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@@ -4500,7 +4500,7 @@ T(n) = 3 + 2n
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<p><span class="arithmatex">\(T(n)\)</span> 是一次函式,說明其執行時間的增長趨勢是線性的,因此它的時間複雜度是線性階。</p>
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<p>我們將線性階的時間複雜度記為 <span class="arithmatex">\(O(n)\)</span> ,這個數學符號稱為<u>大 <span class="arithmatex">\(O\)</span> 記號(big-<span class="arithmatex">\(O\)</span> notation)</u>,表示函式 <span class="arithmatex">\(T(n)\)</span> 的<u>漸近上界(asymptotic upper bound)</u>。</p>
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<p>時間複雜度分析本質上是計算“操作數量 <span class="arithmatex">\(T(n)\)</span>”的漸近上界,它具有明確的數學定義。</p>
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<div class="admonition abstract">
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<div class="admonition note">
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<p class="admonition-title">函式漸近上界</p>
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<p>若存在正實數 <span class="arithmatex">\(c\)</span> 和實數 <span class="arithmatex">\(n_0\)</span> ,使得對於所有的 <span class="arithmatex">\(n > n_0\)</span> ,均有 <span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span> ,則可認為 <span class="arithmatex">\(f(n)\)</span> 給出了 <span class="arithmatex">\(T(n)\)</span> 的一個漸近上界,記為 <span class="arithmatex">\(T(n) = O(f(n))\)</span> 。</p>
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</div>
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