結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
 hiromi_ayase
|
| 提出日時 | 2020-07-18 19:30:09 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 452 ms / 2,000 ms |
| コード長 | 7,216 bytes |
| コンパイル時間 | 2,931 ms |
| コンパイル使用メモリ | 89,332 KB |
| 実行使用メモリ | 51,400 KB |
| 最終ジャッジ日時 | 2024-12-14 03:06:47 |
| 合計ジャッジ時間 | 10,214 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 38 |
ソースコード
import java.util.Arrays;import java.util.HashMap;import java.util.Map;public class Main {private static int mod = 998244353;private static long inv2 = invl(2, mod);private static int[][] fif;private static long[] p2;private static int[] from;private static int[] to;private static int n;private static int m;private static int k;private static void solve() {n = ni();m = ni();from = new int[m];to = new int[m];for (int i = 0; i < m; i++) {from[i] = ni() - 1;to[i] = ni() - 1;}fif = enumFIF(n * 2, mod);p2 = new long[n + 1];p2[0] = 1;for (int i = 1; i <= n; i++) {p2[i] = p2[i - 1] * 2 % mod;}k = m * 2;int[][][][] cnt = new int[k + 1][m + 1][2][2];for (int i = 0; i < 1 << m; i++) {int[] v = f(i);if (v == null)continue;cnt[v[0]][v[1]][v[2]][v[3]]++;}long ret = 0;for (int i = 0; i <= k; i++) {for (int j = 0; j <= m; j++) {for (int s = 0; s < 2; s++) {for (int t = 0; t < 2; t++) {if (cnt[i][j][s][t] == 0)continue;long now = g(i, j, t == 1) * cnt[i][j][s][t] % mod;long x = s == 0 ? 1 : -1;ret += mod + x * now;ret %= mod;}}}}System.out.println(ret);}private static long g(int v, int u, boolean loop) {if (loop) {return u == 1 ? 1 : 0;}long ret = 0;int nlast = n - v;for (int i = Math.max(0, 3 - v); i <= nlast; i++) {long now = CX(nlast, i, mod, fif);now = now * p2[u] % mod;now = now * fif[0][i + u - 1] % mod;now = now * inv2 % mod;ret += now;ret %= mod;}if (ret < 0) {throw new RuntimeException();}return ret;}private static int[] f(int s) {Map<Integer, Integer> map = new HashMap<>();int cnt = 0;int[] deg = new int[k];DisjointSet uf = new DisjointSet(k);boolean loop = false;for (int i = 0; i < m; i++) {if ((s >> i & 1) == 1) {int a = from[i];int b = to[i];if (!map.containsKey(a)) {map.put(a, cnt++);}if (!map.containsKey(b)) {map.put(b, cnt++);}a = map.get(a);b = map.get(b);if (deg[a] == 2 || deg[b] == 2 || loop && uf.equiv(a, b)) {return null;}if (!loop && uf.equiv(a, b)) {loop = true;}deg[a]++;deg[b]++;uf.union(a, b);}}int v = 0;for (int i = 0; i < cnt; i++) {if (uf.upper[i] < 0) {v++;}}return new int[] { cnt, v, Integer.bitCount(s) % 2, loop ? 1 : 0 };}private static long invl(long a, long mod) {long b = mod;long p = 1, q = 0;while (b > 0) {long c = a / b;long d;d = a;a = b;b = d % b;d = p;p = q;q = d - c * q;}return p < 0 ? p + mod : p;}public static class DisjointSet {public int[] upper; // minus:num_element(root) plus:root(normal)// public int[] w;public DisjointSet(int n) {upper = new int[n];Arrays.fill(upper, -1);}public DisjointSet(DisjointSet ds) {this.upper = Arrays.copyOf(ds.upper, ds.upper.length);}public int root(int x) {return upper[x] < 0 ? x : (upper[x] = root(upper[x]));}public boolean equiv(int x, int y) {return root(x) == root(y);}public boolean union(int x, int y) {x = root(x);y = root(y);if (x != y) {if (upper[y] < upper[x]) {int d = x;x = y;y = d;}upper[x] += upper[y];upper[y] = x;}return x == y;}}public static long CX(long n, long r, int p, int[][] fif) {if (n < 0 || r < 0 || r > n)return 0;int np = (int) (n % p), rp = (int) (r % p);if (np < rp)return 0;if (n == 0 && r == 0)return 1;int nrp = np - rp;if (nrp < 0)nrp += p;return (long) fif[0][np] * fif[1][rp] % p * fif[1][nrp] % p * CX(n / p, r / p, p, fif) % p;}public static int[][] enumFIF(int n, int mod) {int[] f = new int[n + 1];int[] invf = new int[n + 1];f[0] = 1;for (int i = 1; i <= n; i++) {f[i] = (int) ((long) f[i - 1] * i % mod);}long a = f[n];long b = mod;long p = 1, q = 0;while (b > 0) {long c = a / b;long d;d = a;a = b;b = d % b;d = p;p = q;q = d - c * q;}invf[n] = (int) (p < 0 ? p + mod : p);for (int i = n - 1; i >= 0; i--) {invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);}return new int[][] { f, invf };}public static void main(String[] args) {new Thread(null, new Runnable() {@Overridepublic void run() {long start = System.currentTimeMillis();String debug = args.length > 0 ? args[0] : null;if (debug != null) {try {is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));} catch (Exception e) {throw new RuntimeException(e);}}reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);solve();out.flush();tr((System.currentTimeMillis() - start) + "ms");}}, "", 64000000).start();}private static java.io.InputStream is = System.in;private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);private static java.util.StringTokenizer tokenizer = null;private static java.io.BufferedReader reader;public static String next() {while (tokenizer == null || !tokenizer.hasMoreTokens()) {try {tokenizer = new java.util.StringTokenizer(reader.readLine());} catch (Exception e) {throw new RuntimeException(e);}}return tokenizer.nextToken();}private static double nd() {return Double.parseDouble(next());}private static long nl() {return Long.parseLong(next());}private static int[] na(int n) {int[] a = new int[n];for (int i = 0; i < n; i++)a[i] = ni();return a;}private static char[] ns() {return next().toCharArray();}private static long[] nal(int n) {long[] a = new long[n];for (int i = 0; i < n; i++)a[i] = nl();return a;}private static int[][] ntable(int n, int m) {int[][] table = new int[n][m];for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {table[i][j] = ni();}}return table;}private static int[][] nlist(int n, int m) {int[][] table = new int[m][n];for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {table[j][i] = ni();}}return table;}private static int ni() {return Integer.parseInt(next());}private static void tr(Object... o) {if (is != System.in)System.out.println(java.util.Arrays.deepToString(o));}}