Give this problem a try USACO Silver 2020 January - Wormhole Sort.
Approach
Example Code
import java.io.*;
import java.util.*;
public class Solution {
static class DSU {
int[] parent;
int[] sz;
public DSU(int N) {
parent = new int[N];
sz = new int[N];
for (int i = 0; i < N; i++) {
parent[i] = i;
sz[i] = 1;
}
}
public int find(int v) {
if (parent[v] == v) return parent[v];
return parent[v] = find(parent[v]);
}
public void union(int a, int b) {
a = find(a);
b = find(b);
if (a != b) {
if (sz[a] <= sz[b]) {
int tmp = a;
a = b;
b = tmp;
}
parent[b] = a;
sz[a] += sz[b];
}
}
}
public static boolean check(int x, int max, int[] cows, int[][] wormholes) {
int N = cows.length;
DSU dsu = new DSU(N);
for (int[] wh : wormholes) {
if (x <= wh[2]) dsu.union(wh[0], wh[1]);
}
boolean ok = true;
for (int i = 0; i < N; i++) {
int pcow = dsu.find(cows[i]);
int pi = dsu.find(i);
if (pcow != pi) {
ok = false;
break;
}
}
return ok;
}
public static int search(int max, int[] cows, int[][] wormholes) {
int pos = 0;
for (int x = max; x >= 1; x /= 2) {
while (check(pos+x, max, cows, wormholes)) {
pos += x;
}
}
return pos;
}
public static void main(String[] args) throws Exception {
FastScanner io = new FastScanner("wormsort");
// FastScanner io = new FastScanner();
int N = io.nextInt(), M = io.nextInt();
int[] cows = new int[N];
boolean sorted = true;
for (int i = 0; i < N; i++) {
cows[i] = io.nextInt()-1;
if (cows[i] != i) sorted = false;
}
if (sorted) {
io.println(-1);
io.close();
return;
}
int[][] wormholes = new int[M][3];
int maxWidth = 0;
for (int i = 0; i < M; i++) {
wormholes[i] = new int[]{io.nextInt()-1, io.nextInt()-1, io.nextInt()};
maxWidth = Math.max(maxWidth, wormholes[i][2]);
}
Arrays.sort(wormholes, (a, b) -> a[2] - b[2]);
int answer = search(maxWidth+1, cows, wormholes);
io.println(answer);
io.close();
}
/**
RESERVED NUMBERS
*/
public static int MOD = 1_000_000_007; // prime number
public static int INF = 1_000_000_007; // infinity number
/**
DATA STRUCTURES
*/
static class MultiSet {
static TreeMap<Integer, Integer> multiset;
public MultiSet() { multiset = new TreeMap<>(); }
static void add(int x) {
multiset.putIfAbsent(x, 0);
multiset.put(x, multiset.get(x)+1);
}
static void remove(int x) {
multiset.putIfAbsent(x, 0);
multiset.put(x, multiset.get(x)-1);
if (multiset.get(x) <= 0) multiset.remove(x);
}
}
/**
IO
*/
static class FastScanner extends PrintWriter {
private BufferedReader br;
private StringTokenizer st;
// standard input
public FastScanner() { this(System.in, System.out); }
public FastScanner(InputStream i, OutputStream o) {
super(o);
st = new StringTokenizer("");
br = new BufferedReader(new InputStreamReader(i));
}
// USACO-style file input
public FastScanner(String problemName) throws IOException {
super(problemName + ".out");
st = new StringTokenizer("");
br = new BufferedReader(new FileReader(problemName + ".in"));
}
// returns null if no more input
public String next() {
try {
while (st == null || !st.hasMoreTokens())
st = new StringTokenizer(br.readLine());
return st.nextToken();
} catch (Exception e) { }
return null;
}
public int nextInt() { return Integer.parseInt(next()); }
public double nextDouble() { return Double.parseDouble(next()); }
public long nextLong() { return Long.parseLong(next()); }
}
}
Complexity Analysis
- Time Complexity:
- Space Complexity:
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Congratulations on making it this far! Best of luck in your future competitions!