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