combinations

Author: zgpeace

code/LeetCode/src/backtracking/Combinations.java

@@ -0,0 +1,67 @@
+package backtracking;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.LinkedList;
+import java.util.List;
+
+// https://leetcode.com/problems/combinations/
+public class Combinations {
+
+  public static void main(String[] args) {
+    Combinations obj = new Combinations();
+    int n = 4;
+    int k = 2;
+    List<List<Integer>> resultList = obj.combineBaseOnFormular(n , k);
+    System.out.println("resultList > " + Arrays.toString(resultList.toArray()));
+  }
+
+  public List<List<Integer>> combine(int n, int k) {
+    List<List<Integer>> resultList = new ArrayList<List<Integer>>();
+    if (n == 0 || k == 0) {
+      return resultList;
+    }
+
+    // dfs
+    dfs(n, k, resultList, new ArrayList<Integer>(), 1);
+
+    return resultList;
+  }
+
+  public void dfs(int n, int k, List<List<Integer>> resultList, List<Integer> list, int start) {
+    if (k == 0) {
+      resultList.add(new ArrayList<Integer>(list));
+      return;
+    }
+
+    for (int i = start; i <= n - k + 1; i++) {
+      // [1, 2], [1, 3], [1, 4]
+      // [2, 3], [2, 4]
+      // [3, 4]
+      list.add(i);
+      dfs(n, k - 1, resultList, list, i + 1);
+      list.remove(list.size() - 1);
+    }
+  }
+
+  // based on C(n,k)=C(n-1,k-1)+C(n-1,k)
+  public List<List<Integer>> combineBaseOnFormular(int n, int k) {
+    List<List<Integer>> resultList = new LinkedList<List<Integer>>();
+    if (n < k || k == 0) {
+      return resultList;
+    }
+    resultList = combineBaseOnFormular(n - 1, k - 1);
+    // if at this point resultList is empty, it can only be that k - 1 == 0,
+    // n - 1 < k - 1 is not possible since n >= k (if n < k, the function would have already returned at an early point)
+    if (resultList.isEmpty()) {
+      resultList.add(new LinkedList<Integer>());
+    }
+    for (List<Integer> list: resultList) {
+      list.add(n);
+    }
+
+    resultList.addAll(combineBaseOnFormular(n - 1, k));
+
+    return resultList;
+  }
+}