952 Time Limit Exceeded

Author: aQuaYi

Algorithms/0952.largest-component-size-by-common-factor/largest-component-size-by-common-factor.go

@@ -1,6 +1,87 @@
 package problem0952
 
 func largestComponentSize(A []int) int {
+	size := len(A)
+	u := newUnion(size)
 
-	return 0
+	for i := 0; i < size-1; i++ {
+		for j := i + 1; j < size; j++ {
+			a, b := A[i], A[j]
+			if gcd(a, b) > 1 {
+				u.union(i, j)
+			}
+		}
+	}
+
+	return u.max
+}
+
+// Greatest Common Divisor(GCD)
+func gcd(a, b int) int {
+	if a < b {
+		return gcd(b, a)
+	}
+	for b != 0 {
+		a, b = b, a%b
+	}
+	return a
+}
+
+// Robert Sedgewick 算法（第4版） 1.5.2.7
+// union-find (加权 quick-union)，还作了路径压缩优化
+
+type union struct {
+	id  []int // 父链接数组(由触点索引)
+	sz  []int // (由触点索引的) 各个根节点所对应的分量的大小
+	max int   // 连通分量的数量
+}
+
+func newUnion(N int) *union {
+	id := make([]int, N)
+	for i := range id {
+		id[i] = i
+	}
+	sz := make([]int, N)
+	for i := range sz {
+		sz[i] = 1
+	}
+	return &union{
+		id:  id,
+		sz:  sz,
+		max: 1,
+	}
+}
+
+func (u *union) isConnected(p, q int) bool {
+	return u.find(p) == u.find(q)
+}
+
+func (u *union) find(p int) int {
+	// 跟随连接找到根节点
+	for p != u.id[p] {
+		p = u.id[p]
+	}
+	return p
+}
+
+func (u *union) union(p, q int) {
+	i, j := u.find(p), u.find(q)
+	if i == j {
+		return
+	}
+	if u.sz[i] > u.sz[j] {
+		i, j = j, i
+	}
+	// 将小树的根节点连接到大树的根节点
+	u.id[i] = j
+	u.sz[j] += u.sz[i]
+	u.max = max(u.max, u.sz[j])
+	return
+}
+
+func max(a, b int) int {
+	if a > b {
+		return a
+	}
+	return b
 }

Algorithms/0952.largest-component-size-by-common-factor/largest-component-size-by-common-factor_test.go

@@ -0,0 +1,54 @@
+package unionfind
+
+// Robert Sedgewick 算法（第4版） 1.5.2.7
+// union-find (加权 quick-union)，还作了路径压缩优化
+
+// union is ...
+type union struct {
+	id    []int // 父链接数组(由触点索引)
+	sz    []int // (由触点索引的) 各个根节点所对应的分量的大小
+	count int   // 连通分量的数量
+}
+
+func newUnion(N int) *union {
+	id := make([]int, N)
+	for i := range id {
+		id[i] = i
+	}
+	sz := make([]int, N)
+	for i := range sz {
+		sz[i] = 1
+	}
+	return &union{
+		id:    id,
+		sz:    sz,
+		count: N,
+	}
+}
+
+func (u *union) isConnected(p, q int) bool {
+	return u.find(p) == u.find(q)
+}
+
+func (u *union) find(p int) int {
+	// 跟随连接找到根节点
+	for p != u.id[p] {
+		p = u.id[p]
+	}
+	return p
+}
+
+func (u *union) union(p, q int) {
+	i, j := u.find(p), u.find(q)
+	if i == j {
+		return
+	}
+	if u.sz[i] > u.sz[j] {
+		i, j = j, i
+	}
+	// 将小树的根节点连接到大树的根节点
+	u.id[i] = j
+	u.sz[j] += u.sz[i]
+	u.count--
+	return
+}