leetcode-problemset/leetcode/originData/maximum-xor-product.json

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            "title": "Maximum Xor Product",
            "titleSlug": "maximum-xor-product",
            "content": "<p>Given three integers <code>a</code>, <code>b</code>, and <code>n</code>, return <em>the <strong>maximum value</strong> of</em> <code>(a XOR x) * (b XOR x)</code> <em>where</em> <code>0 &lt;= x &lt; 2<sup>n</sup></code>.</p>\n\n<p>Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p><strong>Note</strong> that <code>XOR</code> is the bitwise XOR operation.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 12, b = 5, n = 4\n<strong>Output:</strong> 98\n<strong>Explanation:</strong> For x = 2, (a XOR x) = 14 and (b XOR x) = 7. Hence, (a XOR x) * (b XOR x) = 98. \nIt can be shown that 98 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup><span style=\"font-size: 10.8333px;\">.</span>\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 6, b = 7 , n = 5\n<strong>Output:</strong> 930\n<strong>Explanation:</strong> For x = 25, (a XOR x) = 31 and (b XOR x) = 30. Hence, (a XOR x) * (b XOR x) = 930.\nIt can be shown that 930 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> a = 1, b = 6, n = 3\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> For x = 5, (a XOR x) = 4 and (b XOR x) = 3. Hence, (a XOR x) * (b XOR x) = 12.\nIt can be shown that 12 is the maximum value of (a XOR x) * (b XOR x) for all 0 &lt;= x &lt; 2<sup>n</sup>.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= a, b &lt; 2<sup>50</sup></code></li>\n\t<li><code>0 &lt;= n &lt;= 50</code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    int maximumXorProduct(long long a, long long b, int n) {\n        \n    }\n};",
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                    "lang": "Python",
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                    "code": "class Solution(object):\n    def maximumXorProduct(self, a, b, n):\n        \"\"\"\n        :type a: int\n        :type b: int\n        :type n: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "public class Solution {\n    public int MaximumXorProduct(long a, long b, int n) {\n        \n    }\n}",
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                    "lang": "JavaScript",
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                    "code": "/**\n * @param {number} a\n * @param {number} b\n * @param {number} n\n * @return {number}\n */\nvar maximumXorProduct = function(a, b, n) {\n    \n};",
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                    "code": "function maximumXorProduct(a: number, b: number, n: number): number {\n    \n};",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer $a\n     * @param Integer $b\n     * @param Integer $n\n     * @return Integer\n     */\n    function maximumXorProduct($a, $b, $n) {\n        \n    }\n}",
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                    "code": "class Solution {\n    func maximumXorProduct(_ a: Int, _ b: Int, _ n: Int) -> Int {\n        \n    }\n}",
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                    "lang": "Kotlin",
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                    "code": "class Solution {\n    fun maximumXorProduct(a: Long, b: Long, n: Int): Int {\n        \n    }\n}",
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                    "lang": "Dart",
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                    "code": "class Solution {\n  int maximumXorProduct(int a, int b, int n) {\n    \n  }\n}",
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                    "lang": "Go",
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                    "code": "func maximumXorProduct(a int64, b int64, n int) int {\n    \n}",
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                    "code": "# @param {Integer} a\n# @param {Integer} b\n# @param {Integer} n\n# @return {Integer}\ndef maximum_xor_product(a, b, n)\n    \nend",
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                    "code": "object Solution {\n    def maximumXorProduct(a: Long, b: Long, n: Int): Int = {\n        \n    }\n}",
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                    "lang": "Rust",
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                    "code": "impl Solution {\n    pub fn maximum_xor_product(a: i64, b: i64, n: i32) -> i32 {\n        \n    }\n}",
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                    "lang": "Racket",
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                    "code": "(define/contract (maximum-xor-product a b n)\n  (-> exact-integer? exact-integer? exact-integer? exact-integer?)\n  )",
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                    "code": "defmodule Solution do\n  @spec maximum_xor_product(a :: integer, b :: integer, n :: integer) :: integer\n  def maximum_xor_product(a, b, n) do\n    \n  end\nend",
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            "hints": [
                "Iterate over bits from most significant to least significant.",
                "For the <code>i<sup>th</sup></code> bit, if both <code>a</code> and <code>b</code> have the same value, we can always make <code>x</code>’s <code>i<sup>th</sup></code> bit different from <code>a</code> and <code>b</code>, so <code>a ^ x</code> and <code>b ^ x</code> both have the <code>i<sup>th</sup></cod> bit set.",
                "Otherwise, we can only set the <code>i<sup>th</sup></code> bit of one of <code>a ^ x</code> or <code>b ^ x</code>. Depending on the previous bits of  <code>a ^ x</code> or <code>b ^ x</code>, we should set the smaller value’s <code>i<sup>th</sup></code> bit."
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