77. Combinations

README.md

@@ -78,6 +78,9 @@ continually updating 😃.
 * [435. Non-overlapping Intervals](./src/0435_non_overlapping_intervals/greedy_solution.go)   *`greedy;`*  *`dynamic programming`*
 * [455. Assign Cookies](./src/0455_assign_cookies/assign_cookies.go)
 
+### Backtracking
+* [77. Combinations](src/0077_combinations/combinations.go)   *`combine`*
+
 ### Binary Tree
 * [94. Binary Tree Inorder Traversal](./src/0094_binary_tree_inorder_traversal/binary_tree_inorder_traversal.go)   *`stack`*
 * [100. Same Tree](./src/0100_same_tree/same_tree.go)   *`dfs`*

src/0077_combinations/combinations.go

@@ -0,0 +1,40 @@
+/*
+77. Combinations
+https://leetcode.com/problems/combinations/
+
+Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
+*/
+// time: 2019-01-04
+
+package combinations
+
+// backtracking
+// time complexity: O(n^k)
+// space complexity: O(k)
+func combine(n int, k int) [][]int {
+	if n <= 0 || k <= 0 || k > n {
+		return [][]int{}
+	}
+	res := make([][]int, 0)
+	c := make([]int, 0, k)
+	generateCombinations(n, k, 1, c, &res)
+	return res
+}
+
+// 求解C(n,k), 当前已经找到的组合存储在c中，需要从start开始搜索新元素。
+func generateCombinations(n, k, start int, c []int, res *[][]int) {
+	if len(c) == k {
+		cpy := make([]int, k)
+		copy(cpy, c)
+		*res = append(*res, cpy)
+		return
+	}
+	// 回朔法剪枝。
+	// 还有k - len(c)个空位，所以， [i...n]中至少要有k - len(c)个元素
+	// i最多为n-(k-len(c))+1
+	for i := start; i <= n-(k-len(c))+1; i++ {
+		c = append(c, i)
+		generateCombinations(n, k, i+1, c, res)
+		c = c[:len(c)-1]
+	}
+}

src/0077_combinations/combinations_test.go

@@ -0,0 +1,31 @@
+package combinations
+
+import (
+	"reflect"
+	"testing"
+)
+
+func TestCombine(t *testing.T) {
+	type arg struct {
+		n, k int
+	}
+
+	testCases := []arg{
+		{n: 0, k: 2},
+		{n: 2, k: 0},
+		{n: 1, k: 5},
+		{n: 4, k: 2},
+	}
+	expected := [][][]int{
+		{},
+		{},
+		{},
+		{{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}},
+	}
+
+	for index, data := range testCases {
+		if res := combine(data.n, data.k); !reflect.DeepEqual(res, expected[index]) {
+			t.Errorf("expected %v, got %v", expected[index], res)
+		}
+	}
+}

src/README.md

@@ -37,6 +37,7 @@
 |0070|[Climbing Stairs](./0070_climbing_stairs/climbing_stairs.go)|Easy|*`dynamic programming`*|
 |0075|[75. Sort Colors](0075_sort_colors/sort_colors.go)|Medium|*`sort`*|
 |0076|[Minimum Window Substring](./0076_minimum_window_substring/minimum_window_substring.go)|Hard|*`sliding window`*|
+|0077|[77. Combinations](0077_combinations/combinations.go)|Medium|*`backtracking;`**`combine`*|
 |0080|[80. Remove Duplicates from Sorted Array II](0080_remove_duplicates_from_sorted_array2/rdfsa2.go)|Medium|*`double index`*|
 |0088|[88. Merge Sorted Array](0088_merge_sorted_array/msa.go)|Easy|*`sort`*|
 |0094|[Binary Tree Inorder Traversal](./0094_binary_tree_inorder_traversal/binary_tree_inorder_traversal.go)|Medium|*`binary tree`*|