add 667

fishercoder1534 · fishercoder1534 · commit aa503b94ccba · 2017-08-28T19:37:37.000-07:00
diff --git a/README.md b/README.md
@@ -23,6 +23,7 @@ Your ideas/fixes/algorithms are more than welcome!
 |  #  |      Title     |   Solutions   | Time          | Space         | Difficulty  | Tag          | Notes
 |-----|----------------|---------------|---------------|---------------|-------------|--------------|-----
 |668|[Kth Smallest Number in Multiplication Table](https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_668.java) | O(logm*n) | O(1) | Hard | Binary Search
+|667|[Beautiful Arrangement II](https://leetcode.com/problems/beautiful-arrangement-ii/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_667.java) | O(n) | O(1) | Medium | Array
 |666|[Path Sum IV](https://leetcode.com/problems/path-sum-iv/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_666.java) | O(1) | O(1) | Medium | Tree, DFS
 |665|[Non-decreasing Array](https://leetcode.com/problems/non-decreasing-array/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_665.java) | O(n) | O(n) | Easy |
 |664|[Strange Printer](https://leetcode.com/problems/strange-printer/)|[Solution](../master/src/main/java/com/fishercoder/solutions/_664.java) | O(n^3) | O(n^2) | Hard | DP
diff --git a/src/main/java/com/fishercoder/solutions/_667.java b/src/main/java/com/fishercoder/solutions/_667.java
@@ -0,0 +1,112 @@
+package com.fishercoder.solutions;
+
+import java.util.ArrayList;
+import java.util.HashSet;
+import java.util.List;
+import java.util.Set;
+
+/**
+ * 667. Beautiful Arrangement II
+ *
+ *  Given two integers n and k, you need to construct a list which contains n different positive integers ranging from 1 to n
+ *  and obeys the following requirement:
+ *  Suppose this list is [a1, a2, a3, ... , an],
+ *  then the list [|a1 - a2|, |a2 - a3|, |a3 - a4|, ... , |an-1 - an|] has exactly k distinct integers.
+ *  If there are multiple answers, print any of them.
+
+ Example 1:
+
+ Input: n = 3, k = 1
+ Output: [1, 2, 3]
+ Explanation: The [1, 2, 3] has three different positive integers ranging from 1 to 3, and the [1, 1] has exactly 1 distinct integer: 1.
+
+ Example 2:
+
+ Input: n = 3, k = 2
+ Output: [1, 3, 2]
+ Explanation: The [1, 3, 2] has three different positive integers ranging from 1 to 3, and the [2, 1] has exactly 2 distinct integers: 1 and 2.
+
+ Note:
+
+ The n and k are in the range 1 <= k < n <= 104.
+ */
+
+public class _667 {
+
+	public static class Solutoin1 {
+		/**This brute force solution will result in TLE as soon as n = 10 and k = 4.*/
+		public int[] constructArray(int n, int k) {
+			List<List<Integer>> allPermutaions = findAllPermutations(n);
+			int[] result = new int[n];
+			for (List<Integer> perm : allPermutaions) {
+				if (isBeautifulArrangement(perm, k)) {
+					convertListToArray(result, perm);
+					break;
+				}
+			}
+			return result;
+		}
+
+		private void convertListToArray(int[] result, List<Integer> perm) {
+			for (int i = 0; i < perm.size(); i++) {
+				result[i] = perm.get(i);
+			}
+		}
+
+		private boolean isBeautifulArrangement(List<Integer> perm, int k) {
+			Set<Integer> diff = new HashSet<>();
+			for (int i = 0; i < perm.size() - 1; i++) {
+				diff.add(Math.abs(perm.get(i) - perm.get(i + 1)));
+			}
+			return diff.size() == k;
+		}
+
+		private List<List<Integer>> findAllPermutations(int n) {
+			List<List<Integer>> result = new ArrayList<>();
+			backtracking(new ArrayList<>(), result, n);
+			return result;
+		}
+
+		private void backtracking(List<Integer> list, List<List<Integer>> result, int n) {
+			if (list.size() == n) {
+				result.add(new ArrayList<>(list));
+				return;
+			}
+			for (int i = 1; i <= n; i++) {
+				if (list.contains(i)) {
+					continue;
+				}
+				list.add(i);
+				backtracking(list, result, n);
+				list.remove(list.size() - 1);
+			}
+		}
+	}
+
+	public static class Solutoin2 {
+		/**This is a very smart solution:
+		 * First, we can see that the max value k could reach is n-1 which
+		 * comes from a sequence like this:
+		 * when n = 8, k = 5, one possible sequence is:
+		 * 1, 8, 2, 7, 3, 4, 5, 6
+		 * absolute diffs are:
+		 *  7, 6, 5, 4, 1, 1, 1
+		 *  so, there are total 5 distinct integers.
+		 *
+		 *  So, we can just form such a sequence by putting the first part first and
+		 *  decrement k along the way, when k becomes 1, we just put the rest numbers in order.*/
+		public int[] constructArray(int n, int k) {
+			int[] result = new int[n];
+			int left = 1;
+			int right = n;
+			for (int i = 0; i < n && left <= right; i++) {
+				if (k > 1) {
+					result[i] = k-- % 2 != 0 ? left++ : right--;
+				} else {
+					result[i] = k % 2 != 0 ? left++ : right--;
+				}
+			}
+			return result;
+		}
+	}
+}
diff --git a/src/test/java/com/fishercoder/_667Test.java b/src/test/java/com/fishercoder/_667Test.java
@@ -0,0 +1,44 @@
+package com.fishercoder;
+
+import com.fishercoder.solutions._667;
+import org.junit.BeforeClass;
+import org.junit.Ignore;
+import org.junit.Test;
+
+import static org.junit.Assert.assertArrayEquals;
+
+public class _667Test {
+	private static _667.Solutoin1 solution1;
+	private static _667.Solutoin2 solution2;
+	private static int[] expected;
+
+	@BeforeClass
+	public static void setup() {
+		solution1 = new _667.Solutoin1();
+		solution2 = new _667.Solutoin2();
+	}
+
+	@Test
+	public void test1() {
+		expected = new int[] { 1, 2, 3 };
+		assertArrayEquals(expected, solution1.constructArray(3, 1));
+		assertArrayEquals(expected, solution2.constructArray(3, 1));
+	}
+
+	@Test
+	@Ignore//this problem requires you to return any one of the legit answer, so the results vary from time to time, so comment out this test
+	public void test2() {
+		expected = new int[] { 1, 3, 2 };
+		assertArrayEquals(expected, solution1.constructArray(3, 2));
+		assertArrayEquals(expected, solution2.constructArray(3, 2));
+	}
+
+	@Test
+	@Ignore//this problem requires you to return any one of the legit answer, so the results vary from time to time, so comment out this test
+	public void test3() {
+		expected = new int[] { 1, 5, 2, 4, 3, 6, 7, 8, 9, 10 };
+		//		assertArrayEquals(expected, solution1.constructArray(10, 4));//this is not working, so comment out
+		assertArrayEquals(expected, solution2.constructArray(10, 4));
+	}
+
+}
