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@@ -124,7 +131,7 @@ Functions</h2></td></tr>
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<p >Bubble Sort Worst Case Performance is O (n²). Why is that? Because if you remember Big O Notation, we were calculating the complexity of the algorithms in the nested loops. The n * (n - 1) product gives us O (n²) performance. In the worst case all the steps of the cycle will occur. Bubble Sort (Avarage Case) Performance. Bubble Sort is not an optimal algorithm. in average, O (n²) performance is taken. Bubble Sort Best Case Performance. O (n). However, you can't get the best status in the code we shared above. This happens on the optimized bubble sort algorithm. It's right down there. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="textblock"><p >Range query here is range sum, but the code can be modified to make different queries like range max or min. </p>
|
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<h2 class="memtitle"><span class="permalink"><a href="#ace7f57935b3bb9446f11c239fd89ae79">◆ </a></span>lazy()</h2>
|
||||
<h2 class="memtitle"><span class="permalink"><a href="#ace7f57935b3bb9446f11c239fd89ae79">◆ </a></span>lazy()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae8ae4b1835e5e8aec32f68c5059ed4d4">◆ </a></span>query() <span class="overload">[1/2]</span></h2>
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<div class="line"><span class="lineno"> 178</span> <span class="keywordflow">return</span> curr->val;</div>
|
||||
<div class="line"><span class="lineno"> 179</span> }</div>
|
||||
<div class="line"><span class="lineno"> 180</span> uint32_t mid = i + (j - i) / 2;</div>
|
||||
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|
||||
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|
||||
<div class="line"><span class="lineno"> 181</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="../../dd/d1b/structquery.html">query</a>(i, mid, l, r, curr->left) +</div>
|
||||
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|
||||
<div class="line"><span class="lineno"> 183</span> }</div>
|
||||
<div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_ace7f57935b3bb9446f11c239fd89ae79"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79">range_queries::perSegTree::lazy</a></div><div class="ttdeci">void lazy(const uint32_t &i, const uint32_t &j, std::shared_ptr< Node > const &curr)</div><div class="ttdoc">If there is some value to be propagated to the passed node, value is added to the node and the childr...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:83</div></div>
|
||||
<div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_ae8ae4b1835e5e8aec32f68c5059ed4d4"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">range_queries::perSegTree::query</a></div><div class="ttdeci">int64_t query(const uint32_t &i, const uint32_t &j, const uint32_t &l, const uint32_t &r, std::shared_ptr< Node > const &curr)</div><div class="ttdoc">Querying the range from index l to index r, checking at every node if it has some value to be propaga...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:171</div></div>
|
||||
<div class="ttc" id="astructquery_html"><div class="ttname"><a href="../../dd/d1b/structquery.html">query</a></div><div class="ttdef"><b>Definition:</b> mo.cpp:6</div></div>
|
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<h2 class="memtitle"><span class="permalink"><a href="#ad484002bcb701820d55f32ea5d525571">◆ </a></span>query() <span class="overload">[2/2]</span></h2>
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<dl class="section return"><dt>Returns</dt><dd>sum of elements whose index x satisfies l<=x<=r </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 246</span> {</div>
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<div class="line"><span class="lineno"> 247</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(0, n - 1, l, r, <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[version]);</div>
|
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<div class="line"><span class="lineno"> 247</span> <span class="keywordflow">return</span> <a class="code hl_struct" href="../../dd/d1b/structquery.html">query</a>(0, n - 1, l, r, <a class="code hl_variable" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5">ptrs</a>[version]);</div>
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<div class="line"><span class="lineno"> 248</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a24487eda25123bc4d112e8430821a6c6">◆ </a></span>update() <span class="overload">[1/2]</span></h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a24487eda25123bc4d112e8430821a6c6">◆ </a></span>update() <span class="overload">[1/2]</span></h2>
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<div class="line"><span class="lineno"> 154</span> <span class="keywordflow">return</span> newNode;</div>
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<div class="line"><span class="lineno"> 155</span> }</div>
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<div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_a24487eda25123bc4d112e8430821a6c6"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a24487eda25123bc4d112e8430821a6c6">range_queries::perSegTree::update</a></div><div class="ttdeci">std::shared_ptr< Node > update(const uint32_t &i, const uint32_t &j, const uint32_t &l, const uint32_t &r, const int64_t &value, std::shared_ptr< Node > const &curr)</div><div class="ttdoc">Doing range update, checking at every node if it has some value to be propagated. All nodes affected ...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:135</div></div>
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<div class="ttc" id="ashared_ptr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr< Node ></a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#af87494e6cf012d28c4f5b9d1c15f9c5d">◆ </a></span>update() <span class="overload">[2/2]</span></h2>
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<h2 class="groupheader">Member Data Documentation</h2>
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<ul>
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<li class="navelem"><a class="el" href="../../dd/d69/namespacerange__queries.html">range_queries</a></li><li class="navelem"><a class="el" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html">perSegTree</a></li>
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@@ -121,20 +128,20 @@ Functions</h2></td></tr>
|
||||
<p >Fermat's Little Theorem state that </p><p class="formulaDsp">
|
||||
\[ϕ(m) = m-1\]
|
||||
</p>
|
||||
<p> where \(m\) is a prime number. </p><p class="formulaDsp">
|
||||
<p> where \(m\) is a prime number. </p><p class="formulaDsp">
|
||||
\begin{eqnarray*}
|
||||
a \cdot x &≡& 1 \;\text{mod}\; m\\
|
||||
x &≡& a^{-1} \;\text{mod}\; m
|
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\end{eqnarray*}
|
||||
</p>
|
||||
<p> Using Euler's theorem we can modify the equation. </p><p class="formulaDsp">
|
||||
<p> Using Euler's theorem we can modify the equation. </p><p class="formulaDsp">
|
||||
\[
|
||||
a^{ϕ(m)} ≡ 1 \;\text{mod}\; m
|
||||
\]
|
||||
</p>
|
||||
<p> (Where '^' denotes the exponent operator)</p>
|
||||
<p >Here 'ϕ' is Euler's Totient Function. For modular inverse existence 'a' and 'm' must be relatively primes numbers. To apply Fermat's Little Theorem is necessary that 'm' must be a prime number. Generally in many competitive programming competitions 'm' is either 1000000007 (1e9+7) or 998244353.</p>
|
||||
<p >We considered m as large prime (1e9+7). \(a^{ϕ(m)} ≡ 1 \;\text{mod}\; m\) (Using Euler's Theorem) \(ϕ(m) = m-1\) using Fermat's Little Theorem. \(a^{m-1} ≡ 1 \;\text{mod}\; m\) Now multiplying both side by \(a^{-1}\). </p><p class="formulaDsp">
|
||||
<p >We considered m as large prime (1e9+7). \(a^{ϕ(m)} ≡ 1 \;\text{mod}\; m\) (Using Euler's Theorem) \(ϕ(m) = m-1\) using Fermat's Little Theorem. \(a^{m-1} ≡ 1 \;\text{mod}\; m\) Now multiplying both side by \(a^{-1}\). </p><p class="formulaDsp">
|
||||
\begin{eqnarray*}
|
||||
a^{m-1} \cdot a^{-1} &≡& a^{-1} \;\text{mod}\; m\\
|
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a^{m-2} &≡& a^{-1} \;\text{mod}\; m
|
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@@ -149,7 +156,7 @@ Hence, \(3^{-1} \;\text{mod}\; 7 = 5\) or \(3 \times 5 \;\text{mod}\; 7 = 1 \;\
|
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</ul>
|
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</div><h2 class="groupheader">Function Documentation</h2>
|
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<a id="a4c6eefd1254eab3e8d34bf02c205e0f4" name="a4c6eefd1254eab3e8d34bf02c205e0f4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a4c6eefd1254eab3e8d34bf02c205e0f4">◆ </a></span>binExpo()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a4c6eefd1254eab3e8d34bf02c205e0f4">◆ </a></span>binExpo()</h2>
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@@ -197,7 +204,7 @@ Hence, \(3^{-1} \;\text{mod}\; 7 = 5\) or \(3 \times 5 \;\text{mod}\; 7 = 1 \;\
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<h2 class="memtitle"><span class="permalink"><a href="#a09660096b134753128952246f4f4e4bd">◆ </a></span>isPrime()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a09660096b134753128952246f4f4e4bd">◆ </a></span>isPrime()</h2>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p >Implementation of [Morse Code] (<a href="https://en.wikipedia.org/wiki/Morse_code">https://en.wikipedia.org/wiki/Morse_code</a>). </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/imdeep2905" target="_blank">Deep Raval</a></dd></dl>
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<p>Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called dots and dashes or dits and dahs. Morse code is named after Samuel Morse, an inventor of the telegraph. </p>
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<p >Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called dots and dashes or dits and dahs. Morse code is named after Samuel Morse, an inventor of the telegraph. </p>
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<div class="line"><span class="lineno"> 257</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(A.size(), sub_size); <span class="comment">// Return shape as pair</span></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d8/d77/namespacemachine__learning_ae868ad43698a1d69ba46ea3827d7d2c3_cgraph.svg" width="556" height="307"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#ac1bdaa2a724b4ce6a6bb371a5dbe2e7e">◆ </a></span>zeroes_initialization()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ac1bdaa2a724b4ce6a6bb371a5dbe2e7e">◆ </a></span>zeroes_initialization()</h2>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a7220dbb7fa896d83bfb7a50e4fce1786">◆ </a></span>MIN_DISTANCE</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a7220dbb7fa896d83bfb7a50e4fce1786">◆ </a></span>MIN_DISTANCE</h2>
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