<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 ceilInd(vector<int>tail,int l ,int r ,int k)
    {
        
        while(l<r)
        {
            int m = l+(r-l)/2;
            if(tail[m]>=k)
            r = m;
            else
            l = m+1;
        }
        return r;
    }
    int lengthOfLIS(vector<int>& nums) 
    {
        int n = nums.size();
        vector<int>temp(n);
        int l=0;
        for(int i=0;i<n;i++)
        {
            if(i==0||nums[i]>temp[l-1])
            temp[l++] = nums[i];
            else
            {
                int t = ceilInd(temp,0,l-1,nums[i]);
                temp[t] = nums[i];
            }
        }
        return l;
    }
};
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