<p>Given an integer array <code>nums</code>, return <em>the length of the longest <strong>strictly increasing </strong></em><span data-keyword="subsequence-array"><em><strong>subsequence</strong></em></span>.</p>

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

<pre>
<strong>Input:</strong> nums = [10,9,2,5,3,7,101,18]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,1,0,3,2,3]
<strong>Output:</strong> 4
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7,7,7]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2500</code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

<p>&nbsp;</p>
<p><b>Follow up:</b>&nbsp;Can you come up with an algorithm that runs in&nbsp;<code>O(n log(n))</code> time complexity?</p>

class Solution {
public:
    int lengthOfLIS(std::vector<int> &nums) {
        std::vector<int> dp(nums.size());
        auto comparator = [&nums](int a, int b) { return nums[a] > nums[b]; };

        std::priority_queue<int, std::vector<int>, decltype(comparator)> pq(
            comparator);

        for (int i = nums.size() - 1; i >= 0; i--) {
            std::vector<int> popped;
            while (!pq.empty() && nums[i] >= nums[pq.top()]) {
                popped.push_back(pq.top());
                pq.pop();
            }

            if (pq.empty()) {
                dp[i] = 1;
            } else {
                dp[i] = dp[pq.top()] + 1;
            }

            for (auto idx : popped) {
                if (dp[idx] >= dp[i]) {
                    pq.push(idx);
                }
            }
            pq.push(i);
        }

        int max = 0;
        for (auto d : dp) {
            max = std::max(max, d);
        }

        return max;
    }
};
74475