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<div class="headertitle"><div class="title">longest_increasing_subsequence_using_binary_search.cpp File Reference</div></div>
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<div class="contents">
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<p>find the length of the Longest Increasing Subsequence (LIS) using <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence" target="_blank">Binary Search</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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<code>#include <algorithm></code><br />
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<code>#include <cstdint></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for longest_increasing_subsequence_using_binary_search.cpp:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a313539d9a97fc6e121ce496873ba892e" id="r_a313539d9a97fc6e121ce496873ba892e"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a313539d9a97fc6e121ce496873ba892e"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< T > &nums)</td></tr>
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<tr class="memdesc:a313539d9a97fc6e121ce496873ba892e"><td class="mdescLeft"> </td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> <br /></td></tr>
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<tr class="separator:a313539d9a97fc6e121ce496873ba892e"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
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<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft"> </td><td class="mdescRight">Test cases for Longest Increasing Subsequence function. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function to run tests. <br /></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>find the length of the Longest Increasing Subsequence (LIS) using <a href="https://en.wikipedia.org/wiki/Longest_increasing_subsequence" target="_blank">Binary Search</a> </p>
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||||
<p>Given an integer array nums, return the length of the longest strictly increasing subsequence. The longest increasing subsequence is described as a subsequence of an array where: All elements of the subsequence are in increasing order. This subsequence itself is of the longest length possible.</p>
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<p>For solving this problem we have Three Approaches :-</p>
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<p>Approach 1 :- Using Brute Force The first approach that came to your mind is the Brute Force approach where we generate all subsequences and then manually filter the subsequences whose elements come in increasing order and then return the longest such subsequence. Time Complexity :- O(2^n) It's time complexity is exponential. Therefore we will try some other approaches.</p>
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<p>Approach 2 :- Using Dynamic Programming To generate all subsequences we will use recursion and in the recursive logic we will figure out a way to solve this problem. Recursive Logic to solve this problem:-</p><ol type="1">
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<li>We only consider the element in the subsequence if the element is grater then the last element present in the subsequence</li>
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<li>When we consider the element we will increase the length of subsequence by 1 Time Complexity: O(N*N) Space Complexity: O(N*N) + O(N)</li>
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</ol>
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<p>This approach is better then the previous Brute Force approach so, we can consider this approach.</p>
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<p>But when the Constraints for the problem is very larger then this approach fails</p>
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<p>Approach 3 :- Using Binary Search Other approaches use additional space to create a new subsequence Array. Instead, this solution uses the existing nums Array to build the subsequence array. We can do this because the length of the subsequence array will never be longer than the current index.</p>
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<p>Time complexity: O(n∗log(n)) Space complexity: O(1)</p>
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<p>This approach consider Most optimal Approach for solving this problem</p>
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||||
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/namanmodi65" target="_blank">Naman Jain</a> </dd></dl>
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||||
</div><h2 class="groupheader">Function Documentation</h2>
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||||
<a id="a313539d9a97fc6e121ce496873ba892e" name="a313539d9a97fc6e121ce496873ba892e"></a>
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||||
<h2 class="memtitle"><span class="permalink"><a href="#a313539d9a97fc6e121ce496873ba892e">◆ </a></span>longest_increasing_subsequence_using_binary_search()</h2>
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<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
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template<typename T > </div>
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<table class="memname">
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||||
<tr>
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||||
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> longest_increasing_subsequence_using_binary_search </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< T > &</td> <td class="paramname"><span class="paramname"><em>nums</em></span></td><td>)</td>
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<td></td>
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</tr>
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</div><div class="memdoc">
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> </p>
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||||
<p>for std::assert for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">std::lower_bound</a></p>
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<p>Function to find the length of the Longest Increasing Subsequence (LIS) using Binary Search </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>The type of the elements in the input vector </td></tr>
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</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">nums</td><td>The input vector of elements of type T </td></tr>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>The length of the longest increasing subsequence </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (nums.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/empty.html">empty</a>()) <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 67</span> </div>
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<div class="line"><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<T></a> ans;</div>
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<div class="line"><span class="lineno"> 69</span> ans.push_back(nums[0]);</div>
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<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> i = 1; i < nums.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
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<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (nums[i] > ans.back()) {</div>
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<div class="line"><span class="lineno"> 72</span> ans.push_back(nums[i]);</div>
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<div class="line"><span class="lineno"> 73</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 74</span> <span class="keyword">auto</span> idx = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">std::lower_bound</a>(ans.begin(), ans.end(), nums[i]) - ans.begin();</div>
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<div class="line"><span class="lineno"> 75</span> ans[idx] = nums[i];</div>
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<div class="line"><span class="lineno"> 76</span> }</div>
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<div class="line"><span class="lineno"> 77</span> }</div>
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<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> <span class="keyword">static_cast<</span><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a><span class="keyword">></span>(ans.size());</div>
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<div class="line"><span class="lineno"> 79</span>}</div>
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<div class="ttc" id="aempty_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/empty.html">std::vector::empty</a></div><div class="ttdeci">T empty(T... args)</div></div>
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||||
<div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a></div></div>
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<div class="ttc" id="alower_bound_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">std::lower_bound</a></div><div class="ttdeci">T lower_bound(T... args)</div></div>
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||||
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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||||
<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a></div></div>
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<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d9/d5f/longest__increasing__subsequence__using__binary__search_8cpp_a313539d9a97fc6e121ce496873ba892e_cgraph.svg" width="372" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memproto">
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<table class="memname">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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</tr>
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</div><div class="memdoc">
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<p>Main function to run tests. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 114</span> {</div>
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<div class="line"><span class="lineno"> 115</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self test implementation</span></div>
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<div class="line"><span class="lineno"> 116</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 117</span>}</div>
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<div class="ttc" id="alongest__increasing__subsequence__using__binary__search_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Test cases for Longest Increasing Subsequence function.</div><div class="ttdef"><b>Definition</b> longest_increasing_subsequence_using_binary_search.cpp:85</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">◆ </a></span>tests()</h2>
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<td class="memname">static void tests </td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Test cases for Longest Increasing Subsequence function. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 85</span> {</div>
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<div class="line"><span class="lineno"> 86</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> arr = {10, 9, 2, 5, 3, 7, 101, 18};</div>
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<div class="line"><span class="lineno"> 87</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr) == 4);</div>
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<div class="line"><span class="lineno"> 88</span> </div>
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<div class="line"><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> arr2 = {0, 1, 0, 3, 2, 3};</div>
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<div class="line"><span class="lineno"> 90</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr2) == 4);</div>
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<div class="line"><span class="lineno"> 91</span> </div>
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<div class="line"><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> arr3 = {7, 7, 7, 7, 7, 7, 7};</div>
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<div class="line"><span class="lineno"> 93</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr3) == 1);</div>
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<div class="line"><span class="lineno"> 94</span> </div>
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<div class="line"><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> arr4 = {-10, -1, -5, 0, 5, 1, 2};</div>
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<div class="line"><span class="lineno"> 96</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr4) == 5);</div>
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<div class="line"><span class="lineno"> 97</span> </div>
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<div class="line"><span class="lineno"> 98</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<double></a> arr5 = {3.5, 1.2, 2.8, 3.1, 4.0};</div>
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<div class="line"><span class="lineno"> 99</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr5) == 4);</div>
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<div class="line"><span class="lineno"> 100</span> </div>
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<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<char></a> arr6 = {<span class="charliteral">'a'</span>, <span class="charliteral">'b'</span>, <span class="charliteral">'c'</span>, <span class="charliteral">'a'</span>, <span class="charliteral">'d'</span>};</div>
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<div class="line"><span class="lineno"> 102</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr6) == 4);</div>
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<div class="line"><span class="lineno"> 103</span> </div>
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<div class="line"><span class="lineno"> 104</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> arr7 = {};</div>
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<div class="line"><span class="lineno"> 105</span> assert(<a class="code hl_function" href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a>(arr7) == 0);</div>
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<div class="line"><span class="lineno"> 106</span> </div>
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<div class="line"><span class="lineno"> 107</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"All tests have successfully passed!\n"</span>;</div>
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<div class="line"><span class="lineno"> 108</span>}</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="alongest__increasing__subsequence__using__binary__search_8cpp_html_a313539d9a97fc6e121ce496873ba892e"><div class="ttname"><a href="#a313539d9a97fc6e121ce496873ba892e">longest_increasing_subsequence_using_binary_search</a></div><div class="ttdeci">std::uint32_t longest_increasing_subsequence_using_binary_search(std::vector< T > &nums)</div><div class="ttdoc">for std::uint32_t</div><div class="ttdef"><b>Definition</b> longest_increasing_subsequence_using_binary_search.cpp:65</div></div>
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