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16777 | 16777 | <ul class="md-nav__list">
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16778 | 16778 |
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16779 | 16779 | <li class="md-nav__item">
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16780 |
| - <a href="#solution-1" class="md-nav__link"> |
| 16780 | + <a href="#solution-1-mathematics" class="md-nav__link"> |
16781 | 16781 | <span class="md-ellipsis">
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16782 |
| - Solution 1 |
16783 |
| - </span> |
16784 |
| - </a> |
16785 |
| - |
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| -</li> |
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| - |
16788 |
| - <li class="md-nav__item"> |
16789 |
| - <a href="#solution-2" class="md-nav__link"> |
16790 |
| - <span class="md-ellipsis"> |
16791 |
| - Solution 2 |
| 16782 | + Solution 1: Mathematics |
16792 | 16783 | </span>
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16793 | 16784 | </a>
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16794 | 16785 |
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@@ -80718,7 +80709,25 @@ <h2 id="description">Description</h2>
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80718 | 80709 | <h2 id="solutions">Solutions</h2>
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80719 | 80710 | <!-- solution:start -->
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80720 | 80711 |
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80721 |
| -<h3 id="solution-1">Solution 1</h3> |
| 80712 | +<h3 id="solution-1-mathematics">Solution 1: Mathematics</h3> |
| 80713 | +<p>Let the minimum value of the array $\textit{nums}$ be $\textit{mi}$, the sum of the array be $\textit{s}$, and the length of the array be $\textit{n}$.</p> |
| 80714 | +<p>Assume the minimum number of operations is $\textit{k}$, and the final value of all elements in the array is $\textit{x}$. Then we have:</p> |
| 80715 | +<p>$$ |
| 80716 | +\begin{aligned} |
| 80717 | +\textit{s} + (\textit{n} - 1) \times \textit{k} &= \textit{n} \times \textit{x} \ |
| 80718 | +\textit{x} &= \textit{mi} + \textit{k} \ |
| 80719 | +\end{aligned} |
| 80720 | +$$</p> |
| 80721 | +<p>Substituting the second equation into the first equation, we get:</p> |
| 80722 | +<p>$$ |
| 80723 | +\begin{aligned} |
| 80724 | +\textit{s} + (\textit{n} - 1) \times \textit{k} &= \textit{n} \times (\textit{mi} + \textit{k}) \ |
| 80725 | +\textit{s} + (\textit{n} - 1) \times \textit{k} &= \textit{n} \times \textit{mi} + \textit{n} \times \textit{k} \ |
| 80726 | +\textit{k} &= \textit{s} - \textit{n} \times \textit{mi} \ |
| 80727 | +\end{aligned} |
| 80728 | +$$</p> |
| 80729 | +<p>Therefore, the minimum number of operations is $\textit{s} - \textit{n} \times \textit{mi}$.</p> |
| 80730 | +<p>The time complexity is $O(n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array.</p> |
80722 | 80731 | <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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80723 | 80732 | <div class="tabbed-content">
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80724 | 80733 | <div class="tabbed-block">
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@@ -80815,39 +80824,6 @@ <h3 id="solution-1">Solution 1</h3>
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80815 | 80824 | </div>
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80816 | 80825 | <!-- solution:end -->
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80817 | 80826 |
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80818 |
| -<!-- solution:start --> |
80819 |
| - |
80820 |
| -<h3 id="solution-2">Solution 2</h3> |
80821 |
| -<div class="tabbed-set tabbed-alternate" data-tabs="2:1"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label></div> |
80822 |
| -<div class="tabbed-content"> |
80823 |
| -<div class="tabbed-block"> |
80824 |
| -<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 1</span> |
80825 |
| -<span class="normal"> 2</span> |
80826 |
| -<span class="normal"> 3</span> |
80827 |
| -<span class="normal"> 4</span> |
80828 |
| -<span class="normal"> 5</span> |
80829 |
| -<span class="normal"> 6</span> |
80830 |
| -<span class="normal"> 7</span> |
80831 |
| -<span class="normal"> 8</span> |
80832 |
| -<span class="normal"> 9</span> |
80833 |
| -<span class="normal">10</span> |
80834 |
| -<span class="normal">11</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">class</span> <span class="nc">Solution</span><span class="w"> </span><span class="p">{</span> |
80835 |
| -<span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">minMoves</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> |
80836 |
| -<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> |
80837 |
| -<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mi</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">30</span><span class="p">;</span> |
80838 |
| -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> |
80839 |
| -<span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span> |
80840 |
| -<span class="w"> </span><span class="n">mi</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">mi</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">);</span> |
80841 |
| -<span class="w"> </span><span class="p">}</span> |
80842 |
| -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">mi</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span> |
80843 |
| -<span class="w"> </span><span class="p">}</span> |
80844 |
| -<span class="p">}</span> |
80845 |
| -</code></pre></div></td></tr></table></div> |
80846 |
| -</div> |
80847 |
| -</div> |
80848 |
| -</div> |
80849 |
| -<!-- solution:end --> |
80850 |
| - |
80851 | 80827 | <!-- problem:end -->
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80852 | 80828 |
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80853 | 80829 |
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