你真的会写二分查找吗?

二分查找

 

 1 //二分查找
 2 int binarySearch(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key < arr[mid]) {//key在左边
11             right = mid - 1;
12         } else if (arr[mid] < key) {//key在右边
13             left = mid + 1;
14         } else {
15             return mid;
16         }
17     }
18     return -1;
19 }

 

 

二分查找变形

随着二分查找的进行,如果找到key并不结束循环的话,最终的结束状态会是right < left,并且right + 1 = left。

当数组中存在key时,根据二分区间选择的不同,这里又分为两种情况,如下图(key为2时),

当数组中不存在key时,最后仅有一种情况,即把图中的黄色框框去掉。

那么,可以找到

1 最后一个小于key的元素,1,

2 第一个大于等于key的元素,2,

3 最后一个小于等于key的元素,2,

4 第一个大于key的元素,5,

另外,如果存在多个key时,稍加判断,就可以找到

5 第一个与key相等的元素

6 最后一个与key相等的元素

 

1 查找最后一个小于key的元素

 1 //1 查找最后一个小于key的元素
 2 int findLastLess(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key <= arr[mid]) {
11             right = mid - 1;
12         } else {
13             left = mid + 1;
14         }
15     }
16     return right;
17 }
View Code

2 查找第一个大于等于key的元素

 1 //2 查找第一个大于等于key的元素
 2 int findFirstGreaterEqual(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key <= arr[mid]) {
11             right = mid - 1;
12         }
13         else {
14             left = mid + 1;
15         }
16     }
17     return left;
18 }
View Code

3 查找最后一个小于等于key的元素

 1 //3 查找最后一个小于等于key的元素
 2 int findLastLessEqual(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key < arr[mid]) {
11             right = mid - 1;
12         } else {
13             left = mid + 1;
14         }
15     }
16     return right;
17 }
View Code

4 查找第一个大于key的元素

 1 //4 查找第一个大于key的元素
 2 int findFirstGreater(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key < arr[mid]) {
11             right = mid - 1;
12         }
13         else {
14             left = mid + 1;
15         }
16     }
17     return left;
18 }
View Code

5 查找第一个与key相等的元素

 1 //5 查找第一个与key相等的元素
 2 int findFirstEqual(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key <= arr[mid]) {
11             right = mid - 1;
12         } else {//arr[mid] < key
13             left = mid + 1;
14         }
15     }
16     //arr[right] < key <= arr[left]
17     //right是最后一个小于key的
18     //left是第一个大于等于key的
19     if (left < len && arr[left] == key) {
20         return left;
21     }
22     return -1;
23 }
View Code

6 查找最后一个与key相等的元素

 1 //6 查找最后一个与key相等的元素
 2 int findLastEqual(int arr[], int len, int key)
 3 {
 4     int left = 0;
 5     int right = len - 1;
 6     int mid;
 7 
 8     while (left <= right) {
 9         mid = (left + right) / 2;
10         if (key < arr[mid]) {
11             right = mid - 1;
12         } else {//arr[mid] <= key
13             left = mid + 1;
14         }
15     }
16     //arr[right] <= key < arr[left]
17     //right是最后一个小于等于key的
18     //left是第一个大于key的
19     if (right >= 0 && arr[right] == key) {
20         return right;
21     }
22     return -1;
23 }
View Code

 

最后补一张图,辅助理解,

 

怎么记呢?

看到其它博客的总结,也不错,

http://www.cnblogs.com/luoxn28/p/5767571.html

但是我觉得不够清晰好记,这里我总结为:

只要记住上面两幅图就好了,哈哈...

 

其实,只要记住比较符号和返回值,其它的代码都一样,

1     while (left <= right) {
2         mid = (left + right) / 2;
3         if (key ? arr[mid]) {
4             right = mid - 1;
5         } else {
6             left = mid + 1;
7         }
8     }
9     return ?;

 

根据要求的值的位置,先确定比较符号,再确定返回值,

比较符号:左<=,右<

返回值:左right,右left

 

 

贴一个完整的测试代码吧,

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 
  4 //二分查找
  5 int binarySearch(int arr[], int len, int key)
  6 {
  7     int left = 0;
  8     int right = len - 1;
  9     int mid;
 10 
 11     while (left <= right) {
 12         mid = (left + right) / 2;
 13         if (key < arr[mid]) {//key在左边
 14             right = mid - 1;
 15         } else if (arr[mid] < key) {//key在右边
 16             left = mid + 1;
 17         } else {
 18             return mid;
 19         }
 20     }
 21     return -1;
 22 }
 23 
 24 //1 查找最后一个小于key的元素
 25 int findLastLess(int arr[], int len, int key)
 26 {
 27     int left = 0;
 28     int right = len - 1;
 29     int mid;
 30 
 31     while (left <= right) {
 32         mid = (left + right) / 2;
 33         if (key <= arr[mid]) {
 34             right = mid - 1;
 35         } else {
 36             left = mid + 1;
 37         }
 38     }
 39     return right;
 40 }
 41 
 42 //2 查找第一个大于等于key的元素
 43 int findFirstGreaterEqual(int arr[], int len, int key)
 44 {
 45     int left = 0;
 46     int right = len - 1;
 47     int mid;
 48 
 49     while (left <= right) {
 50         mid = (left + right) / 2;
 51         if (key <= arr[mid]) {
 52             right = mid - 1;
 53         }
 54         else {
 55             left = mid + 1;
 56         }
 57     }
 58     return left;
 59 }
 60 
 61 //3 查找最后一个小于等于key的元素
 62 int findLastLessEqual(int arr[], int len, int key)
 63 {
 64     int left = 0;
 65     int right = len - 1;
 66     int mid;
 67 
 68     while (left <= right) {
 69         mid = (left + right) / 2;
 70         if (key < arr[mid]) {
 71             right = mid - 1;
 72         } else {
 73             left = mid + 1;
 74         }
 75     }
 76     return right;
 77 }
 78 
 79 //4 查找第一个大于key的元素
 80 int findFirstGreater(int arr[], int len, int key)
 81 {
 82     int left = 0;
 83     int right = len - 1;
 84     int mid;
 85 
 86     while (left <= right) {
 87         mid = (left + right) / 2;
 88         if (key < arr[mid]) {
 89             right = mid - 1;
 90         }
 91         else {
 92             left = mid + 1;
 93         }
 94     }
 95     return left;
 96 }
 97 
 98 //5 查找第一个与key相等的元素
 99 int findFirstEqual(int arr[], int len, int key)
100 {
101     int left = 0;
102     int right = len - 1;
103     int mid;
104 
105     while (left <= right) {
106         mid = (left + right) / 2;
107         if (key <= arr[mid]) {
108             right = mid - 1;
109         } else {//arr[mid] < key
110             left = mid + 1;
111         }
112     }
113     //arr[right] < key <= arr[left]
114     //right是最后一个小于key的
115     //left是第一个大于等于key的
116     if (left < len && arr[left] == key) {
117         return left;
118     }
119     return -1;
120 }
121 
122 //6 查找最后一个与key相等的元素
123 int findLastEqual(int arr[], int len, int key)
124 {
125     int left = 0;
126     int right = len - 1;
127     int mid;
128 
129     while (left <= right) {
130         mid = (left + right) / 2;
131         if (key < arr[mid]) {
132             right = mid - 1;
133         } else {//arr[mid] <= key
134             left = mid + 1;
135         }
136     }
137     //arr[right] <= key < arr[left]
138     //right是最后一个小于等于key的
139     //left是第一个大于key的
140     if (right >= 0 && arr[right] == key) {
141         return right;
142     }
143     return -1;
144 }
145 
146 
147 void test()
148 {
149 //  int a[] = {0, 1, 2, 3, 4, 5, 6};
150     int a[] = {0, 1, 2, 2, 2, 5, 6};
151     int len = 7;
152     int key = 2;
153 
154     int index;
155 
156     int i;
157     for (i = 0; i < len; ++i) {
158         printf("%d ", i);
159     }
160     printf("\n");
161     for (i = 0; i < len; ++i) {
162         printf("%d ", a[i]);
163     }
164     printf("\n");
165 
166 //    index = binarySearch(a, 10, 2);
167     printf("%d binarySearch\n", binarySearch(a, len, key));
168     printf("%d findLastLess\n", findLastLess(a, len, key));
169     printf("%d findFirstGreaterEqual\n", findFirstGreaterEqual(a, len, key));
170     printf("%d findLastLessEqual\n", findLastLessEqual(a, len, key));
171     printf("%d findFirstGreater\n", findFirstGreater(a, len, key));
172     printf("%d findFirstEqual\n", findFirstEqual(a, len, key));
173     printf("%d findLastEqual\n", findLastEqual(a, len, key));
174 }
175 
176 int main()
177 {
178     test();
179     return 0;
180 }
View Code

 

posted @ 2017-04-25 12:28  gongpixin  阅读(13275)  评论(14编辑  收藏  举报