Submission #968666

---

Source Code Expand

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

public class Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		int n = ni(), X = ni();
		if(n <= 3){
			int[][] g = new int[n][n];
			for(int i = 0;i < n;i++){
				Arrays.fill(g[i], X);
				g[i][i] = 0;
			}
			for(int i = 0;i < n-1;i++){
				int f = ni()-1;
				int t = ni()-1;
				g[f][t] = g[t][f] = ni();
			}
			
			for (int k = 0; k < n; k++) {
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < n; j++) {
						if (g[i][j] > g[i][k] + g[k][j]) {
							g[i][j] = g[i][k] + g[k][j];
						}
					}
				}
			}
			long ret = 0;
			for(int i = 0;i < n;i++){
				for(int j = i+1;j < n;j++){
					ret += g[i][j];
				}
			}
			out.println(ret);
			return;
		}
		
		
		int[] from = new int[n-1];
		int[] to = new int[n-1];
		int[] w = new int[n-1];
		for(int i = 0;i < n-1;i++){
			from[i] = ni()-1;
			to[i] = ni()-1;
			w[i] = ni();
		}
		int[][][] g = packWU(n, from, to, w);
		
		for(int i = 0;i < n;i++){
			for(int[] e : g[i]){
				if(g[i].length + g[e[0]].length < n){
					e[1] = Math.min(e[1], 2*X);
				}
			}
		}
		
		int[] neimin = new int[n];
		Arrays.fill(neimin, Integer.MAX_VALUE / 2);
		for(int i = 0;i < n;i++){
			for(int[] e : g[i]){
				neimin[i] = Math.min(neimin[i], e[1]);
			}
		}
		for(int i = 0;i < n;i++){
			for(int[] e : g[i]){
				e[1] = Math.min(e[1], neimin[i] + X);
				e[1] = Math.min(e[1], neimin[e[0]] + X);
			}
		}
		
		int[][] pars = parents(g, 0);
		int[] par = pars[0], dep = pars[2];
		int[] ord = pars[1], pw = pars[4];
		long[] dw = new long[n];
		for(int i = 1;i < n;i++){
			int cur = ord[i];
			dw[cur] = dw[par[cur]] + pw[cur];
		}
		int[][] spar = logstepParents(par);
		int[] cpar = buildCentroidTree(g);
		CentroidTreeDistanceArrays ctda = dfsTop(cpar, g);
		long[][] gdscum = new long[n][];
		for(int i = 0;i < n;i++){
			gdscum[i] = new long[ctda.gds[i].length+1];
			for(int j = 0;j < ctda.gds[i].length;j++){
				gdscum[i][j+1] = gdscum[i][j] + ctda.gds[i][j];
			}
		}
		long[][][] dscum = new long[n][][];
		for(int i = 0;i < n;i++){
			dscum[i] = new long[ctda.ds[i].length][];
			for(int j = 0;j < ctda.ds[i].length;j++){
				dscum[i][j] = new long[ctda.ds[i][j].length+1];
				for(int k = 0;k < dscum[i][j].length-1;k++){
					dscum[i][j][k+1] = dscum[i][j][k] + ctda.ds[i][j][k];
				}
			}
		}
		
		long lownum = 0;
		long lowsum = 0;
		for(int i = 0;i < n;i++){
			int pre = -1;
			for(int x = i;x != -1;x = cpar[x]){
				int lca = lca2(x, i, spar, dep);
				long base = dw[x] + dw[i] - 2*dw[lca];
				{
					int lb = lowerBound(ctda.gds[x], X-base);
					lownum += lb;
					lowsum += gdscum[x][lb] + base * lb;
				}
				if(pre != -1){
					int preind = Arrays.binarySearch(ctda.ctch[x], pre);
					int lb = lowerBound(ctda.ds[x][preind], X-base);
					lownum -= lb;
					lowsum -= dscum[x][preind][lb] + base * lb;
				}
				pre = x;
			}
		}
		for(int i = 1;i < n;i++){
			if(pw[i] > X){
				lownum += 2;
				lowsum += pw[i]*2L;
			}
		}
		lownum = (lownum - n) / 2;
		lowsum /= 2;
		lowsum += ((long)n*(n-1)/2-lownum) * X;
		out.println(lowsum);
	}
	
	public static int lowerBound(long[] a, long v)
	{
		int low = -1, high = a.length;
		while(high-low > 1){
			int h = high+low>>>1;
			if(a[h] >= v){
				high = h;
			}else{
				low = h;
			}
		}
		return high;
	}

	
	public static class CentroidTreeDistanceArrays
	{
		public long[][] gds; // distances subject to v in centroid tree
		public long[][][] ds; // distances subject to par[v] in centroid tree and neck is v
		public int[][] ctch;
	}
	
	/**
	 * Centroid Treeからの距離配列列挙
	 * 別に下のseparate関数に処理を追加してもよい
	 * 
	 * sep : 現在処理しようとするseparator
	 * seps : マークしたseparatorリスト (volatile)
	 * q : BFS用キュー (volatile)
	 * lds : 特定幹部を通る距離配列の一時リスト (volatile)
	 * glds : sepからの距離配列の一時リスト (volatile)
	 * dd : sepからの距離配列(頂点からの表引き用) (volatile)
	 * ds : 特定幹部を通る距離配列
	 * gds : sepからの距離配列
	 * g : 辺重み付き木 (const)
	 * ctch : Centroid Treeの子へのリンク (const)
	 * 
	 * @param cpar Centroid Treeの親へのリンク
	 * @param g 辺重み付き木
	 * @return
	 */
	public static CentroidTreeDistanceArrays dfsTop(int[] cpar, int[][][] g) {
		int n = g.length;
		int ctroot = -1;
		for(int i = 0;i < n;i++)if(cpar[i] == -1)ctroot = i;
		int[][] ctch = parentToChildren(cpar);
		for(int[] row : ctch){
			Arrays.sort(row);
		}
		long I = Long.MAX_VALUE / 2;
		long[] dd = new long[n];
		Arrays.fill(dd, I);
		long[][][] ds = new long[n][][];
		long[][] gds = new long[n][];
		int[] iind = new int[n];
		Arrays.fill(iind, -1);
		dfs(ctroot, new boolean[n], new int[n], new long[n], new long[n], dd, ds, gds, g, ctch, iind);
		CentroidTreeDistanceArrays ret = new CentroidTreeDistanceArrays();
		ret.ds = ds;
		ret.gds = gds;
		ret.ctch = ctch;
		return ret;
	}
	
	public static int[][] parentToChildren(int[] par)
	{
		int n = par.length;
		int[] ct = new int[n];
		for(int i = 0;i < n;i++){
			if(par[i] >= 0){
				ct[par[i]]++;
			}
		}
		int[][] g = new int[n][];
		for(int i = 0;i < n;i++){
			g[i] = new int[ct[i]];
		}
		for(int i = 0;i < n;i++){
			if(par[i] >= 0){
				g[par[i]][--ct[par[i]]] = i;
			}
		}
		
		return g;
	}

	
	private static void dfs(int sep, boolean[] seps, int[] q, long[] lds, long[] glds, long[] dd, long[][][] ds, long[][] gds, int[][][] g, int[][] ctch, int[] iind)
	{
		long I = Long.MAX_VALUE / 2;
		seps[sep] = true;
		int gdp = 0;
		dd[sep] = 0;
		glds[gdp++] = 0;

		for(int i = 0;i < ctch[sep].length;i++){
			iind[ctch[sep][i]] = i;
		}
		ds[sep] = new long[ctch[sep].length][];
		for(int[] neck : g[sep]){
			int dp = 0;
			int p = 0;
			int wind = -1;
			if(!seps[neck[0]]){
				q[p++] = neck[0];
				dd[neck[0]] = neck[1];
				lds[dp++] = dd[neck[0]];
				glds[gdp++] = dd[neck[0]];
				for(int j = 0;j < p;j++){
					int cur = q[j];
					if(iind[cur] != -1)wind = iind[cur];
					for(int[] e : g[cur]){
						if(!seps[e[0]] && dd[e[0]] == I){
							dd[e[0]] = dd[cur] + e[1];
							lds[dp++] = dd[e[0]];
							glds[gdp++] = dd[e[0]];
							q[p++] = e[0];
						}
					}
				}
				for(int j = 0;j < p;j++){
					dd[q[j]] = I;
				}
				ds[sep][wind] = Arrays.copyOf(lds, dp);
				Arrays.sort(ds[sep][wind]);
			}
			
		}
		gds[sep] = Arrays.copyOf(glds, gdp);
		Arrays.sort(gds[sep]);
		
		for(int i = 0;i < ctch[sep].length;i++){
			iind[ctch[sep][i]] = -1;
		}
		for(int e : ctch[sep]){
			dfs(e, seps, q, lds, glds, dd, ds, gds, g, ctch, iind);
		}
		seps[sep] = false;
	}
	
	
	public static int[] buildCentroidTree(int[][][] g) {
		int n = g.length;
		int[] ctpar = new int[n];
		Arrays.fill(ctpar, -1);
		buildCentroidTree(g, 0, new boolean[n], new int[n], new int[n], new int[n], ctpar);
		return ctpar;
	}
	
	private static int buildCentroidTree(int[][][] g, int root, boolean[] sed, int[] par, int[] ord, int[] des, int[] ctpar)
	{
		// parent and level-order
		ord[0] = root;
		par[root] = -1;
		int r = 1;
		for(int p = 0;p < r;p++) {
			int cur = ord[p];
			for(int[] nex : g[cur]){
				if(par[cur] != nex[0] && !sed[nex[0]]){
					ord[r++] = nex[0];
					par[nex[0]] = cur;
				}
			}
		}
		// if(r == 1)return;
		
		// DP and find a separator
		int sep = -1; // always exists
		outer:
		for(int i = r-1;i >= 0;i--){
			int cur = ord[i];
			des[cur] = 1;
			for(int[] e : g[cur]){
				if(par[cur] != e[0] && !sed[e[0]])des[cur] += des[e[0]];
			}
			if(r-des[cur] <= r/2){
				for(int[] e : g[cur]){
					if(par[cur] != e[0] && !sed[e[0]] && des[e[0]] >= r/2+1)continue outer;
				}
				sep = cur;
				break;
			}
		}
		
		sed[sep] = true;
		for(int[] e : g[sep]){
			if(!sed[e[0]])ctpar[buildCentroidTree(g, e[0], sed, par, ord, des, ctpar)] = sep;
		}
		return sep;
	}

	
	public static int lca2(int a, int b, int[][] spar, int[] depth) {
		if (depth[a] < depth[b]) {
			b = ancestor(b, depth[b] - depth[a], spar);
		} else if (depth[a] > depth[b]) {
			a = ancestor(a, depth[a] - depth[b], spar);
		}

		if (a == b)
			return a;
		int sa = a, sb = b;
		for (int low = 0, high = depth[a], t = Integer.highestOneBit(high), k = Integer
				.numberOfTrailingZeros(t); t > 0; t >>>= 1, k--) {
			if ((low ^ high) >= t) {
				if (spar[k][sa] != spar[k][sb]) {
					low |= t;
					sa = spar[k][sa];
					sb = spar[k][sb];
				} else {
					high = low | t - 1;
				}
			}
		}
		return spar[0][sa];
	}

	protected static int ancestor(int a, int m, int[][] spar) {
		for (int i = 0; m > 0 && a != -1; m >>>= 1, i++) {
			if ((m & 1) == 1)
				a = spar[i][a];
		}
		return a;
	}

	public static int[][] logstepParents(int[] par) {
		int n = par.length;
		int m = Integer.numberOfTrailingZeros(Integer.highestOneBit(n - 1)) + 1;
		int[][] pars = new int[m][n];
		pars[0] = par;
		for (int j = 1; j < m; j++) {
			for (int i = 0; i < n; i++) {
				pars[j][i] = pars[j - 1][i] == -1 ? -1 : pars[j - 1][pars[j - 1][i]];
			}
		}
		return pars;
	}

	
	
	
	public static int[][] parents(int[][][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);
		int[] dw = new int[n];
		int[] pw = new int[n];
		int[] dep = new int[n];

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int[] nex : g[cur]) {
				if (par[cur] != nex[0]) {
					q[r++] = nex[0];
					par[nex[0]] = cur;
					dep[nex[0]] = dep[cur] + 1;
					dw[nex[0]] = dw[cur] + nex[1];
					pw[nex[0]] = nex[1];
				}
			}
		}
		return new int[][] { par, q, dep, dw, pw };
	}

	
	public static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
		int[][][] g = new int[n][][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int t : to)
			p[t]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]][2];
		for (int i = 0; i < from.length; i++) {
			--p[from[i]];
			g[from[i]][p[from[i]]][0] = to[i];
			g[from[i]][p[from[i]]][1] = w[i];
			--p[to[i]];
			g[to[i]][p[to[i]]][0] = from[i];
			g[to[i]][p[to[i]]][1] = w[i];
		}
		return g;
	}

	
	public static void main(String[] args) throws Exception
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static 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 static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static 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 static 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 static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static 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 static 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();
		}
	}
	
	private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}

Submission Info

Judge Result