希尔排序是一种高效的排序算法，它基于插入排序算法。如果较小的值在最右边并且必须移到最左边，则该算法避免了在插入排序的情况下的移位操作。
该算法对广泛分布的元素使用插入排序，首先对它们进行排序，然后对间距较小的元素进行排序。该间隔是根据Knuth的公式计算的-
Knuth公式
h=h * 3 + 1 where - h is interval with initial value 1
对于中等大小的数据集，此算法非常有效，因为该算法的平均复杂度和最坏情况的复杂度取决于间隙序列，众所周知，该间隙序列是Ο(n)，其中n是项数，最坏的情况是空间复杂度为O(n)。
希尔排序原理
让我们考虑以下示例，以了解希尔排序的工作原理，我们采用与先前示例相同的数组，对于我们的示例和易于理解，我们采用4的间隔。为位于4个位置的间隔的所有值创建一个虚拟子列表。这些值是{35，14}，{33，19}，{42，27}和{10，44}
我们比较每个子列表中的值，并在原始数组中交换它们(如果需要)。完成此步骤后，新数组应如下所示:
然后，我们取间隔1，此间隔生成两个子列表-{14，27，35，42}，{19，10，33，44}
如果需要，我们将比较并交换原始数组中的值。完成此步骤后，数组应如下所示:
最后，我们使用值1的间隔对数组的其余部分进行排序。希尔排序使用插入排序对数组进行排序。
以下是分步描述-
我们看到它只需要四个交换就可以对数组的其余部分进行排序。
希尔排序伪代码
以下是用于希尔排序的伪代码。
procedure shellSort()
A : array of items
/* calculate interval*/
while interval < A.length /3 do:
interval = interval * 3 + 1
end while
while interval > 0 do:
</span><span class="kwd">for</span><span class="pln"> outer </span><span class="pun">=</span><span class="pln"> interval</span><span class="pun">;</span><span class="pln"> outer </span><span class="pun"><</span><span class="pln"> A</span><span class="pun">.</span><span class="pln">length</span><span class="pun">;</span><span class="pln"> outer </span><span class="pun">++</span><span class="pln"> </span><span class="kwd">do</span><span class="pun">:</span><span class="pln">
</span><span class="com">/* select value to be inserted */</span><span class="pln">
valueToInsert </span><span class="pun">=</span><span class="pln"> A</span><span class="pun">[</span><span class="pln">outer</span><span class="pun">]</span><span class="pln">
inner </span><span class="pun">=</span><span class="pln"> outer</span><span class="pun">;</span><span class="pln">
</span><span class="com">/*shift element towards right*/</span><span class="pln">
</span><span class="kwd">while</span><span class="pln"> inner </span><span class="pun">></span><span class="pln"> interval </span><span class="pun">-</span><span class="lit">1</span><span class="pln"> </span><span class="pun">&&</span><span class="pln"> A</span><span class="pun">[</span><span class="pln">inner </span><span class="pun">-</span><span class="pln"> interval</span><span class="pun">]</span><span class="pln"> </span><span class="pun">>=</span><span class="pln"> valueToInsert </span><span class="kwd">do</span><span class="pun">:</span><span class="pln">
A</span><span class="pun">[</span><span class="pln">inner</span><span class="pun">]</span><span class="pln"> </span><span class="pun">=</span><span class="pln"> A</span><span class="pun">[</span><span class="pln">inner </span><span class="pun">-</span><span class="pln"> interval</span><span class="pun">]</span><span class="pln">
inner </span><span class="pun">=</span><span class="pln"> inner </span><span class="pun">-</span><span class="pln"> interval
</span><span class="kwd">end</span><span class="pln"> </span><span class="kwd">while</span><span class="pln">
</span><span class="com">/* insert the number at hole position */</span><span class="pln">
A</span><span class="pun">[</span><span class="pln">inner</span><span class="pun">]</span><span class="pln"> </span><span class="pun">=</span><span class="pln"> valueToInsert
</span><span class="kwd">end</span><span class="pln"> </span><span class="kwd">for</span><span class="pln">
/* calculate interval*/
interval = (interval -1) /3;
end while
end procedure
C实现希尔排序
#include <stdio.h>
#include <stdbool.h>
#define MAX 7
int intArray[MAX] = {4,6,3,2,1,9,7};
void printline(int count) {
int i;
for(i = 0;i < count-1;i++) {
printf("=");
}
printf("=\n");
}
void display() {
int i;
printf("[");
// navigate through all items
for(i = 0;i < MAX;i++) {
printf("%d ",intArray[i]);
}
printf("]\n");
}
void shellSort() {
int inner, outer;
int valueToInsert;
int interval = 1;
int elements = MAX;
int i = 0;
while(interval <= elements/3) {
interval = interval*3 +1;
}
while(interval > 0) {
printf("iteration %d#:",i);
display();
</span><span class="kwd">for</span><span class="pun">(</span><span class="pln">outer </span><span class="pun">=</span><span class="pln"> interval</span><span class="pun">;</span><span class="pln"> outer </span><span class="pun"><</span><span class="pln"> elements</span><span class="pun">;</span><span class="pln"> outer</span><span class="pun">++)</span><span class="pln"> </span><span class="pun">{</span><span class="pln">
valueToInsert </span><span class="pun">=</span><span class="pln"> intArray</span><span class="pun">[</span><span class="pln">outer</span><span class="pun">];</span><span class="pln">
inner </span><span class="pun">=</span><span class="pln"> outer</span><span class="pun">;</span><span class="pln">
</span><span class="kwd">while</span><span class="pun">(</span><span class="pln">inner </span><span class="pun">></span><span class="pln"> interval </span><span class="pun">-</span><span class="lit">1</span><span class="pln"> </span><span class="pun">&&</span><span class="pln"> intArray</span><span class="pun">[</span><span class="pln">inner </span><span class="pun">-</span><span class="pln"> interval</span><span class="pun">]</span><span class="pln">
</span><span class="pun">>=</span><span class="pln"> valueToInsert</span><span class="pun">)</span><span class="pln"> </span><span class="pun">{</span><span class="pln">
intArray</span><span class="pun">[</span><span class="pln">inner</span><span class="pun">]</span><span class="pln"> </span><span class="pun">=</span><span class="pln"> intArray</span><span class="pun">[</span><span class="pln">inner </span><span class="pun">-</span><span class="pln"> interval</span><span class="pun">];</span><span class="pln">
inner </span><span class="pun">-=</span><span class="pln">interval</span><span class="pun">;</span><span class="pln">
printf</span><span class="pun">(</span><span class="str">" item moved :%d\n"</span><span class="pun">,</span><span class="pln">intArray</span><span class="pun">[</span><span class="pln">inner</span><span class="pun">]);</span><span class="pln">
</span><span class="pun">}</span><span class="pln">
intArray</span><span class="pun">[</span><span class="pln">inner</span><span class="pun">]</span><span class="pln"> </span><span class="pun">=</span><span class="pln"> valueToInsert</span><span class="pun">;</span><span class="pln">
printf</span><span class="pun">(</span><span class="str">" item inserted :%d, at position :%d\n"</span><span class="pun">,</span><span class="pln">valueToInsert</span><span class="pun">,</span><span class="pln">inner</span><span class="pun">);</span><span class="pln">
</span><span class="pun">}</span><span class="pln">
interval </span><span class="pun">=</span><span class="pln"> </span><span class="pun">(</span><span class="pln">interval </span><span class="pun">-</span><span class="lit">1</span><span class="pun">)</span><span class="pln"> </span><span class="pun">/</span><span class="lit">3</span><span class="pun">;</span><span class="pln">
i</span><span class="pun">++;</span><span class="pln">
}
}
int main() {
printf("Input Array: ");
display();
printline(50);
shellSort();
printf("Output Array: ");
display();
printline(50);
return 1;
}
Input Array: [4 6 3 2 1 9 7 ] ================================================== iteration 0#:[4 6 3 2 1 9 7 ] item moved :4 item inserted :1, at position :0 item inserted :9, at position :5 item inserted :7, at position :6 iteration 1#:[1 6 3 2 4 9 7 ] item inserted :6, at position :1 item moved :6 item inserted :3, at position :1 item moved :6 item moved :3 item inserted :2, at position :1 item moved :6 item inserted :4, at position :3 item inserted :9, at position :5 item moved :9 item inserted :7, at position :5 Output Array: [1 2 3 4 6 7 9 ] ==================================================
