LeetCode 89: Gray Code Generator

最新推荐文章于 2021-04-24 18:14:16 发布

原创最新推荐文章于 2021-04-24 18:14:16 发布 · 286 阅读

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本文介绍了一种递归算法来生成任意位数的格雷码序列。通过展示1到4位格雷码的具体实例，文章详细解释了如何利用已知的n位格雷码生成n+1位格雷码，并提供了C++实现代码。

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See explain of Gray Code: https://en.wikipedia.org/wiki/Gray_code

1-bit Grey Code: 0, 1

2-bits Grey Code: 00, 01, 11, 10

3-bits Grey Code: 000, 001, 011, 010, 110, 111, 101, 100

4-bits Grey Code: 0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, 1101, 1111, 1110, 1010, 1011, 1001, 1000

.....

From the above, we can get a rule of generating n+1 bits Grey Code once we know n bits Grey Code.

n+1 bits Gray Code = 0 + n bits Gray Code, Reverse_Order(n bits Gray Code) + 1; // recursion

    vector<int> grayCode(int n) {
        if(n == 0) return {0};
        if(n == 1) return {0, 1};
        vector<int> bits = grayCode(n-1); // recursion happens here.
        vector<int> result;
        result = bits;
        reverse(bits.begin(), bits.end());
        int mask = 1 << (n-1);
        for(int i = 0; i < bits.size(); ++i) {
                result.push_back(mask | bits[i]);
        }
        return result;
    }