subsets with duplicates

README.md

@@ -1,4 +1,4 @@
-# 115+ Coding Interview Problems with Detailed Solutions
+# 116+ Coding Interview Problems with Detailed Solutions
 
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@@ -165,6 +165,7 @@ list here →](https://tinyletter.com/hoanhan)
     - [Find the median of a number stream](gtci/median_number_stream_test.go)
   - Subsets
     - [Subsets](gtci/subsets_test.go)
+    - [Subsets with duplicates](gtci/subsets_duplicates_test.go)
 - **[Grokking Dynamic Programming Patterns](https://www.educative.io/courses/grokking-dynamic-programming-patterns-for-coding-interviews)**
   - Knapsack
     - [0/1 Knapsack](gtci/knapsack_test.go)

gtci/subsets_duplicates_test.go

@@ -0,0 +1,88 @@
+/*
+Problem:
+- Given a set with duplicate elements, find all the distinct subsets.
+
+Example:
+- Input: [1 2]
+  Output: [[] [1] [2] [1 2]]
+- Input: [1 2 5]
+  Output: [[] [1] [2] [1 2] [3] [1 3] [2 3] [1 2 3]]
+
+Approach:
+- Similar to the previous problem, but we do two more steps.
+- First, sort the set so that duplicates are next to each other.
+- Second, when we encounter a duplicate while iterating the set,
+  only create subsets from the subsets that added previously.
+- Can use a two-pointer approach to update their start and end window
+  accordingly.
+
+Cost:
+- O(2^n) time, O(2^n) space since we would have a total of 2^n subsets.
+*/
+
+package gtci
+
+import (
+	"sort"
+	"testing"
+
+	"github.com/hoanhan101/algo/common"
+)
+
+func TestFindSubsetsWithDuplicates(t *testing.T) {
+	tests := []struct {
+		in       []int
+		expected [][]int
+	}{
+		{[]int{}, [][]int{{}}},
+		{[]int{1}, [][]int{{}, {1}}},
+		{[]int{1, 2}, [][]int{{}, {1}, {2}, {1, 2}}},
+		{[]int{1, 2, 2}, [][]int{{}, {1}, {2}, {1, 2}, {2, 2}, {1, 2, 2}}},
+		{[]int{2, 1, 2}, [][]int{{}, {1}, {2}, {1, 2}, {2, 2}, {1, 2, 2}}},
+		{[]int{2, 2, 1}, [][]int{{}, {1}, {2}, {1, 2}, {2, 2}, {1, 2, 2}}},
+		{[]int{1, 2, 3}, [][]int{{}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}}},
+		{[]int{3, 2, 1}, [][]int{{}, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}}},
+	}
+
+	for _, tt := range tests {
+		common.Equal(
+			t,
+			tt.expected,
+			findSubsetsWithDuplicates(tt.in),
+		)
+	}
+}
+
+func findSubsetsWithDuplicates(nums []int) [][]int {
+	// sort the set in ascending order.
+	sort.Slice(nums, func(i, j int) bool {
+		return nums[i] < nums[j]
+	})
+
+	// start with an empty set.
+	subsets := [][]int{}
+	subsets = append(subsets, []int{})
+
+	start, end := 0, 0
+
+	// for each number in the set, add it to all existing sets.
+	for i := 0; i < len(nums); i++ {
+		// if the current item and the previous one are the same, update the
+		// start index accordingly so that we only create subset from the one
+		// that added in the previous step.
+		start = 0
+		if i > 0 && nums[i] == nums[i-1] {
+			start = end + 1
+		}
+
+		end = len(subsets) - 1
+
+		for j := start; j < end+1; j++ {
+			set := subsets[j]
+			set = append(set, nums[i])
+			subsets = append(subsets, set)
+		}
+	}
+
+	return subsets
+}