[Leetcode][第35题][JAVA][搜索插入位置][二分法]

向右看齐 2023-02-27 10:51 2阅读 0赞

#### 【问题描述】\[中等\] ####

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70]

#### 【解答思路】 ####

###### 二分法 ######

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 1]

**时间复杂度：O(LogN) 空间复杂度：O(1)**  
![在这里插入图片描述][20200717104636665.png]

public class Solution { 
    
        public int searchInsert(int[] nums, int target) { 
            int len = nums.length;
            if (len == 0) { 
                return 0;
            }
    
            // 特判
            if (nums[len - 1] < target) { 
                return len;
            }
            int left = 0;
            int right = len - 1;
            while (left < right) { 
                int mid = left + (right - left) / 2;
                // 严格小于 target 的元素一定不是解
                if (nums[mid] < target) { 
                    // 下一轮搜索区间是 [mid + 1, right]
                    left = mid + 1;
                } else { 
                    // 下一轮搜索区间是 [left, mid]
                    right = mid;
                }
            }
            return left;
        }
    }

public class Solution { 
    
        public int searchInsert(int[] nums, int target) { 
            int len = nums.length;
            if (len == 0) { 
                return 0;
            }
            
            int left = 0;
            // 因为有可能数组的最后一个元素的位置的下一个是我们要找的，故右边界是 len
            int right = len;
            while (left < right) { 
                int mid = left + (right - left) / 2;
                // 小于 target 的元素一定不是解
                if (nums[mid] < target) { 
                    // 下一轮搜索的区间是 [mid + 1, right]
                    left = mid + 1;
                } else { 
                  	// 下一轮搜索的区间是 [left, mid]
                    right = mid;
                }
            }
            return left;
        }
    }

#### 【总结】 ####

###### 1. 二分查找的思想 ######

减而治之，即将大规模问题转化成小规模问题。减而治之是分而治之的特例，将大问题划分成若干个子问题以后，最终答案只在其中一个子问题里。

###### 3.去中间数 ######

int mid = left + (right - left) / 2;  
int mid = (left + right) >>> 1;

###### 3.排除法思想 ######

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 2]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 3]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 4]

##### 4.二分查找模板 一般步骤 #####

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 5]

##### 5. 与其他二分查找的比较 #####

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 6]  
6. [二分法整理][Link 1]

作者：liweiwei1419  
链接：https://leetcode-cn.com/problems/search-insert-position/solution/te-bie-hao-yong-de-er-fen-cha-fa-fa-mo-ban-python-/

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70]: /images/20230209/43e6049d59174dada669c9c2013f6e38.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20200717104433881.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[20200717104636665.png]: https://img-blog.csdnimg.cn/20200717104636665.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/20200717105536864.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 3]: https://img-blog.csdnimg.cn/20200717105543917.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 5]: https://img-blog.csdnimg.cn/20200717111019343.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk_size_16_color_FFFFFF_t_70 6]: https://img-blog.csdnimg.cn/20200717111214525.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2RhZG9uZ3d1ZGk=,size_16,color_FFFFFF,t_70
[Link 1]: https://blog.csdn.net/dadongwudi/article/details/105345157