From 86a394378a5a064658bacde101c1d3413a740838 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=B7=A6=E7=A8=8B=E4=BA=91?= <algorithmzuo@163.com>
Date: Tue, 22 Dec 2020 16:43:02 +0800
Subject: [PATCH] add problem

---
 ...04_LargestComponentSizebyCommonFactor.java | 104 ++++++++++++++++++
 1 file changed, 104 insertions(+)
 create mode 100644 src/class09_15/Code04_LargestComponentSizebyCommonFactor.java

diff --git a/src/class09_15/Code04_LargestComponentSizebyCommonFactor.java b/src/class09_15/Code04_LargestComponentSizebyCommonFactor.java
new file mode 100644
index 0000000..ffe66df
--- /dev/null
+++ b/src/class09_15/Code04_LargestComponentSizebyCommonFactor.java
@@ -0,0 +1,104 @@
+package class09_15;
+
+import java.util.HashMap;
+
+// 本题为leetcode原题
+// 测试链接：https://leetcode.com/problems/largest-component-size-by-common-factor/
+// 方法1会超时，但是方法2直接通过
+public class Code04_LargestComponentSizebyCommonFactor {
+
+	public static int largestComponentSize1(int[] arr) {
+		int N = arr.length;
+		UnionFind set = new UnionFind(N);
+		for (int i = 0; i < N; i++) {
+			for (int j = i + 1; j < N; j++) {
+				if (gcd(arr[i], arr[j]) != 1) {
+					set.union(i, j);
+				}
+			}
+		}
+		return set.maxSize();
+	}
+
+	public static int largestComponentSize2(int[] arr) {
+		int N = arr.length;
+		UnionFind unionFind = new UnionFind(N);
+		HashMap<Integer, Integer> fatorsMap = new HashMap<>();
+		for (int i = 0; i < N; i++) {
+			int num = arr[i];
+			int limit = (int) Math.sqrt(num);
+			for (int j = 1; j <= limit; j++) {
+				if (num % j == 0) {
+					if (j != 1) {
+						if (!fatorsMap.containsKey(j)) {
+							fatorsMap.put(j, i);
+						} else {
+							unionFind.union(fatorsMap.get(j), i);
+						}
+					}
+					int other = num / j;
+					if (other != 1) {
+						if (!fatorsMap.containsKey(other)) {
+							fatorsMap.put(other, i);
+						} else {
+							unionFind.union(fatorsMap.get(other), i);
+						}
+					}
+				}
+			}
+		}
+		return unionFind.maxSize();
+	}
+
+	public static int gcd(int m, int n) {
+		return n == 0 ? m : gcd(n, m % n);
+	}
+
+	public static class UnionFind {
+		private int[] parents;
+		private int[] sizes;
+		private int[] help;
+
+		public UnionFind(int N) {
+			parents = new int[N];
+			sizes = new int[N];
+			help = new int[N];
+			for (int i = 0; i < N; i++) {
+				parents[i] = i;
+				sizes[i] = 1;
+			}
+		}
+
+		public int maxSize() {
+			int ans = 0;
+			for (int size : sizes) {
+				ans = Math.max(ans, size);
+			}
+			return ans;
+		}
+
+		private int find(int i) {
+			int hi = 0;
+			while (i != parents[i]) {
+				help[hi++] = i;
+				i = parents[i];
+			}
+			for (hi--; hi >= 0; hi--) {
+				parents[help[hi]] = i;
+			}
+			return i;
+		}
+
+		public void union(int i, int j) {
+			int f1 = find(i);
+			int f2 = find(j);
+			if (f1 != f2) {
+				int big = sizes[f1] >= sizes[f2] ? f1 : f1;
+				int small = big == f1 ? f2 : f1;
+				parents[small] = big;
+				sizes[big] = sizes[f1] + sizes[f2];
+			}
+		}
+	}
+
+}