常见的排序算法有选择排序、冒泡排序、插入排序、希尔排序、归并排序、堆排序、快速排序这些都是以前教科书上教给我们的。科技在发展,人类在进步,在前人们不懈努力下新的排序算法总是层出不穷,特别是大数据时代关于海量数据的处理方面显得尤为重要,所以出现了诸如计数排序(couting sort)、桶排序(bucket sort)、基数排序(radix sort)。这些暂不属于我们的讨论范围。
选择排序
所谓的“选择”就是在待排序列里,找出一个最大(小)的元素,然后将它放在序列某个位置,这就完成了一次选择过程。如果将这样的选择循环继续下去,就是我们所说的选择排序。这也是选择排序的精髓。
注:本文所讨论的都是升序排序,降序也一样,没啥本质区别。
假如,有一个无须序列A={6,3,1,9,2,5,8,7,4},选择排序的过程应该如下:
第一趟:选择最小的元素,然后将其放置在数组的第一个位置A[0],将A[0]=6和A[2]=1进行交换,此时A={1,3,6,9,2,5,8,7,4};
第二趟:由于A[0]位置上已经是最小的元素了,所以这次从A[1]开始,在剩下的序列里再选择一个最小的元素将其与A[1]进行交换。即这趟选择过程找到了最小元素A[4]=2,然后与A[1]=3进行交换,此时A={1,2,6,9,3,5,8,7,4};
第三趟:由于A[0]、A[1]已经有序,所以在A[2]~A[8]里再选择一个最小元素与A[2]进行交换,然后将这个过程一直循环下去直到A里所有的元素都排好序为止。这就是选择排序的精髓。因此,我们很容易写出选择排序的核心代码部分,即选择的过程,就是不断的比较、交换的过程。
整个选择的过程如下图所示:
其中,黄色表示即将要选择的位置,即该位置上要安放从该位置往后开始最小的那个元素;桔色表示在无须序列里最小元素所在的位置,经过交换后的结果如右边箭头所示。而所有的灰色块,表示那些位置上的元素已经排好序了。所以,整个选择排序算法的核心代码如下:
点击(此处)折叠或打开
- int min,tmp,i,j;
-
for(i=0;i<len-1;i++){
-
min = i; //在本趟选择过程中,我们要将最小的元素放在a[i]的位置上
-
-
for(j=i+1;j<len;j++) /××××××××××××××××××××××××××××××××××××××××××××××××××××××××
-
if(a[min]>a[j]) ×在剩下的len-i个元素里选择一个最小,然后用min记住其下标
- min = j; ××××××××××××××××××××××××××××××××××××××××××××××××××××××××/
- /× 如果a[i]本身就已经是最小的元素,则不要交换,这样可以提高一点算法的效率×/
-
if(min != i){
- swap(a[min],a[i]) //交换两个数
-
}
- }
1+2+3+4+5+... ...+(n-2)+(n-1)=n*(n-1)/2,其时间复杂度是O(n^2)。任何情况下,无论待排序列是否有序,选择排序所耗费的比较时间都是O(n^2)。唯一的区别在于,如果待排序列已经是升序的,那么最好的情况就是不需要任何交换;如果待排序列是逆序的,则最坏的情况就是总共需要交换n/2次。
所以,选择排序算法,最好、最坏和平均时间复杂度都是O(n^2)。
冒泡排序
冒泡排序算法的核心是每次冒泡过程中,比较相邻的两个元素,如果A[i]大于A[i+1],则将其交换,然后A[i+1]和A[i+2]再进行比较,将大的元素往后放。这样一趟下来,最大元素就被逐次“冒”到序列的末尾了。继续以前面的序列A为例:我们将序列“竖起来”,这样看冒泡的效果会更好。
点击(此处)折叠或打开
- int i;
-
while(len--){
-
for(i=0;i<len;i++){
-
if(a[i]>a[i+1]){
- swap(a[i],a[i+1]); //交换两个数
-
}
-
}
- }
关于冒泡排序的时间复杂度,如果序列的长度为n,第一趟的冒泡需要的比较次数是n-1,第二趟冒泡比较时最后一个元素已经脱颖而出,所以第二趟冒泡的总比较次数是n-2,以此类推,第i次冒泡的比较次数是n-i。同样地,和选择排序一样,冒泡排序在最坏和最好的情况下,其时间复杂度都是O(n^2)。
让我们把冒泡排序第五趟及剩下的过程再分析一下:
点击(此处)折叠或打开
- int i,goon=1;
-
while(goon && len--){
-
goon=0;
-
for(i=0;i<len;i++){
-
if(a[i]>a[i+1]){
- swap(a[i],a[i+1]); //交换两个数
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goon = 1;
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}
- }
- }
未完,待续...
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