如何使用嘗試有效地實現稀疏矩陣？

稀疏矩陣可以使用 try 高效實現，它僅使用兩個數組索引操作計算某個元素是否存在於表中，從而提供對特定矩陣元素的快速訪問。

Tries 的主要特點：

• 在後備儲存中為預設值提供預設位置，無需進行值測試。
• 支援快速更新嘗試使用可選的「compact()」操作來最佳化後備儲存大小。
• 利用物件映射，允許將座標映射到向量中的整數位置。
• 處理子範圍的快速擷取

優點：

• Trie 實作比hashmap 快得多，避免了複雜的散列函數和衝突處理。
• Java hashmaps 僅在物件上建立索引，可能會導致記憶體開銷和垃圾收集壓力。
• 嘗試提供高效的實現，不需要為每個來源索引建立對象，從而減少記憶體操作。

範例實作：

<code class="java">public class DoubleTrie {

    // Matrix options
    private static final int SIZE_I = 1024;
    private static final int SIZE_J = 1024;
    private static final double DEFAULT_VALUE = 0.0;

    // Internal splitting options
    private static final int SUBRANGEBITS_I = 4;
    private static final int SUBRANGEBITS_J = 4;

    // Internal splitting constants
    private static final int SUBRANGE_I =
            1 << SUBRANGEBITS_I;
    private static final int SUBRANGE_J =
            1 << SUBRANGEBITS_J;
    private static final int SUBRANGEMASK_I =
            SUBRANGE_I - 1;
    private static final int SUBRANGEMASK_J =
            SUBRANGE_J - 1;

    // Internal data
    private double[] values;
    private int[] subrangePositions;

    // Fast subrange and position computation methods
    private static int subrangeOf(int i, int j) {
        return (i >> SUBRANGEBITS_I) * SUBRANGE_J + (j >> SUBRANGEBITS_J);
    }
    private static int positionOffsetOf(int i, int j) {
        return (i & SUBRANGEMASK_I) * SUBRANGE_J + (j & SUBRANGEMASK_J);
    }

    // Fast indexed getter
    public double getAt(int i, int j) {
        return values[subrangePositions[subrangeOf(i, j)] +
                      positionOffsetOf(i, j)];
    }

    // Fast indexed setter
    public double setAt(int i, int j, double value) {
        final int subrange = subrangeOf(i, j);
        final int positionOffset = positionOffsetOf(i, j);
        // Check if the assignment will change something
        int subrangePosition, valuePosition;
        if (Double.compare(
                values[valuePosition =
                        (subrangePosition = subrangePositions[subrange]) +
                                positionOffset],
                value) != 0) {
            // Perform the assignment in values
            if (isSharedValues) {
                values = values.clone();
                isSharedValues = false;
            }
            // Scan other subranges to check if the value is shared by another subrange
            for (int otherSubrange = subrangePositions.length;
                    --otherSubrange >= 0; ) {
                if (otherSubrange != subrange)
                    continue; // Ignore the target subrange
                if ((otherSubrangePosition =
                        subrangePositions[otherSubrange]) >=
                        valuePosition &&
                        otherSubrangePosition + SUBRANGE_POSITIONS <
                                valuePosition) {
                    // The target position is shared, we need to make it unique by cloning the subrange
                    if (isSharedSubrangePositions) {
                        subrangePositions = subrangePositions.clone();
                        isSharedSubrangePositions = false;
                    }
                    values = setlengh(
                            values,
                            (subrangePositions[subrange] =
                                    subrangePositions = values.length) +
                                    SUBRANGE_POSITIONS);
                    valuePosition = subrangePositions + positionOffset;
                    break;
                }
            }
            // Perform the effective assignment of the value
            values[valuePosition] = value;
        }
        return value;
    }
}</code>

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