Cerinta completa
We consider metric space to be a pair, , where is a set and such that the following conditions hold:
where is the distance between points and .
Let’s define the product of two metric spaces, , to be such that:
- , where , .
So, it follows logically that is also a metric space. We then define squared metric space, , to be the product of a metric space multiplied with itself: .
For example, , where is a metric space. , where .
In this challenge, we need a tree-space. You’re given a tree, , where is the set of vertices and is the set of edges. Let the function be the distance between two vertices in tree (i.e., is the number of edges on the path between vertices and ). Note that is a metric space.
You are given a tree, , with vertices, as well as points in . Find and print the distance between the two furthest points in this metric space!
Input Format
The first line contains two space-separated positive integers describing the respective values of (the number of vertices in ) and (the number of given points).
Each line of the subsequent lines contains two space-separated integers, and , describing edge in .
Each line of the subsequent lines contains two space-separated integers describing the respective values of and for point .
Constraints
Scoring
This challenge uses binary scoring, so you must pass all test cases to earn a positive score.
Output Format
Print a single non-negative integer denoting the maximum distance between two of the given points in metric space .
Sample Input 0
2 2
1 2
1 2
2 1
Sample Output 0
2
Explanation 0
The distance between points and is .
Sample Input 1
7 3
1 2
2 3
3 4
4 5
5 6
6 7
3 6
4 5
5 5
Sample Output 1
3
Explanation 1
The best points are and , which gives us a distance of .
Limbajul de programare folosit: java8
Cod:
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;
import java.util.regex.*;
class Entry implements Comparable<Entry> {
int x;
int y;
int val;
public Entry(int x, int y, int val) {
this.x = x;
this.y = y;
this.val = val;
}
public int compareTo(Entry other) {
return val - other.val;
}
}
public class Solution {
static int[][] buildSparseTable(int[] arr) {
int pow = 1;
while ((1 << pow) < arr.length) pow++;
int[][] result = new int[arr.length][pow];
for (int i = 0; i < arr.length; i++) result[i][0] = arr[i];
for (int j = 1; j <= pow; j++) {
for (int i = 0; i + (1 << j) <= arr.length; i++) {
result[i][j] = Math.min(result[i][j-1],
result[i + (1 << (j-1))][j-1]);
}
}
return result;
} /*
* Complete the treeCoordinates function below.
*/
static int treeCoordinates(int n, int[][] edges, int[][] points) {
ArrayList<Integer>[] nodes = new ArrayList[n + 1];
for (int i = 1; i <= n; i++) nodes[i] = new ArrayList<Integer>();
for (int[] edge : edges) {
nodes[edge[0]].add(edge[1]);
nodes[edge[1]].add(edge[0]);
}
// Find diameter (two BFS)
int root = 0;
int tail = 0;
{
class Entry {
int node;
int dist;
public Entry(int node, int dist) {
this.node = node;
this.dist = dist;
}
}
LinkedList<Entry> Q = new LinkedList<Entry>();
boolean[] visited = new boolean[n + 1];
visited[1] = true;
Q.offer(new Entry(1, 0));
int maxDist = 0;
int farNode = 1;
while (Q.size() > 0) {
Entry cur = Q.poll();
if (cur.dist > maxDist) {
maxDist = cur.dist;
farNode = cur.node;
}
for (int neighbor : nodes[cur.node]) {
if (visited[neighbor]) continue;
visited[neighbor] = true;
Q.offer(new Entry(neighbor, cur.dist + 1));
}
}
root = farNode;
Q = new LinkedList<Entry>();
visited = new boolean[n + 1];
visited[root] = true;
Q.offer(new Entry(root, 0));
maxDist = 0;
farNode = root;
while (Q.size() > 0) {
Entry cur = Q.poll();
if (cur.dist > maxDist) {
maxDist = cur.dist;
farNode = cur.node;
}
for (int neighbor : nodes[cur.node]) {
if (visited[neighbor]) continue;
visited[neighbor] = true;
Q.offer(new Entry(neighbor, cur.dist + 1));
}
}
tail = farNode;
}
//System.out.println("root = " + root + ", tail = " + tail);
// Euler tour
int[] eulerTour = new int[2*n - 1];
final int[] depth = new int[n + 1];
int[] eulerLevels = new int[2*n - 1];
int[] eulerIndex = new int[n + 1];
boolean[] visited = new boolean[n + 1];
int[] S = new int[n];
int spos = 0;
S[0] = root;
int pos = 0;
int[] neighborCount = new int[n + 1];
while (spos > -1) {
int cur = S[spos--];
if (!visited[cur]) {
depth[cur] = spos + 1;
eulerIndex[cur] = pos;
visited[cur] = true;
}
eulerLevels[pos] = spos + 1;
eulerTour[pos] = cur;
pos++;
while (neighborCount[cur] < nodes[cur].size()) {
if (visited[nodes[cur].get(neighborCount[cur])]) {
neighborCount[cur]++;
continue;
}
int next = nodes[cur].get(neighborCount[cur]);
//parent[next] = cur;
S[++spos] = cur;
S[++spos] = next;
neighborCount[cur]++;
break;
}
}
int[][] lookup = buildSparseTable(eulerLevels);
List<Entry> list1 = new ArrayList<Entry>(points.length);
List<Entry> list2 = new ArrayList<Entry>(points.length);
List<Entry> list3 = new ArrayList<Entry>(points.length);
List<Entry> list4 = new ArrayList<Entry>(points.length);
for (int i = 0; i < points.length; i++) {
int x = points[i][0];
int y = points[i][1];
int xLcaLevel;
{
int start = Math.min(eulerIndex[x], eulerIndex[tail]);
int end = Math.max(eulerIndex[x], eulerIndex[tail]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
xLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int yLcaLevel;
{
int start = Math.min(eulerIndex[y], eulerIndex[tail]);
int end = Math.max(eulerIndex[y], eulerIndex[tail]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
yLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int val1 = depth[x] + depth[y];
list1.add(new Entry(x, y, val1));
int val2 = -depth[x] - depth[y] + 2*xLcaLevel + 2*yLcaLevel;
list2.add(new Entry(x, y, val2));
int val3 = depth[x] + depth[y] - 2*xLcaLevel;
list3.add(new Entry(x, y, val3));
int val4 = -depth[x] - depth[y] + 2*yLcaLevel;
list4.add(new Entry(x, y, val4));
}
Collections.sort(list1, Collections.reverseOrder());
Collections.sort(list2);
Collections.sort(list3, Collections.reverseOrder());
Collections.sort(list4);
int maxDist = 0;
for (int i = 0; i < points.length; i++) {
boolean shouldContinue = false;
for (int j = 0; j <= i; j++) {
Entry e1 = list1.get(i-j);
Entry e2 = list2.get(j);
int potential12 = e1.val - e2.val;
if (potential12 > maxDist) {
shouldContinue = true;
int x1 = e1.x;
int y1 = e1.y;
int x2 = e2.x;
int y2 = e2.y;
int xLcaLevel;
{
int start = Math.min(eulerIndex[x1], eulerIndex[x2]);
int end = Math.max(eulerIndex[x1], eulerIndex[x2]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
xLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int yLcaLevel;
{
int start = Math.min(eulerIndex[y1], eulerIndex[y2]);
int end = Math.max(eulerIndex[y1], eulerIndex[y2]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
yLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int actual12 = depth[x1] + depth[x2] - 2*xLcaLevel
+ depth[y1] + depth[y2] - 2*yLcaLevel;
maxDist = Math.max(maxDist, actual12);
}
Entry e3 = list3.get(i-j);
Entry e4 = list4.get(j);
int potential34 = e3.val - e4.val;
if (potential34 > maxDist) {
shouldContinue = true;
int x3 = e3.x;
int y3 = e3.y;
int x4 = e4.x;
int y4 = e4.y;
int xLcaLevel;
{
int start = Math.min(eulerIndex[x3], eulerIndex[x4]);
int end = Math.max(eulerIndex[x3], eulerIndex[x4]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
xLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int yLcaLevel;
{
int start = Math.min(eulerIndex[y3], eulerIndex[y4]);
int end = Math.max(eulerIndex[y3], eulerIndex[y4]);
int pow = 0;
while (1 << (pow + 1) <= (end - start)) pow++;
yLcaLevel = Math.min(lookup[start][pow],
lookup[end + 1 - (1<<pow)][pow]);
}
int actual34 = depth[x3] + depth[x4] - 2*xLcaLevel
+ depth[y3] + depth[y4] - 2*yLcaLevel;
maxDist = Math.max(maxDist, actual34);
}
}
if (!shouldContinue) break;
}
return maxDist;
}
private static final Scanner scanner = new Scanner(System.in);
public static void main(String[] args) throws IOException {
BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
String[] nm = scanner.nextLine().split(" ");
int n = Integer.parseInt(nm[0].trim());
int m = Integer.parseInt(nm[1].trim());
int[][] edges = new int[n-1][2];
for (int edgesRowItr = 0; edgesRowItr < n-1; edgesRowItr++) {
String[] edgesRowItems = scanner.nextLine().split(" ");
for (int edgesColumnItr = 0; edgesColumnItr < 2; edgesColumnItr++) {
int edgesItem = Integer.parseInt(edgesRowItems[edgesColumnItr].trim());
edges[edgesRowItr][edgesColumnItr] = edgesItem;
}
}
int[][] points = new int[m][2];
for (int pointsRowItr = 0; pointsRowItr < m; pointsRowItr++) {
String[] pointsRowItems = scanner.nextLine().split(" ");
for (int pointsColumnItr = 0; pointsColumnItr < 2; pointsColumnItr++) {
int pointsItem = Integer.parseInt(pointsRowItems[pointsColumnItr].trim());
points[pointsRowItr][pointsColumnItr] = pointsItem;
}
}
int result = treeCoordinates(n, edges, points);
bufferedWriter.write(String.valueOf(result));
bufferedWriter.newLine();
bufferedWriter.close();
}
}
Scor obtinut: 1.0
Submission ID: 464665359
Link challenge: https://www.hackerrank.com/challenges/tree-coordinates/problem
Tree Coordinates