21 days learning challenge 】 【 sequential search

One-dimensional array element search method

顺序查找

Start with one side of the array,Perform element-by-element comparisons,The search succeeds until the element to be searched is the same as the given element,If no matching element is found after the search is complete, the search fails.

二分查找

Under the premise of orderly calculation,Keep it as narrow as possible,提高查找效率.

索引查找

对于无序的数据集合,Create an index table first,Yes the index table is ordered or chunked ordered,The lookup is done by combining sequential lookup and index lookup.

顺序查找

输入：n个数字（无序）.
输出：If the search is successful, the subscript is output,失败则返回-1.

int nums[10],x;
cin>>x;
for(int i=0;i<nums.size();i++){
  if(x==nums[i]) return i;

return -1;

The space complexity is only introduced abovei这个变量为O（1）.
The time complexity is worst caseO（n）

插入排序

原理：每次插入一个元素,Each pass completes the placement of an element to be queued,直到全部插入完成.

直接插入排序

将每个待排元素Insert into knownalready arranged sequence中.（Each time a new arrangement is taken from the original data,Insert into a previously arranged sequence,until all numbers are taken,This new arrangement is complete）

算法详解：
假设前面 n-1(其中 n>=2)个数已经是排好顺序的,现将第 n 个数插到前面already arranged sequence中,然后找到合适自己的位置,使得插入第n个数的这个序列也是排好顺序的.

从小到大的插入排序整个过程如图示：

第一轮：从第二位置的 6 开始比较,比前面 7 小,交换位置.

第二轮：第三位置的 9 比前一位置的 7 大,无需交换位置.

第三轮：第四位置的 3 比前一位置的 9 小交换位置,依次往前比较.

第四轮：第五位置的 1 比前一位置的 9 小,交换位置,再依次往前比较.

public class InsertionSort {
    
    public static void sort(Comparable[] arr){
    
    
        int n = arr.length;
        for (int i = 0; i < n; i++) {
    
            // 寻找元素 arr[i] 合适的插入位置
           for( int j = i ; j > 0 ; j -- )
                if( arr[j].compareTo( arr[j-1] ) < 0 )
                    swap( arr, j , j-1 );
                else
                    break;
        }
    }
    //核心代码---结束
   }
 }

折半插入排序

Due to the insertion sort process,One has been generated有序序列.So when inserting elements to be sorted, it is faster to use halved searchDetermine the position of the new element.when the number of elements is large,Half-insertion sort is better than direct insertion sort.

希尔排序

After dividing all elements into groups,Use inline insertion sort within each group,Then continue to reduce the spacing,Form a new group for sorting,直到间距为0为止.