@@ -34495,18 +34495,18 @@
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<ul class="md-nav__list">
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<li class="md-nav__item">
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- <a href="#solution-1" class="md-nav__link">
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+ <a href="#solution-1-direct-enumeration " class="md-nav__link">
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<span class="md-ellipsis">
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- Solution 1
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+ Solution 1: Direct Enumeration
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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- <a href="#solution-2" class="md-nav__link">
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+ <a href="#solution-2-direct-enumeration-alternative-approach " class="md-nav__link">
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<span class="md-ellipsis">
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- Solution 2
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+ Solution 2: Direct Enumeration (Alternative Approach)
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</span>
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</a>
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@@ -75820,8 +75820,10 @@ <h2 id="description">Description</h2>
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<h2 id="solutions">Solutions</h2>
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<!-- solution:start -->
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- <h3 id="solution-1">Solution 1</h3>
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- <div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label></div>
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+ <h3 id="solution-1-direct-enumeration">Solution 1: Direct Enumeration</h3>
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+ <p>Starting from $1$, we enumerate $a$, then $b = n - a$. For each $a$ and $b$, we convert them to strings and concatenate them, then check if they contain the character '0'. If they do not contain '0', we have found the answer and return $[a, b]$.</p>
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+ <p>The time complexity is $O(n \times \log n)$, where $n$ is the integer given in the problem. The space complexity is $O(\log n)$.</p>
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+ <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">TypeScript</label></div>
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<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1</span>
@@ -75901,14 +75903,34 @@ <h3 id="solution-1">Solution 1</h3>
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<span class="p">}</span>
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</code></pre></div></td></tr></table></div>
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</div>
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+ <div class="tabbed-block">
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+ <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal">1</span>
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+ <span class="normal">2</span>
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+ <span class="normal">3</span>
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+ <span class="normal">4</span>
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+ <span class="normal">5</span>
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+ <span class="normal">6</span>
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+ <span class="normal">7</span>
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+ <span class="normal">8</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">getNoZeroIntegers</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">a</span><span class="p">;</span>
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+ <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="sb">`</span><span class="si">${</span><span class="nx">a</span><span class="si">}${</span><span class="nx">b</span><span class="si">}</span><span class="sb">`</span><span class="p">.</span><span class="nx">includes</span><span class="p">(</span><span class="s1">'0'</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">];</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="p">}</span>
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+ </code></pre></div></td></tr></table></div>
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+ </div>
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</div>
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</div>
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<!-- solution:end -->
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<!-- solution:start -->
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- <h3 id="solution-2">Solution 2</h3>
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- <div class="tabbed-set tabbed-alternate" data-tabs="2:4"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python3</label><label for="__tabbed_2_2">Java</label><label for="__tabbed_2_3">C++</label><label for="__tabbed_2_4">Go</label></div>
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+ <h3 id="solution-2-direct-enumeration-alternative-approach">Solution 2: Direct Enumeration (Alternative Approach)</h3>
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+ <p>In Solution 1, we converted $a$ and $b$ into strings and concatenated them, then checked if they contained the character '0'. Here, we can use a function $f(x)$ to check whether $x$ contains the character '0', and then directly enumerate $a$, checking whether both $a$ and $b = n - a$ do not contain the character '0'. If they do not, we have found the answer and return $[a, b]$.</p>
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+ <p>The time complexity is $O(n \times \log n)$, where $n$ is the integer given in the problem. The space complexity is $O(1)$.</p>
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+ <div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python3</label><label for="__tabbed_2_2">Java</label><label for="__tabbed_2_3">C++</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">TypeScript</label></div>
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<div class="tabbed-content">
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<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 1</span>
@@ -76052,6 +76074,40 @@ <h3 id="solution-2">Solution 2</h3>
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<span class="p">}</span>
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</code></pre></div></td></tr></table></div>
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</div>
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+ <div class="tabbed-block">
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+ <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 1</span>
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+ <span class="normal"> 2</span>
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+ <span class="normal"> 3</span>
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+ <span class="normal"> 4</span>
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+ <span class="normal"> 5</span>
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+ <span class="normal"> 6</span>
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+ <span class="normal"> 7</span>
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+ <span class="normal"> 8</span>
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+ <span class="normal"> 9</span>
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+ <span class="normal">10</span>
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+ <span class="normal">11</span>
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+ <span class="normal">12</span>
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+ <span class="normal">13</span>
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+ <span class="normal">14</span>
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+ <span class="normal">15</span>
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+ <span class="normal">16</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">getNoZeroIntegers</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">f</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(;</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
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+ <span class="w"> </span><span class="p">};</span>
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+ <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">a</span><span class="p">;</span>
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+ <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">f</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">f</span><span class="p">(</span><span class="nx">b</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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+ <span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">];</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="w"> </span><span class="p">}</span>
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+ <span class="p">}</span>
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+ </code></pre></div></td></tr></table></div>
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+ </div>
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</div>
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</div>
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<!-- solution:end -->
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