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<h1 id="31">3.1 &nbsp; 資料結構分類<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
<p>常見的資料結構包括陣列、鏈結串列、堆疊、佇列、雜湊表、樹、堆積、圖，它們可以從“邏輯結構”和“物理結構”兩個維度進行分類。</p>
<h2 id="311">3.1.1 &nbsp; 邏輯結構：線性與非線性<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
<p><strong>邏輯結構揭示了資料元素之間的邏輯關係</strong>。在陣列和鏈結串列中，資料按照一定順序排列，體現了資料之間的線性關係；而在樹中，資料從頂部向下按層次排列，表現出“祖先”與“後代”之間的派生關係；圖則由節點和邊構成，反映了複雜的網路關係。</p>
<p>如圖 3-1 所示，邏輯結構可分為“線性”和“非線性”兩大類。線性結構比較直觀，指資料在邏輯關係上呈線性排列；非線性結構則相反，呈非線性排列。</p>
<ul>
<li><strong>線性資料結構</strong>：陣列、鏈結串列、堆疊、佇列、雜湊表，元素之間是一對一的順序關係。</li>
<li><strong>非線性資料結構</strong>：樹、堆積、圖、雜湊表。</li>
</ul>
<p>非線性資料結構可以進一步劃分為樹形結構和網狀結構。</p>
<ul>
<li><strong>樹形結構</strong>：樹、堆積、雜湊表，元素之間是一對多的關係。</li>
<li><strong>網狀結構</strong>：圖，元素之間是多對多的關係。</li>
</ul>
<p><a class="glightbox" href="../classification_of_data_structure.assets/classification_logic_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="線性資料結構與非線性資料結構" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></a></p>
<p align="center"> 圖 3-1 &nbsp; 線性資料結構與非線性資料結構 </p>

<h2 id="312">3.1.2 &nbsp; 物理結構：連續與分散<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
<p><strong>當演算法程式執行時，正在處理的資料主要儲存在記憶體中</strong>。圖 3-2 展示了一個計算機記憶體條，其中每個黑色方塊都包含一塊記憶體空間。我們可以將記憶體想象成一個巨大的 Excel 表格，其中每個單元格都可以儲存一定大小的資料。</p>
<p><strong>系統透過記憶體位址來訪問目標位置的資料</strong>。如圖 3-2 所示，計算機根據特定規則為表格中的每個單元格分配編號，確保每個記憶體空間都有唯一的記憶體位址。有了這些位址，程式便可以訪問記憶體中的資料。</p>
<p><a class="glightbox" href="../classification_of_data_structure.assets/computer_memory_location.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="記憶體條、記憶體空間、記憶體位址" class="animation-figure" src="../classification_of_data_structure.assets/computer_memory_location.png" /></a></p>
<p align="center"> 圖 3-2 &nbsp; 記憶體條、記憶體空間、記憶體位址 </p>

<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>值得說明的是，將記憶體比作 Excel 表格是一個簡化的類比，實際記憶體的工作機制比較複雜，涉及位址空間、記憶體管理、快取機制、虛擬記憶體和物理記憶體等概念。</p>
</div>
<p>記憶體是所有程式的共享資源，當某塊記憶體被某個程式佔用時，則無法被其他程式同時使用了。<strong>因此在資料結構與演算法的設計中，記憶體資源是一個重要的考慮因素</strong>。比如，演算法所佔用的記憶體峰值不應超過系統剩餘空閒記憶體；如果缺少連續大塊的記憶體空間，那麼所選用的資料結構必須能夠儲存在分散的記憶體空間內。</p>
<p>如圖 3-3 所示，<strong>物理結構反映了資料在計算機記憶體中的儲存方式</strong>，可分為連續空間儲存（陣列）和分散空間儲存（鏈結串列）。物理結構從底層決定了資料的訪問、更新、增刪等操作方法，兩種物理結構在時間效率和空間效率方面呈現出互補的特點。</p>
<p><a class="glightbox" href="../classification_of_data_structure.assets/classification_phisical_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連續空間儲存與分散空間儲存" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></a></p>
<p align="center"> 圖 3-3 &nbsp; 連續空間儲存與分散空間儲存 </p>

<p>值得說明的是，<strong>所有資料結構都是基於陣列、鏈結串列或二者的組合實現的</strong>。例如，堆疊和佇列既可以使用陣列實現，也可以使用鏈結串列實現；而雜湊表的實現可能同時包含陣列和鏈結串列。</p>
<ul>
<li><strong>基於陣列可實現</strong>：堆疊、佇列、雜湊表、樹、堆積、圖、矩陣、張量（維度 <span class="arithmatex">\(\geq 3\)</span> 的陣列）等。</li>
<li><strong>基於鏈結串列可實現</strong>：堆疊、佇列、雜湊表、樹、堆積、圖等。</li>
</ul>
<p>鏈結串列在初始化後，仍可以在程式執行過程中對其長度進行調整，因此也稱“動態資料結構”。陣列在初始化後長度不可變，因此也稱“靜態資料結構”。值得注意的是，陣列可透過重新分配記憶體實現長度變化，從而具備一定的“動態性”。</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>如果你感覺物理結構理解起來有困難，建議先閱讀下一章，然後再回顧本節內容。</p>
</div>

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