From eb94e9748a892ec513ddfb9dbddca3872a69ad2c Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:06 +0800 Subject: [PATCH] =?UTF-8?q?Update=2053.=20=E6=95=B0=E5=AD=97=E5=9C=A8?= =?UTF-8?q?=E6=8E=92=E5=BA=8F=E6=95=B0=E7=BB=84=E4=B8=AD=E5=87=BA=E7=8E=B0?= =?UTF-8?q?=E7=9A=84=E6=AC=A1=E6=95=B0.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充二分查找边界过程的配图,调整二分查找返回第一个大于等于目标值位置及计算次数的说明,精简右边界初始值取值的示例阐述。 --- notes/53. 数字在排序数组中出现的次数.md | 26 ++++-------------------- notes/pics/offer53-lower-bound.png | Bin 0 -> 126230 bytes 2 files changed, 4 insertions(+), 22 deletions(-) create mode 100644 notes/pics/offer53-lower-bound.png diff --git a/notes/53. 数字在排序数组中出现的次数.md b/notes/53. 数字在排序数组中出现的次数.md index ed08922b..bda9aca5 100644 --- a/notes/53. 数字在排序数组中出现的次数.md +++ b/notes/53. 数字在排序数组中出现的次数.md @@ -38,23 +38,11 @@ public int binarySearch(int[] nums, int K) { } ``` -但是在查找第一个位置时,找到元素之后应该继续往前找。也就是当 nums[m]\>=k 时,在左区间继续查找,左区间应该包含 m 位置。 +但是在查找第一个位置时,找到元素之后应该继续往前找。也就是当 nums[m]\>=k 时,在左区间继续查找,左区间应该包含 m 位置。这样 binarySearch 返回的是第一个大于等于 k 的位置。 -```java -private int binarySearch(int[] nums, int target) { - int l = 0, h = nums.length; - while (l < h) { - int m = l + (h - l) / 2; - if (nums[m] >= target) - h = m; - else - l = m + 1; - } - return l; -} -``` +查找最后一个位置可以转换成寻找 k+1 的第一个位置,并再往前移动一个位置,因此出现次数为 binarySearch(k + 1) - binarySearch(k)。以题目中的数组为例,查找区间为左闭右开的 [l, h): -查找最后一个位置可以转换成寻找 k+1 的第一个位置,并再往前移动一个位置。 +

```java public int countTarget(int[] scores, int target) { @@ -76,10 +64,4 @@ private int binarySearch(int[] nums, int target) { } ``` -需要注意以上实现的查找第一个位置的 binarySearch 方法,h 的初始值为 nums.length,而不是 nums.length - 1。先看以下示例: - -```text -nums = [2,2], k = 2 -``` - -如果 h 的取值为 nums.length - 1,那么在查找最后一个位置时,binarySearch(nums, k + 1) - 1 = 1 - 1 = 0。这是因为 binarySearch 只会返回 [0, nums.length - 1] 范围的值,而 binarySearch([2,2], 3) 应该返回 3 插入 nums 中的位置,也就是数组最后一个位置再往后一个位置,即 nums.length。所以需要将 h 取值为 nums.length,从而使得 binarySearch 返回的区间更大,能够覆盖 k 大于 nums 最后一个元素的情况。 +需要注意 binarySearch 中 h 的初始值为 nums.length,而不是 nums.length - 1。k 比所有元素都大时,第一个大于等于 k 的位置在数组之外,应该返回 nums.length。例如 nums = [2, 2]、k = 2 时,binarySearch(nums, 3) 应返回 2,次数为 2 - 0 = 2;如果 h 从 nums.length - 1 开始,返回值最大只能是 1,得到的次数就变成了 1。 diff --git a/notes/pics/offer53-lower-bound.png b/notes/pics/offer53-lower-bound.png new file mode 100644 index 0000000000000000000000000000000000000000..33fc89acca7b25c5b138d801b6e0e94f3c29860f GIT binary patch literal 126230 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