[英]How "pi+1" statement does tail call elimination in quicksort function which is using the Lomuto Algorithm for partitioning?
/* 尾调用消除后的快速排序 */
#include<stdio.h>
交换两个元素的实用函数
void swap(int* a, int* b)
{
int t = *a;
*a = *b;
*b = t;
}
/* 此函数以最后一个元素作为主元,将主元元素放置在已排序数组中的正确位置,并将所有较小(小于主元)的元素放在主元的左侧,将所有较大的元素放在主元的右侧。 它使用 Lomuto 分区算法。 */
int partition (int arr[], int low, int high)
{
int pivot = arr[high]; `// pivot`
int i = (low - 1); `// Index of smaller element`
for (int j = low; j <= high- 1; j++)
{
`// If the current element is smaller than or equal to pivot `
if (arr[j] <= pivot)
{
i++; `// increment index of smaller element`
swap(&arr[i], &arr[j]);
}
}
swap(&arr[i + 1], &arr[high]);
return (i + 1);
}
/*实现QuickSort的main函数arr[] -->要排序的数组,低-->起始索引,高-->结束索引*/
void quickSort(int arr[], int low, int high)
{
while (low < high)
{
`/* pi is partitioning index, arr[p] is now at right place */`
int pi = partition(arr, low, high);
`// Separately sort elements before partition and after partition`
quickSort(arr, low, pi - 1);
low = pi+1;
}
}
打印数组的函数
void printArray(int arr[], int size)
{
for (int i=0; i < size; i++)
printf("%d ", arr[i]);
printf("\n");
}
测试以上功能的驱动程序
int main()
{
int arr[] = {10, 7, 8, 9, 1, 5};
int n = sizeof(arr)/sizeof(arr[0]);
quickSort(arr, 0, n-1);
printf("Sorted array: \n");
printArray(arr, n);
return 0;
}
“pi+1”语句如何在quicksort函数中消除尾调用
它没有。 所有主流 x86 编译器都无法从您的代码中展开递归。 例如 gcc -O3 ( Godbolt ):
quickSort:
cmp esi, edx
jge .L6
push r13
mov r13, rdi
push r12
mov r12d, edx
push rbp
mov ebp, esi
push rbx
sub rsp, 8
.L3:
mov esi, ebp
mov edx, r12d
mov rdi, r13
call partition
mov esi, ebp
mov rdi, r13
mov ebx, eax
lea edx, [rax-1]
call quickSort // recursive call
lea ebp, [rbx+1]
cmp r12d, ebp
jg .L3
add rsp, 8
pop rbx
pop rbp
pop r12
pop r13
ret
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