<p>Given an integer array <code>nums</code>, return <em>the maximum result of </em><code>nums[i] XOR nums[j]</code>, where <code>0 &lt;= i &lt;= j &lt; n</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,10,5,25,2,8]
<strong>Output:</strong> 28
<strong>Explanation:</strong> The maximum result is 5 XOR 25 = 28.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [14,70,53,83,49,91,36,80,92,51,66,70]
<strong>Output:</strong> 127
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

std::string fromIntToBitString(uint32_t num)
{
    std::string bits;
    for(int i=0; i<32; i++){
        bits.push_back('0' + ((num >> i) & 1));
    }

    std::reverse(bits.begin(), bits.end());
    return bits;
}


struct BitPrefixNode {
    BitPrefixNode* zero_left;
    BitPrefixNode* one_right;
};

void add(BitPrefixNode* trie, const std::string& bits)
{
    for(char bit : bits){
        if(bit == '0') {
            if(trie->zero_left == nullptr) 
                trie->zero_left = new BitPrefixNode();
            trie = trie->zero_left;
        }
        else {
            if(trie->one_right == nullptr)
                trie->one_right = new BitPrefixNode();
            trie = trie->one_right;
        }
    }

}


std::string max_XOR_for_num(BitPrefixNode* trie, const std::string& num)
{
    std::string max_xor;
    for(char bit : num) {
        if(bit == '0') {
            if(trie->one_right != nullptr){
                max_xor.push_back('1');
                trie = trie->one_right;
            } else {
                max_xor.push_back('0');
                trie = trie->zero_left;
            }
        } else { //1
            if(trie->zero_left != nullptr) {
                max_xor.push_back('1');
                trie = trie->zero_left;     
            } else {
                max_xor.push_back('0');
                trie = trie->one_right;
            }
        }
    }

    return max_xor;
}



class Solution {
public:
    int findMaximumXOR(std::vector<int>& nums) {
        BitPrefixNode* trie = new BitPrefixNode();
        std::string max_xor(32,'0');
        for(u_int32_t num : nums){
            std::string bits_num = fromIntToBitString(num);
            add(trie, bits_num);
            
            std::string max_xor_candidate = max_XOR_for_num(trie, bits_num);
            if(max_xor_candidate > max_xor)
                max_xor = max_xor_candidate;
        }

        
        return std::stoi(max_xor, nullptr, 2);
    }
};
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