Merge pull request #1443 from wzqwtt/backtracking05

添加（0078.子集、0090.子集II、0491.递增子序列） Scala版本

problems/0078.子集.md

@@ -373,6 +373,60 @@ func subsets(_ nums: [Int]) -> [[Int]] {
 }
 ```
 
+## Scala
+
+思路一: 使用本题解思路
+
+```scala
+object Solution {
+  import scala.collection.mutable
+  def subsets(nums: Array[Int]): List[List[Int]] = {
+    var result = mutable.ListBuffer[List[Int]]()
+    var path = mutable.ListBuffer[Int]()
+
+    def backtracking(startIndex: Int): Unit = {
+      result.append(path.toList) // 存放结果
+      if (startIndex >= nums.size) {
+        return
+      }
+      for (i <- startIndex until nums.size) {
+        path.append(nums(i)) // 添加元素
+        backtracking(i + 1)
+        path.remove(path.size - 1) // 删除
+      }
+    }
+
+    backtracking(0)
+    result.toList
+  }
+}
+```
+
+思路二: 将原问题转换为二叉树，针对每一个元素都有**选或不选**两种选择，直到遍历到最后，所有的叶子节点即为本题的答案：
+
+```scala
+object Solution {
+  import scala.collection.mutable
+  def subsets(nums: Array[Int]): List[List[Int]] = {
+    var result = mutable.ListBuffer[List[Int]]()
+
+    def backtracking(path: mutable.ListBuffer[Int], startIndex: Int): Unit = {
+      if (startIndex == nums.length) {
+        result.append(path.toList)
+        return
+      }
+      path.append(nums(startIndex))
+      backtracking(path, startIndex + 1)  // 选择元素
+      path.remove(path.size - 1)
+      backtracking(path, startIndex + 1)  // 不选择元素
+    }
+
+    backtracking(mutable.ListBuffer[Int](), 0)
+    result.toList
+  }
+}
+```
+
 
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 <div align="center"><img src=https://code-thinking.cdn.bcebos.com/pics/01二维码一.jpg width=500> </img></div>

problems/0090.子集II.md

@@ -434,6 +434,63 @@ func subsetsWithDup(_ nums: [Int]) -> [[Int]] {
 }
 ```
 
+### Scala
+
+不使用userd数组:
+
+```scala
+object Solution {
+  import scala.collection.mutable
+  def subsetsWithDup(nums: Array[Int]): List[List[Int]] = {
+    var result = mutable.ListBuffer[List[Int]]()
+    var path = mutable.ListBuffer[Int]()
+    var num = nums.sorted // 排序
+
+    def backtracking(startIndex: Int): Unit = {
+      result.append(path.toList)
+      if (startIndex >= num.size){
+        return
+      }
+      for (i <- startIndex until num.size) {
+        // 同一树层重复的元素不进入回溯
+        if (!(i > startIndex && num(i) == num(i - 1))) {
+          path.append(num(i))
+          backtracking(i + 1)
+          path.remove(path.size - 1)
+        }
+      }
+    }
+
+    backtracking(0)
+    result.toList
+  }
+}
+```
+
+使用Set去重:
+```scala
+object Solution {
+  import scala.collection.mutable
+  def subsetsWithDup(nums: Array[Int]): List[List[Int]] = {
+    var result = mutable.Set[List[Int]]()
+    var num = nums.sorted
+    def backtracking(path: mutable.ListBuffer[Int], startIndex: Int): Unit = {
+      if (startIndex == num.length) {
+        result.add(path.toList)
+        return
+      }
+      path.append(num(startIndex))
+      backtracking(path, startIndex + 1)  // 选择
+      path.remove(path.size - 1)
+      backtracking(path, startIndex + 1)  // 不选择
+    }
+
+    backtracking(mutable.ListBuffer[Int](), 0)
+
+    result.toList
+  }
+}
+```
 
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 <div align="center"><img src=https://code-thinking.cdn.bcebos.com/pics/01二维码一.jpg width=500> </img></div>

problems/0491.递增子序列.md

@@ -522,5 +522,39 @@ func findSubsequences(_ nums: [Int]) -> [[Int]] {
 ```
 
 
+## Scala
+
+```scala
+object Solution {
+  import scala.collection.mutable
+  def findSubsequences(nums: Array[Int]): List[List[Int]] = {
+    var result = mutable.ListBuffer[List[Int]]()
+    var path = mutable.ListBuffer[Int]()
+
+    def backtracking(startIndex: Int): Unit = {
+      // 集合元素大于1，添加到结果集
+      if (path.size > 1) {
+        result.append(path.toList)
+      }
+
+      var used = new Array[Boolean](201)
+      // 使用循环守卫，当前层没有用过的元素才有资格进入回溯
+      for (i <- startIndex until nums.size if !used(nums(i) + 100)) {
+        // 如果path没元素或 当前循环的元素比path的最后一个元素大，则可以进入回溯
+        if (path.size == 0 || (!path.isEmpty && nums(i) >= path(path.size - 1))) {
+          used(nums(i) + 100) = true
+          path.append(nums(i))
+          backtracking(i + 1)
+          path.remove(path.size - 1)
+        }
+      }
+    }
+
+    backtracking(0)
+    result.toList
+  }
+}
+```
+
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 <div align="center"><img src=https://code-thinking.cdn.bcebos.com/pics/01二维码一.jpg width=500> </img></div>