結果
問題 | No.2531 Coloring Vertices on Namori |
ユーザー |
|
提出日時 | 2023-11-03 21:50:30 |
言語 | Java (openjdk 23) |
結果 |
AC
|
実行時間 | 491 ms / 2,000 ms |
コード長 | 15,992 bytes |
コンパイル時間 | 5,128 ms |
コンパイル使用メモリ | 94,324 KB |
実行使用メモリ | 58,660 KB |
最終ジャッジ日時 | 2024-09-25 20:00:06 |
合計ジャッジ時間 | 17,794 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 31 |
ソースコード
package contest231103;import java.io.*;import java.util.*;import java.util.function.IntUnaryOperator;import java.util.function.LongUnaryOperator;public class G {InputStream is;FastWriter out;String INPUT = "";public void solve(){int n = ni(), K = ni();int[] from = new int[n];int[] to = new int[n];for(int i = 0;i < n;i++){from[i] = ni()-1;to[i] = ni()-1;}int[][] g = packU(n, from, to);AnalyzeResult res = analyze(g);assert res.cycles.size() == 1;int L = res.cycles.get(0).length;long[] dp = new long[2];dp[0] = K;for(int i = 0;i < L-1;i++){long[] ndp = new long[2];ndp[0] = dp[1];ndp[1] = (dp[0] * (K-1) + dp[1] * (K-2)) % mod;// tr(ndp);dp = ndp;}out.println(dp[1] * pow(K-1, n-L, mod) % mod);}public static long pow(long a, long n, long mod) {// a %= mod;long ret = 1;int x = 63 - Long.numberOfLeadingZeros(n);for (; x >= 0; x--) {ret = ret * ret % mod;if (n << 63 - x < 0) ret = ret * a % mod;}return ret;}static final int mod = 998244353;public static class AnalyzeResult{public int[] par, next, ord, clus, dep, roots;public List<int[]> cycles;}public static AnalyzeResult analyze(int[][] g){AnalyzeResult ret = new AnalyzeResult();int n = g.length;int[][] pn = split(g);int[] par = pn[0], next = pn[1];ret.par = par;ret.next = next;int[] ord = makeOrder(g, ret.par);ret.ord = ord;ret.cycles = cycles(ret.next);int[] depn = new int[n];int[] roots = new int[n];int[] clus = new int[n];Arrays.fill(clus, -1);for(int i = 0;i < ret.cycles.size();i++){for(int v : ret.cycles.get(i))clus[v] = i;}for(int i = 0;i < n;i++){int cur = ord[i];if(next[cur] != -1){roots[cur] = cur;depn[cur] = 0;}else{roots[cur] = roots[par[cur]];clus[cur] = clus[par[cur]];depn[cur] = depn[par[cur]] + 1;}}ret.dep = depn;ret.clus = clus;ret.roots = roots;return ret;}/*** gから親リンクとringの次のリンクを取り出す。ringを含んでいなくても可能。森も取り出す。* 重複辺は事前に除いておかないといけない。* 重複辺を含んでいても大丈夫だとおもう* par!=-1,next==-1 : 木部ノード* par==-1,next!=-1 : 環部ノード* par==-1,next==-1 : 森のルート* @param g 重複辺を除いたpseudoforest* @return {par, next}*/public static int[][] split(int[][] g){int n = g.length;int[] deg = new int[n];int[] par = new int[n];Arrays.fill(par, -1);for(int i = 0;i < n;i++){deg[i] = g[i].length;}Queue<Integer> q = new ArrayDeque<>();for(int i = 0;i < n;i++){if(deg[i] == 1)q.add(i);}while(!q.isEmpty()){int cur = q.poll();deg[cur] = -9999999;for(int e : g[cur]){deg[e]--;if(deg[e] >= 0)par[cur] = e;if(deg[e] >= 0 && deg[e] <= 1)q.add(e);}}boolean[] ved = new boolean[n];int[] next = new int[n];Arrays.fill(next, -1);for(int i = 0;i < n;i++){if(!ved[i] && deg[i] == 2){ved[i] = true;int cur = i;outer:while(true){for(int e : g[cur]){if(deg[e] == 2 && !ved[e]){next[cur] = e;ved[e] = true;cur = e;continue outer;}}next[cur] = i;break;}}}return new int[][]{par, next};}/*** cycle側が先頭にくる* @param g* @param par* @return*/public static int[] makeOrder(int[][] g, int[] par){int n = g.length;int[] ord = new int[n];int p = 0;boolean[] ved = new boolean[n];for(int i = 0;i < n;i++){if(par[i] == -1){ord[p++] = i;ved[i] = true;}}for(int r = 0;r < n;r++){for(int e : g[ord[r]]){if(!ved[e]){ved[e] = true;ord[p++] = e;}}}return ord;}// cycle部分を取り出すpublic static List<int[]> cycles(int[] next){int n = next.length;List<int[]> ret = new ArrayList<>();int[] temp = new int[n];boolean[] ved = new boolean[n];for(int i = 0;i < n;i++){if(!ved[i] && next[i] != -1){int p = 0;int u = i;do {ved[u] = true;temp[p++] = u;u = next[u];} while (u != i);ret.add(Arrays.copyOf(temp, p));}}return ret;}public static int[][] packU(int n, int[] from, int[] to) {return packU(n, from, to, from.length);}public static int[][] packU(int n, int[] from, int[] to, int sup) {int[][] g = new int[n][];int[] p = new int[n];for (int i = 0; i < sup; i++) p[from[i]]++;for (int i = 0; i < sup; i++) p[to[i]]++;for (int i = 0; i < n; i++) g[i] = new int[p[i]];for (int i = 0; i < sup; i++) {g[from[i]][--p[from[i]]] = to[i];g[to[i]][--p[to[i]]] = from[i];}return g;}public static void main(String[] args) {new G().run();}public void run(){long S = System.currentTimeMillis();is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());out = new FastWriter(System.out);solve();out.flush();long G = System.currentTimeMillis();tr(G-S+"ms");// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){// @Override// public void run() {// long s = System.currentTimeMillis();// solve();// out.flush();// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");// }// };// t.start();// t.join();}private boolean eof(){if(lenbuf == -1)return true;int lptr = ptrbuf;while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;try {is.mark(1000);while(true){int b = is.read();if(b == -1){is.reset();return true;}else if(!isSpaceChar(b)){is.reset();return false;}}} catch (IOException e) {return true;}}private final byte[] inbuf = new byte[1024];public int lenbuf = 0, ptrbuf = 0;private int readByte(){if(lenbuf == -1)throw new InputMismatchException();if(ptrbuf >= lenbuf){ptrbuf = 0;try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }if(lenbuf <= 0)return -1;}return inbuf[ptrbuf++];}private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }// private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }private double nd() { return Double.parseDouble(ns()); }private char nc() { return (char)skip(); }private String ns(){int b = skip();StringBuilder sb = new StringBuilder();while(!(isSpaceChar(b))){sb.appendCodePoint(b);b = readByte();}return sb.toString();}private char[] ns(int n){char[] buf = new char[n];int b = skip(), p = 0;while(p < n && !(isSpaceChar(b))){buf[p++] = (char)b;b = readByte();}return n == p ? buf : Arrays.copyOf(buf, p);}private char[][] nm(int n, int m){char[][] map = new char[n][];for(int i = 0;i < n;i++)map[i] = ns(m);return map;}private int[][] nmi(int n, int m){int[][] map = new int[n][];for(int i = 0;i < n;i++)map[i] = na(m);return map;}private int[] na(int n){int[] a = new int[n];for(int i = 0;i < n;i++)a[i] = ni();return a;}private long[] nal(int n){long[] a = new long[n];for(int i = 0;i < n;i++)a[i] = nl();return a;}private int ni(){int num = 0, b;boolean minus = false;while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){minus = true;b = readByte();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = readByte();}}private long nl(){long num = 0;int b;boolean minus = false;while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){minus = true;b = readByte();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = readByte();}}public static class FastWriter{private static final int BUF_SIZE = 1<<13;private final byte[] buf = new byte[BUF_SIZE];private final OutputStream out;private int ptr = 0;private FastWriter(){out = null;}public FastWriter(OutputStream os){this.out = os;}public FastWriter(String path){try {this.out = new FileOutputStream(path);} catch (FileNotFoundException e) {throw new RuntimeException("FastWriter");}}public FastWriter write(byte b){buf[ptr++] = b;if(ptr == BUF_SIZE)innerflush();return this;}public FastWriter write(char c){return write((byte)c);}public FastWriter write(char[] s){for(char c : s){buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();}return this;}public FastWriter write(String s){s.chars().forEach(c -> {buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();});return this;}private static int countDigits(int l) {if (l >= 1000000000) return 10;if (l >= 100000000) return 9;if (l >= 10000000) return 8;if (l >= 1000000) return 7;if (l >= 100000) return 6;if (l >= 10000) return 5;if (l >= 1000) return 4;if (l >= 100) return 3;if (l >= 10) return 2;return 1;}public FastWriter write(int x){if(x == Integer.MIN_VALUE){return write((long)x);}if(ptr + 12 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}private static int countDigits(long l) {if (l >= 1000000000000000000L) return 19;if (l >= 100000000000000000L) return 18;if (l >= 10000000000000000L) return 17;if (l >= 1000000000000000L) return 16;if (l >= 100000000000000L) return 15;if (l >= 10000000000000L) return 14;if (l >= 1000000000000L) return 13;if (l >= 100000000000L) return 12;if (l >= 10000000000L) return 11;if (l >= 1000000000L) return 10;if (l >= 100000000L) return 9;if (l >= 10000000L) return 8;if (l >= 1000000L) return 7;if (l >= 100000L) return 6;if (l >= 10000L) return 5;if (l >= 1000L) return 4;if (l >= 100L) return 3;if (l >= 10L) return 2;return 1;}public FastWriter write(long x){if(x == Long.MIN_VALUE){return write("" + x);}if(ptr + 21 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}public FastWriter write(double x, int precision){if(x < 0){write('-');x = -x;}x += Math.pow(10, -precision)/2;// if(x < 0){ x = 0; }write((long)x).write(".");x -= (long)x;for(int i = 0;i < precision;i++){x *= 10;write((char)('0'+(int)x));x -= (int)x;}return this;}public FastWriter writeln(char c){ return write(c).writeln(); }public FastWriter writeln(int x){ return write(x).writeln(); }public FastWriter writeln(long x){ return write(x).writeln(); }public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }public FastWriter write(int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(IntUnaryOperator f, int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(f.applyAsInt(x));}return this;}public FastWriter write(LongUnaryOperator f, long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(f.applyAsLong(x));}return this;}public FastWriter writeln(){return write((byte)'\n');}public FastWriter writeln(int... xs) { return write(xs).writeln(); }public FastWriter writeln(long... xs) { return write(xs).writeln(); }public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }public FastWriter writeln(char[] line) { return write(line).writeln(); }public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }public FastWriter writeln(String s) { return write(s).writeln(); }private void innerflush(){try {out.write(buf, 0, ptr);ptr = 0;} catch (IOException e) {throw new RuntimeException("innerflush");}}public void flush(){innerflush();try {out.flush();} catch (IOException e) {throw new RuntimeException("flush");}}public FastWriter print(byte b) { return write(b); }public FastWriter print(char c) { return write(c); }public FastWriter print(char[] s) { return write(s); }public FastWriter print(String s) { return write(s); }public FastWriter print(int x) { return write(x); }public FastWriter print(long x) { return write(x); }public FastWriter print(double x, int precision) { return write(x, precision); }public FastWriter println(char c){ return writeln(c); }public FastWriter println(int x){ return writeln(x); }public FastWriter println(long x){ return writeln(x); }public FastWriter println(double x, int precision){ return writeln(x, precision); }public FastWriter print(int... xs) { return write(xs); }public FastWriter print(long... xs) { return write(xs); }public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }public FastWriter println(int... xs) { return writeln(xs); }public FastWriter println(long... xs) { return writeln(xs); }public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }public FastWriter println(char[] line) { return writeln(line); }public FastWriter println(char[]... map) { return writeln(map); }public FastWriter println(String s) { return writeln(s); }public FastWriter println() { return writeln(); }}public static void trnz(int... o){for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");System.out.println();}// print ids which are 1public static void trt(long... o){Queue<Integer> stands = new ArrayDeque<>();for(int i = 0;i < o.length;i++){for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));}System.out.println(stands);}public static void tf(boolean... r){for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}public static void tf(boolean[]... b){for(boolean[] r : b) {for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}System.out.println();}public void tf(long[]... b){if(INPUT.length() != 0) {for (long[] r : b) {for (long x : r) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}System.out.println();}}public void tf(long... b){if(INPUT.length() != 0) {for (long x : b) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}}private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }}