目录

最长异或路径：

题目大意：

思路解析：

代码实现：

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最长异或路径：

题目大意：

思路解析：

现在假设有一棵这样的树，我们并不关心每条边的路径权值为多少，假设划红线的地方是异或值最大的一条路径，那我们可以发现我们只需要知道1-11的异或值，1-7路径的异或值，那我们在贪心的过程一定能得到最优答案

 

第二种情况，最大异或路径不经过顶点，但是我们发现 11 ^ 5 ^ 6 ^ 13 ^ 14等价于（2 ^ 5 ^ 11) ^ （  2 ^ 6 ^ 13 ^ 14) ，可以发现还是相当于1--11的路径异或1-14的路径，所以我们只需要得到顶点到其他任意结点的路径即可，那我们在贪心选择时一定能得到最优解。

 

 

现在得到顶点到其他任意结点的异或路径值后，我们应该考虑我们如何贪心的选择。

假设我们现在路径的异或值为 2，曾经到过的路径异或值有（5 ，4，3，6）他们的二进制数分布为010，101，100，011，110，我们发现我们与5的路径异或后能得到最优答案。那么贪心选择为从二进制位的高位开始抉择，如果能有一个数能和当前值异或后在该位为1就选择这个数。

但是如果我们进行遍历选择，就会时间复杂度过高，那我们可以使用01字典树，这样就可以每次筛去大部分结果。

代码实现：

import java.io.*;
import java.util.*;import static java.lang.String.*;public class Main {static int MAXN = 100010;static int n;static int[][] tree = new int[MAXN << 3][2];static int[] nxt = new int[MAXN << 1];static int[] head = new int[MAXN];static int[] to = new int[MAXN << 1];static int[] weight = new int[MAXN << 1];static int tot = 0;static int ans = 0;static int cnt;static int[] dp = new int[MAXN];public static void main(String[] args) throws IOException {FastScanner f = new FastScanner();PrintWriter w = new PrintWriter(System.out);n = f.nextInt();for (int i = 0; i < n - 1; i++) {int x = f.nextInt();int y = f.nextInt();int v = f.nextInt();add(x, y, v);add(y,x,v);}dfs(1, 0);w.println(ans);w.flush();w.close();}static void dfs(int x, int fa){insert(dp[x]);get(dp[x]);for (int i = head[x]; i != 0; i = nxt[i]) {int y = to[i];if (y == fa) continue;dp[y] = dp[x] ^ weight[i];dfs(y, x);}}static void insert(int x){int p = 0;for(int i = 30; i >= 0; i--){int c = ((x >> i) & 1);if (tree[p][c] == 0){tree[p][c] = ++cnt;}p = tree[p][c];}}static void get(int x){int res = 0;int p = 0;for (int i = 30; i >= 0; i--) {int c = ((x >> i) & 1);if (tree[p][c ^ 1] != 0){res |= (1 << i);p = tree[p][c ^ 1];}else {p = tree[p][c];}}ans = Math.max(ans, res);}static void add(int x, int y, int v){nxt[++tot] = head[x];head[x] = tot;to[tot] = y;weight[tot] = v;}private static class FastScanner {final private int BUFFER_SIZE = 1 << 16;private DataInputStream din;private byte[] buffer;private int bufferPointer, bytesRead;private FastScanner() throws IOException {din = new DataInputStream(System.in);buffer = new byte[BUFFER_SIZE];bufferPointer = bytesRead = 0;}private short nextShort() throws IOException {short ret = 0;byte c = read();while (c <= ' ') c = read();boolean neg = (c == '-');if (neg) c = read();do ret = (short) (ret * 10 + c - '0');while ((c = read()) >= '0' && c <= '9');if (neg) return (short) -ret;return ret;}private int nextInt() throws IOException {int ret = 0;byte c = read();while (c <= ' ') c = read();boolean neg = (c == '-');if (neg) c = read();do ret = ret * 10 + c - '0';while ((c = read()) >= '0' && c <= '9');if (neg) return -ret;return ret;}public long nextLong() throws IOException {long ret = 0;byte c = read();while (c <= ' ') c = read();boolean neg = (c == '-');if (neg) c = read();do ret = ret * 10 + c - '0';while ((c = read()) >= '0' && c <= '9');if (neg) return -ret;return ret;}private char nextChar() throws IOException {byte c = read();while (c <= ' ') c = read();return (char) c;}private String nextString() throws IOException {StringBuilder ret = new StringBuilder();byte c = read();while (c <= ' ') c = read();do {ret.append((char) c);} while ((c = read()) > ' ');return ret.toString();}private void fillBuffer() throws IOException {bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);if (bytesRead == -1) buffer[0] = -1;}private byte read() throws IOException {if (bufferPointer == bytesRead) fillBuffer();return buffer[bufferPointer++];}}}