programming:algorithm:sorting:bubble_sort
Bubble Sort
0x00 原理
- 每一回合由左而右比較相鄰資料,若左側大於右側則交換相鄰資料(大的資料如氣泡往上浮)
- 進行至沒一回合完全沒有交換動作,或進行了 n - 1 回合則結束排序
0x01 實作
#include<stdio.h> #include<stdlib.h> #include<stdbool.h> void bubble_sort(int array[], int size); void print_array(int array[], int size); int main(void) { int average_case[7] = {28, 13, 9, 69, 57, 41, 24}; int best_case[7] = {9 ,13, 24, 28, 41, 57, 69}; int worst_case[7] = {69, 57, 41, 28, 24, 13, 9}; bubble_sort(average_case, sizeof(average_case) / sizeof(average_case[0])); printf("\n\n"); bubble_sort(best_case, sizeof(best_case) / sizeof(best_case[0])); printf("\n\n"); bubble_sort(worst_case, sizeof(worst_case) / sizeof(worst_case[0])); printf("\n\n"); } void bubble_sort(int array[], int size) { printf("%-8s", "initial"); print_array(array, size); printf("%-8s%-2s%-10s\n", "compare", "|", "move"); printf("------------------------------------------------------------\n"); bool exchange = true; int i, j, compare, move; for(i = size - 1; exchange && i > 0; i--) { printf("%-s%-3d", "Pass ", size - i); compare = 0; move = 0; exchange = false; for(j = 0; j < i; j++) { compare++; if(array[j] > array[j + 1]) { int tmp = array[j]; array[j] = array[j + 1]; array[j + 1] = tmp; move++; exchange = true; } } print_array(array, size); printf("%-8d%-2s%-10d\n", compare, "|", move); } } void print_array(int array[], int size) { int i; for(i = 0; i < size; i++) { printf("| %-3d", array[i]); } printf(" | "); }
0x02 時間複雜度
Case | Compare counts | Move counts | Time Complexity |
---|---|---|---|
Best | n - 1 | 0 | O(n) |
Worst | 1 + 2 + 3 +… + (n - 1) = n(n - 1) / 2 | 1 + 2 + 3 +… + (n - 1) = n(n - 1) / 2 | O(n2) |
Average | O(n2) | O(n2) | O(n2) |
0x03 空間複雜度
沒有使用額外陣列空間,排序在 internal space 完成
空間複雜度為: O(1)
0x04 Stable Sort
每一回合由左而右兩兩比較,大的元素上浮到右邊,當遇到相同大小的元素時並不交換,原先在前(左側)的元素排序後會保持在前,為穩定排序
programming/algorithm/sorting/bubble_sort.txt · 上一次變更: 由 127.0.0.1