0089. Gray Code

Author: coderbean

markdown/0089. Gray Code.md

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+### [89\. Gray Code](https://leetcode.com/problems/gray-code/)
+
+Difficulty: **Medium**
+
+
+The gray code is a binary numeral system where two successive values differ in only one bit.
+
+Given a non-negative integer _n_ representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.
+
+**Example 1:**
+
+```
+Input: 2
+Output: [0,1,3,2]
+Explanation:
+00 - 0
+01 - 1
+11 - 3
+10 - 2
+
+For a given n, a gray code sequence may not be uniquely defined.
+For example, [0,2,3,1] is also a valid gray code sequence.
+
+00 - 0
+10 - 2
+11 - 3
+01 - 1
+```
+
+**Example 2:**
+
+```
+Input: 0
+Output: [0]
+Explanation: We define the gray code sequence to begin with 0.
+             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
+             Therefore, for n = 0 the gray code sequence is [0].
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public List<Integer> grayCode(int n) {
+        List<Integer> result = new ArrayList<>();
+        result.add(0);
+        for (int i = 0; i < n; i++) {
+            for (int j = result.size() - 1; j >= 0; j--) { // 从尾部开始，用于保持连续（即每次只差一个bit位）
+                result.add(result.get(j) | 1 << i);
+            }
+        }
+        return result;
+    }
+}
+```
+![pic](https://raw.githubusercontent.com/PicGoBed/PicBed/master/2019-08-01-RdPkMU.jpg)

src/main/java/leetcode/_89_/Main.java

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+package leetcode._89_;
+
+/**
+ * Created by zhangbo54 on 2019-03-04.
+ */
+public class Main {
+    public static void main(String[] args) {
+        Solution solution = new Solution();
+        System.out.println(solution.grayCode(2));
+    }
+}
+

src/main/java/leetcode/_89_/Solution.java

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+package leetcode._89_;
+
+import java.util.ArrayList;
+import java.util.List;
+
+class Solution {
+    public List<Integer> grayCode(int n) {
+        List<Integer> result = new ArrayList<>();
+        result.add(0);
+        for (int i = 0; i < n; i++) {
+            for (int j = result.size() - 1; j >= 0; j--) { // 从尾部开始，用于保持连续（即每次只差一个bit位）
+                result.add(result.get(j) | 1 << i);
+            }
+        }
+        return result;
+    }
+}

src/main/java/leetcode/_89_/solution.md

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+### [89\. Gray Code](https://leetcode.com/problems/gray-code/)
+
+Difficulty: **Medium**
+
+
+The gray code is a binary numeral system where two successive values differ in only one bit.
+
+Given a non-negative integer _n_ representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.
+
+**Example 1:**
+
+```
+Input: 2
+Output: [0,1,3,2]
+Explanation:
+00 - 0
+01 - 1
+11 - 3
+10 - 2
+
+For a given n, a gray code sequence may not be uniquely defined.
+For example, [0,2,3,1] is also a valid gray code sequence.
+
+00 - 0
+10 - 2
+11 - 3
+01 - 1
+```
+
+**Example 2:**
+
+```
+Input: 0
+Output: [0]
+Explanation: We define the gray code sequence to begin with 0.
+             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
+             Therefore, for n = 0 the gray code sequence is [0].
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public List<Integer> grayCode(int n) {
+        List<Integer> result = new ArrayList<>();
+        result.add(0);
+        for (int i = 0; i < n; i++) {
+            for (int j = result.size() - 1; j >= 0; j--) { // 从尾部开始，用于保持连续（即每次只差一个bit位）
+                result.add(result.get(j) | 1 << i);
+            }
+        }
+        return result;
+    }
+}
+```
+![pic](https://raw.githubusercontent.com/PicGoBed/PicBed/master/2019-08-01-RdPkMU.jpg)