<p>Given a positive integer <code>n</code>, return the number of the integers in the range <code>[0, n]</code> whose binary representations <strong>do not</strong> contain consecutive ones.</p>

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

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong>
Here are the non-negative integers &lt;= 5 with their corresponding binary representations:
0 : 0
1 : 1
2 : 10
3 : 11
4 : 100
5 : 101
Among them, only integer 3 disobeys the rule (two consecutive ones) and the other 5 satisfy the rule. 
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    int solve(std::string &str, int start, int len, bool isLimit, bool isOne,
              std::vector<std::vector<std::vector<int>>> &dpTable) {
        if (start >= len) {
            return 1;
        }

        if (dpTable[start][isLimit][isOne] != -1) return dpTable[start][isLimit][isOne];

        int result = 0;
        int maxDigit = isLimit ? str[start] - '0' : 1;
        for (int digit = 0; digit <= maxDigit; ++digit) {
            if (digit && isOne) continue;
            result += solve(str, start + 1, len, isLimit && digit == maxDigit, digit == 1, dpTable);

        }
        return dpTable[start][isLimit][isOne] = result;
    }
    int findIntegers(int n) {
        std::string str = std::bitset<32>( n ).to_string();
        int len = static_cast<int>(str.size());
        std::vector<std::vector<std::vector<int>>> dpTable(len,
            std::vector<std::vector<int>>(2, std::vector<int>(2, -1)));

        return solve(str, 0, len, true, false, dpTable);
    }
};
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