限はない 110110 -> 111001
    public static int nextCombSizeK(int comb, int k)
    {
        int x = comb & -comb; //最下位の1
        int y = comb + x; //連続した下の1を繰り上がらせる
        return ((comb & ~y) / x >> 1) | y;
    }

    public static int keta(long num)
    {
        int res = 0;
        while (num > 0)
        {
            num /= 10;
            res++;
        }
        return res;
    }

    public static long getHashKey(int a, int b)
    {
        return (long) a << 32 | b;
    }

    public static boolean isOutofIndex(int x, int y)
    {
        if (x < 0 || y < 0) return true;
        if (map[0].length <= x || map.length <= y) return true;
        return false;
    }

    public static void setPrimes()
    {
        int n = 100001;
        isPrime = new boolean[n];
        List<Integer> prs = new ArrayList<>();
        Arrays.fill(isPrime, true);
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i * i <= n; i++)
        {
            if (!isPrime[i]) continue;
            prs.add(i);
            for (int j = i * 2; j < n; j += i)
            {
                isPrime[j] = false;
            }
        }
        primes = new int[prs.size()];
        for (int i = 0; i < prs.size(); i++)
            primes[i] = prs.get(i);
    }

    public static void revSort(int[] a)
    {
        Arrays.sort(a);
        reverse(a);
    }

    public static void revSort(long[] a)
    {
        Arrays.sort(a);
        reverse(a);
    }

    public static int[][] copy(int[][] ar)
    {
        int[][] nr = new int[ar.length][ar[0].length];
        for (int i = 0; i < ar.length; i++)
            for (int j = 0; j < ar[0].length; j++)
                nr[i][j] = ar[i][j];
        return nr;
    }


    /**
     * <h1>指定した値以上の先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
     */
    public static int lowerBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        if (arr[high - 1] < value)
        {
            return -1;
        }
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] < value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }

    /**
     * <h1>指定した値より大きい先頭のインデクスを返す</h1>
     * <p>配列要素が０のときは、０が返る。</p>
     *
     * @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
     */
    public static int upperBound(final int[] arr, final int value)
    {
        int low = 0;
        int high = arr.length;
        int mid;
        if (arr[high - 1] <= value)
        {
            return -1;
        }
        while (low < high)
        {
            mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
            if (arr[mid] <= value)
            {
                low = mid + 1;
            }
            else
            {
                high = mid;
            }
        }
        return low;
    }


    //次の順列に書き換える、最大値ならfalseを返す
    public static boolean nextPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] < A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより大きい最小の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] > A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //次の順列に書き換える、最小値ならfalseを返す
    public static boolean prevPermutation(int A[])
    {
        int len = A.length;
        int pos = len - 2;
        for (; pos >= 0; pos--)
        {
            if (A[pos] > A[pos + 1]) break;
        }
        if (pos == -1) return false;

        //posより小さい最大の数を二分探索
        int ok = pos + 1;
        int ng = len;
        while (Math.abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (A[mid] < A[pos]) ok = mid;
            else ng = mid;

        }

        swap(A, pos, ok);
        reverse(A, pos + 1, len - 1);


        return true;
    }

    //↓nCrをmod計算するために必要。　***factorial(N)を呼ぶ必要がある***
    static long ncr(int n, int r)
    {
        if (n < r) return 0;
        else if (r == 0) return 1;

        factorial(n);
        return F[n] / (F[n - r] * F[r]);
    }

    static long ncr2(int a, int b)
    {
        if (b == 0) return 1;
        else if (a < b) return 0;
        long res = 1;
        for (int i = 0; i < b; i++)
        {
            res *= a - i;
            res /= i + 1;
        }
        return res;
    }

    static long ncrdp(int n, int r)
    {
        if (n < r) return 0;
        long[][] dp = new long[n + 1][r + 1];
        for (int ni = 0; ni < n + 1; ni++)
        {
            dp[ni][0] = dp[ni][ni] = 1;
            for (int ri = 1; ri < ni; ri++)
            {
                dp[ni][ri] = dp[ni - 1][ri - 1] + dp[ni - 1][ri];
            }
        }
        return dp[n][r];
    }

    static long modNcr(int n, int r)
    {
        if (n < r) return 0;
        long result = F[n];
        result = result * modInv(F[n - r]) % MOD;
        result = result * modInv(F[r]) % MOD;
        return result;
    }

    public static long modSum(long... lar)
    {
        long res = 0;
        for (long l : lar)
            res = (res + l % MOD) % MOD;
        return res;
    }

    public static long modDiff(long a, long b)
    {
        long res = a - b;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modMul(long... lar)
    {
        long res = 1;
        for (long l : lar)
            res = (res * l) % MOD;
        if (res < 0) res += MOD;
        res %= MOD;
        return res;
    }

    public static long modDiv(long a, long b)
    {
        long x = a % MOD;
        long y = b % MOD;
        long res = (x * modInv(y)) % MOD;
        return res;
    }

    static long modInv(long n)
    {
        return modPow(n, MOD - 2);
    }

    static void factorial(int n)
    {
        F = new long[n + 1];
        F[0] = F[1] = 1;
//        for (int i = 2; i <= n; i++)
//        {
//            F[i] = (F[i - 1] * i) % MOD;
//        }
        //
        for (int i = 2; i <= 100000; i++)
        {
            F[i] = (F[i - 1] * i) % MOD;
        }
        for (int i = 100001; i <= n; i++)
        {
            F[i] = (F[i - 1] * i) % MOD;
        }
    }

    static long modPow(long x, long n)
    {
        long res = 1L;
        while (n > 0)
        {
            if ((n & 1) == 1)
            {
                res = res * x % MOD;
            }
            x = x * x % MOD;
            n >>= 1;
        }
        return res;
    }

    //↑nCrをmod計算するために必要

    static int gcd(int n, int r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static long gcd(long n, long r)
    {
        return r == 0 ? n : gcd(r, n % r);
    }

    static <T> void swap(T[] x, int i, int j)
    {
        T t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    static void swap(int[] x, int i, int j)
    {
        int t = x[i];
        x[i] = x[j];
        x[j] = t;
    }

    public static void reverse(int[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(long[] x)
    {
        int l = 0;
        int r = x.length - 1;
        while (l < r)
        {
            long temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    public static void reverse(int[] x, int s, int e)
    {
        int l = s;
        int r = e;
        while (l < r)
        {
            int temp = x[l];
            x[l] = x[r];
            x[r] = temp;
            l++;
            r--;
        }
    }

    static int length(int a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int length(long a)
    {
        int cou = 0;
        while (a != 0)
        {
            a /= 10;
            cou++;
        }
        return cou;
    }

    static int cou(boolean[] a)
    {
        int res = 0;
        for (boolean b : a)
        {
            if (b) res++;
        }
        return res;
    }

    static int cou(String s, char c)
    {
        int res = 0;
        for (char ci : s.toCharArray())
        {
            if (ci == c) res++;
        }
        return res;
    }

    static int countC2(char[][] a, char c)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == c) co++;
        return co;
    }

    static int countI(int[] a, int key)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            if (a[i] == key) co++;
        return co;
    }

    static int countI(int[][] a, int key)
    {
        int co = 0;
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                if (a[i][j] == key) co++;
        return co;
    }

    static void fill(int[][] a, int v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }


    static void fill(long[][] a, long v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                a[i][j] = v;
    }

    static void fill(int[][][] a, int v)
    {
        for (int i = 0; i < a.length; i++)
            for (int j = 0; j < a[0].length; j++)
                for (int k = 0; k < a[0][0].length; k++)
                    a[i][j][k] = v;
    }

    static int max(int... a)
    {
        int res = Integer.MIN_VALUE;
        for (int i : a)
        {
            res = Math.max(res, i);
        }
        return res;
    }


    static int max(int[][] ar)
    {
        int res = Integer.MIN_VALUE;
        for (int i[] : ar)
            res = Math.max(res, max(i));
        return res;
    }

    static int min(int... a)
    {
        int res = Integer.MAX_VALUE;
        for (int i : a)
        {
            res = Math.min(res, i);
        }
        return res;
    }


    static int min(int[][] ar)
    {
        int res = Integer.MAX_VALUE;
        for (int i[] : ar)
            res = Math.min(res, min(i));
        return res;
    }

    static int sum(int[] a)
    {
        int cou = 0;
        for (int i : a)
            cou += i;
        return cou;
    }

    static int abs(int a)
    {
        return Math.abs(a);
    }

    static class FastScanner
    {

        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public FastScanner(InputStream in)
        {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        /*public String nextChar(){
            return (char)next()[0];
        }*/
        public String nextLine()
        {
            if (tokenizer == null || !tokenizer.hasMoreTokens())
            {
                try
                {
                    return reader.readLine();
                } catch (IOException e)
                {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong()
        {
            return Long.parseLong(next());
        }

        public int nextInt()
        {
            return Integer.parseInt(next());
        }

        public double nextDouble()
        {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public int[] nextIntArrayDec(int n)
        {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt() - 1;
            }
            return a;
        }

        public int[][] nextIntArray2(int h, int w)
        {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextInt();
                }
            }
            return a;
        }

        public int[][] nextIntArray2Dec(int h, int w)
        {
            int[][] a = new int[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextInt() - 1;
                }
            }
            return a;
        }

        //複数の配列を受け取る
        public void nextIntArrays2ar(int[] a, int[] b)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
            }
        }

        public void nextIntArrays2arDec(int[] a, int[] b)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3ar(int[] a, int[] b, int[] c)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt();
                b[i] = sc.nextInt();
                c[i] = sc.nextInt();
            }
        }

        //複数の配列を受け取る
        public void nextIntArrays3arDecLeft2(int[] a, int[] b, int[] c)
        {
            for (int i = 0; i < a.length; i++)
            {
                a[i] = sc.nextInt() - 1;
                b[i] = sc.nextInt() - 1;
                c[i] = sc.nextInt();
            }
        }

        public Integer[] nextIntegerArray(int n)
        {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public char[] nextCharArray(int n)
        {
            char[] a = next().toCharArray();

            return a;
        }

        public char[][] nextCharArray2(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = next().toCharArray();
            }
            return a;
        }

        //スペースが入っている場合
        public char[][] nextCharArray2s(int h, int w)
        {
            char[][] a = new char[h][w];
            for (int i = 0; i < h; i++)
            {
                a[i] = nextLine().replace(" ", "").toCharArray();
            }
            return a;
        }

        public char[][] nextWrapCharArray2(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + next() + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        //スペースが入ってる時用
        public char[][] nextWrapCharArray2s(int h, int w, char c)
        {
            char[][] a = new char[h + 2][w + 2];
            //char c = '*';
            int i;
            for (i = 0; i < w + 2; i++)
                a[0][i] = c;
            for (i = 1; i < h + 1; i++)
            {
                a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
            }
            for (i = 0; i < w + 2; i++)
                a[h + 1][i] = c;
            return a;
        }

        public long[] nextLongArray(int n)
        {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }

        public long[][] nextLongArray2(int h, int w)
        {
            long[][] a = new long[h][w];
            for (int hi = 0; hi < h; hi++)
            {
                for (int wi = 0; wi < w; wi++)
                {
                    a[hi][wi] = nextLong();
                }
            }
            return a;
        }
    }
}