AtCoder Regular Contest 035 C: アットコーダー王国の交通事情

問題

C: アットコーダー王国の交通事情 - AtCoder Regular Contest 035 | AtCoder

解法

まず最初のグラフでワーシャルフロイトして2点間の最短距離を出しておく。新しい道路が建設されるたびに最短距離マップを更新する。この際に、以下のようにするとで更新できる。

for (int i = 0; i < N; i++) {
	for (int j = 0; j < N; j++) {
	map[i][j] = Math.min(map[i][j], map[i][x] + map[y][j] + cost);
	map[i][j] = Math.min(map[i][j], map[i][y] + map[x][j] + cost);
	}
}

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;

public class Main {
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) {
		new Main().solve();
	}

	public void solve() {
		int N = in.nextInt();
		int M = in.nextInt();

		int[][] map = new int[N][N];
		int MAX = 100000000;

		for (int i = 0; i < M; i++) {
			int a = in.nextInt() - 1;
			int b = in.nextInt() - 1;
			int c = in.nextInt();
			map[a][b] = c;
			map[b][a] = c;
		}

		// ワーシャルフロイト
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < N; j++) {
				if (map[i][j] == 0 && i != j) {
					map[i][j] = MAX;
				}
			}
		}
		for (int k = 0; k < N; k++) {
			for (int i = 0; i < N; i++) {
				for (int j = 0; j < N; j++) {
					map[i][j] = Math.min(map[i][j], map[i][k] + map[k][j]);
				}
			}
		}
		// ワーシャルフロイト終わり

		long S = 0;
		for (int i = 0; i < N - 1; i++) {
			for (int j = i + 1; j < N; j++) {
				S += map[i][j];
			}
		}

		int K = in.nextInt();
		for (int k = 0; k < K; k++) {
			int x = in.nextInt() - 1;
			int y = in.nextInt() - 1;
			int cost = in.nextInt();
			if (map[x][y] <= cost) {
				out.println(S);
				continue;
			}

			map[x][y] = cost;
			map[y][x] = cost;

			for (int i = 0; i < N; i++) {
				for (int j = 0; j < N; j++) {
					map[i][j] = Math.min(map[i][j], map[i][x] + map[y][j] + cost);
					map[i][j] = Math.min(map[i][j], map[i][y] + map[x][j] + cost);
				}
			}

			S = 0;
			for (int i = 0; i < N; i++) {
				for (int j = i + 1; j < N; j++) {
					S += map[i][j];
				}
			}
			out.println(S);
		}
		out.close();
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			// stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

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

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

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

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}

MAXを適当に10000とかに設定していると通らないケースが3つだけあって、無駄に悩んでしまった。