From af94cbf1538e4e131144fcc8e5dee4b53bfcc065 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=BB=84=E9=93=AD=E7=8E=A5?= <15718462+vyueeee@user.noreply.gitee.com> Date: Thu, 25 Sep 2025 20:34:23 +0800 Subject: [PATCH] =?UTF-8?q?topic2=E4=BE=8B=E9=A2=98=E6=8F=90=E4=BA=A4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...9_\351\273\204\351\223\255\347\216\245.md" | 26 ++++ ...6_\351\273\204\351\223\255\347\216\245.md" | 39 ++++++ ...6_\351\273\204\351\223\255\347\216\245.md" | 118 ++++++++++++++++++ ...\346\211\276\344\270\223\351\242\230.pptx" | Bin 0 -> 480623 bytes 4 files changed, 183 insertions(+) create mode 100644 "topic02/solution/lc1539_\351\273\204\351\223\255\347\216\245.md" create mode 100644 "topic02/solution/lc2616_\351\273\204\351\223\255\347\216\245.md" create mode 100644 "topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276_\351\273\204\351\223\255\347\216\245.md" create mode 100644 "topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276\344\270\223\351\242\230.pptx" diff --git "a/topic02/solution/lc1539_\351\273\204\351\223\255\347\216\245.md" "b/topic02/solution/lc1539_\351\273\204\351\223\255\347\216\245.md" new file mode 100644 index 0000000..5a3c902 --- /dev/null +++ "b/topic02/solution/lc1539_\351\273\204\351\223\255\347\216\245.md" @@ -0,0 +1,26 @@ +### 题解 + +**解题思路** + +1.如果正整数数组的首位的值大于k,那么第k个缺失的正整数数值为k + +2.如果k在数组中间的话,通过二分找到k所对应的位置,就能通过对应的元素找到缺失的第k个整数。缺失的位置一定是在数组两个数字之间或者在整个数组后面,那我们需要找到一个区间,保证k在这个区间内,最后第k个缺失的数为k-(arr[l-1]-(l-1)-1)+arr[l-1] + +### 示例代码(C++) +```cpp +// https://leetcode.cn/problems/kth-missing-positive-number/submissions/663991637/ +class Solution { +public: + int findKthPositive(vector& arr, int k) { + if(arr[0] > k) return k; + int l = 0 , r = arr.size(); + while(l < r){ + int mid = (l + r) >> 1; + int x = mid < arr.size() ? arr[mid] : INT_MAX; + if(x - mid - 1 >= k) r = mid; + else l = mid + 1; + } + return k - (arr[l - 1] - (l - 1) - 1) + arr[l - 1]; + } +}; +``` \ No newline at end of file diff --git "a/topic02/solution/lc2616_\351\273\204\351\223\255\347\216\245.md" "b/topic02/solution/lc2616_\351\273\204\351\223\255\347\216\245.md" new file mode 100644 index 0000000..73894b6 --- /dev/null +++ "b/topic02/solution/lc2616_\351\273\204\351\223\255\347\216\245.md" @@ -0,0 +1,39 @@ +### 题解 + +**解题思路** + +1.题目要求我们使得p个数对差值的最大值最小 + +2.从示例1可以看出,4个数字不是相邻的时候可以得到最小,那在数组进行排序之后,相邻的数字差值肯定是最小的我们要寻找的x,如果x值越大,那么容纳的下标对越多因此需要对x进行二分查找,找到一个不能再去二分的x的值 + +### 示例代码(C++) +```cpp +// https://leetcode.cn/problems/minimize-the-maximum-difference-of-pairs/submissions/664014506/ +class Solution { +public: + int minimizeMax(vector& nums, int p) { + sort(nums.begin(),nums.end()); + int left = 0; + int right = 1e9+1; + while(left < right){ + int mid = (left+right)/2; + if(check(nums,p,mid)) right = mid; + + else left = mid+1; + + } + return left; + } + + bool check(vector& nums , int p, int mid){ + int count = 0; + for(int i = 0;i= p; + } +}; +``` diff --git "a/topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276_\351\273\204\351\223\255\347\216\245.md" "b/topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276_\351\273\204\351\223\255\347\216\245.md" new file mode 100644 index 0000000..e5b3d36 --- /dev/null +++ "b/topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276_\351\273\204\351\223\255\347\216\245.md" @@ -0,0 +1,118 @@ +# **1.二分查找背景介绍** + +在二分查找出现之前,主要使用线性查找,其时间复杂度为O(n),当数据量达到百万级时,效率极低。而二分查找依托“分治”思想(将目标值与数组中间的元素进行比较),将查找范围每次缩减一半,使时间复杂度降至O(logn)。 + +# **2.二分查找的定义** + +二分查找,也称为折半查找,是一种在有序数组中查找特定元素的搜索算法。它的基本思想是将目标值与数组中间的元素进行比较。 + +# **3.二分查找的具体应用场景** + +(1).**基础值查找**:在有序数组中判断目标值是否存在,并返回其索引。 + +(2).**边界值查找**:当有序数组存在重复元素时,需查找目标值的 “左边界”(第一个出现的位置)或 “右边界”(最后一个出现的位置)。 + +(3).**数值逼近**:在有序数据集中,查找 “满足条件的最接近值” 或 “临界值”。 + +(4).**有序矩阵查找**:在 “行有序且列有序” 的二维矩阵中查找目标值(如每一行从左到右升序,每一列从上到下升序)。 + +# **4.二分查找的模板** + +(1).**基础查找模板** +```cpp +#include +using namespace std; +// 模板1:基础查找(查找目标值是否存在) +// 功能:在有序数组中查找目标值,返回任意匹配元素的索引,若不存在返回-1 +int binarySearchBasic(const vector& nums, int target) { + int left = 0; + int right = nums.size() - 1; // 闭区间[left, right] + while (left <= right) { // 当left == right时,区间仍有效 + int mid = left + (right - left) / 2; // 避免溢出,等价于(left + right) / 2 + if (nums[mid] == target) { + return mid; // 找到目标,直接返回索引 + } else if (nums[mid] < target) { + left = mid + 1; // 目标在右半部分,收缩左边界 + } else { + right = mid - 1; // 目标在左半部分,收缩右边界 + } + } + return -1; // 未找到目标 +} +``` + +(2).**左边界查找模板** +```cpp +#include +using namespace std; +// 模板2:左边界查找(查找第一个出现的目标值) +// 功能:在有序数组中查找目标值第一次出现的位置,若不存在返回-1 +int binarySearchLeftBound(const vector& nums, int target) { + int left = 0; + int right = nums.size() - 1; + int result = -1; // 存储最终左边界索引 + while (left <= right) { + int mid = left + (right - left) / 2; + if (nums[mid] == target) { + result = mid; // 记录当前位置为候选结果 + right = mid - 1; // 继续向左寻找更早出现的位置 + } else if (nums[mid] < target) { + left = mid + 1; + } else { + right = mid - 1; + } + } + return result; // 未找到则返回-1 +} +``` +(3).**右边界查找模板** +```cpp +#include +using namespace std; +// 模板3:右边界查找(查找最后一个出现的目标值) +// 功能:在有序数组中查找目标值最后一次出现的位置,若不存在返回-1 +int binarySearchRightBound(const vector& nums, int target) { + int left = 0; + int right = nums.size() - 1; + int result = -1; // 存储最终右边界索引 + + while (left <= right) { + int mid = left + (right - left) / 2; + if (nums[mid] == target) { + result = mid; // 记录当前位置为候选结果 + left = mid + 1; // 继续向右寻找更晚出现的位置 + } else if (nums[mid] < target) { + left = mid + 1; + } else { + right = mid - 1; + } + } + return result; // 未找到则返回-1 +} +``` + +# **5.题与资料:** +## 例题: +注:一题是“第K个xx”,一题是“最大xx的最小xx”都是比较常见的套路,见到这种问法就可以往二分的方向去想了 + - [1539. 第 k 个缺失的正整数](https://leetcode.cn/problems/kth-missing-positive-number/): 按进阶要求完成,二分+二分查找 + - [2616. 最小化数对的最大差值](https://leetcode.cn/problems/minimize-the-maximum-difference-of-pairs) +## 题单: + - [CF689C](https://codeforces.com/problemset/problem/689/C) + - [222. 完全二叉树的节点个数](https://leetcode.cn/problems/count-complete-tree-nodes/) + - [1011. 在 D 天内送达包裹的能力](https://leetcode.cn/problems/capacity-to-ship-packages-within-d-days/) + - [1552. 两球之间的磁力](https://leetcode.cn/problems/magnetic-force-between-two-balls/) + - [875. 爱吃香蕉的珂珂](https://leetcode.cn/problems/koko-eating-bananas/) + - [1482. 制作 m 束花所需的最少天数](https://leetcode.cn/problems/minimum-number-of-days-to-make-m-bouquets) + - [1552. 两球之间的磁力](https://leetcode.cn/problems/magnetic-force-between-two-balls) + - [1760. 袋子里最少数目的球](https://leetcode.cn/problems/minimum-limit-of-balls-in-a-bag/) + - [1802. 有界数组中指定下标处的最大值](https://leetcode.cn/problems/maximum-value-at-a-given-index-in-a-bounded-array/) + - [2187. 完成旅途的最少时间](https://leetcode.cn/problems/minimum-time-to-complete-trips/) + - [2560. 打家劫舍 IV](https://leetcode.cn/problems/house-robber-iv/): 难度相当于困难(难度分2081) + - [3007. 价值和小于等于 K 的最大数字](https://leetcode.cn/problems/maximum-number-that-sum-of-the-prices-is-less-than-or-equal-to-k) +## 补充:三分法(看时间而定,建议在最后做简单的介绍) +### 山脉数组 - 三分法 +_三分法可用于解决求峰值/谷值问题,限制:极值两边必须严格递增/递减_ + - [852. 山脉数组的峰顶索引](https://leetcode.cn/problems/peak-index-in-a-mountain-array): 进阶要求可用二分或三分法解决,建议两种都要掌握 + - [3139. 使数组中所有元素相等的最小开销](https://leetcode.cn/problems/minimum-cost-to-equalize-array): 最终可以转化为求谷值问题 +## 更多题解与题单(灵茶) +https://leetcode.cn/circle/discuss/SqopEo/ \ No newline at end of file diff --git "a/topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276\344\270\223\351\242\230.pptx" "b/topic02/solution/\344\272\214\345\210\206\346\237\245\346\211\276\344\270\223\351\242\230.pptx" new file mode 100644 index 0000000000000000000000000000000000000000..8137a22673e97b2efdaa35529ae06fc050df53e5 GIT binary patch literal 480623 zcmeFYV|Om^w(c9-=7??Ewr$(Vh;7@pZQIs}lM&nY$(-}-cFx}Gzdpg*^`fe^=dOD3 zRO|hB_1^ERX0RWHzAb_-l>};J)Y@PL#-R(`B zbZFgdtnmv#fXMRzes21|$N%IvFqAfKyFrf-at-1={zY4dR14~ojk#_DQtj<#&~ zkgf-S6El|1ygV8FP^@PjzwuNo?LPTotu&N=EB=GI4u37w)+n(OzrYq`9h4KpXvtoj zi4Vs>po5HH6N5tXYLHW>@@!l~bi?U@pkZr2WuQ&XU@!+}dg2RYqwRVZOkF|X_h9w+ z$a!5P)_!^YUqS6oHohumzlvig1;OG;6wz21_1*nz(G8{EQRU%X_3LdYGCovZQTjB0U6BIB zc8x%IyEp}(v3;pD(+e?QyMwfPh z|I#fzt9MU~*7!Nd}ABx>dR6!n8u}bqtY$w;KI@IM+o}9{8c{ zQ1M=;&IB9>j?&#xWjl3b?G@+P={}5k>GZ>Y$i=msKnr+;-|)0J4VlNtUBsKh%B9I# zOwi{I&%#mD^6;cM@Q_sq0<+LHv(>^vvpsLkM=_IYbsw?Hzh%r{UGwK$R2RMHxWsaf zyGp|CN-;D>gxgVKPnFo5y=4j3ncRhr9tsVjaz!2Qm@@x4XZ+@gv%!D?0G5B2QGVW& zy}dJ?y`zcKk2)JTTiDtDOPeoJw`|wxQAV%HE^!MsWtrLWWchakTJbO)G zPL&8HM65D^c06NTtRoq^-N>1fz|xxcSm)ee23J&h-a`x4*7w|88o9-w3^X(1=6xxc z1i~{UU{o92`q%j4-en!3F-baW{y|U9E&AgwS4G#74tfzPH7JX9PmNPM9n2^>h?`*e z-MwIYMR{D?ACbWcLMqHfT$T6}n*EuOK1;_=a5sZuHJ5{$;0LF&o}CJhzM=+VBS~5i z$tOWt+92&Ldv0=^?Rc@!5x#uLLUqv1`+0dz-v01eK*3otfzy{DGG6j9#4AADGG{+R zVEH{V&bME21q*-!Wc)q3`k&}0fE1Ltd8+^@p#pk^vC5qMyqhosHB@SuAu)&!3*Z6Q@7$F<>0xU7b!x;anAwH`o@dq~D7&OSvbrsknAOt{)}ewNO05qQAa#oqk2Z*5l-G za$bMX@_vHa67; 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