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前缀和

186 道题目
简单: 19中等: 113困难: 54

前缀和 是技术面试里最常出现的能力维度之一。建议先掌握基础题型的边界处理,再逐步过渡到模式识别和复杂度 trade-off。

面试场景

高频考察问题建模、边界条件与口头表达的清晰度。

常见误区

只背模板不解释为什么,容易在追问里失分。

练习策略

每轮练 3-5 题,固定复盘复杂度和可替代解法。

推荐练习顺序

#题目难度
209

长度最小的子数组

Find the minimal length of a subarray whose sum is greater than or equal to the target using efficient algorithms.

中等
238

除了自身以外数组的乘积

Solve the 'Product of Array Except Self' problem by calculating the product of all elements except self for each index e…

中等
303

区域和检索 - 数组不可变

The Range Sum Query - Immutable problem involves implementing a data structure to handle range sum queries efficiently.

简单
304

二维区域和检索 - 矩阵不可变

Design a 2D matrix class that efficiently handles sum queries with O(1) time complexity using a prefix sum approach.

中等
363

矩形区域不超过 K 的最大数值和

Solve the "Max Sum of Rectangle No Larger Than K" problem using binary search over the valid sum space to optimize space…

困难
410

分割数组的最大值

Solve the 'Split Array Largest Sum' problem by minimizing the largest sum across k subarrays using dynamic programming a…

困难
497

非重叠矩形中的随机点

Design an algorithm to pick random points within non-overlapping rectangles using binary search and reservoir sampling.

中等
523

连续的子数组和

Identify if any continuous subarray sums to a multiple of k using prefix sums and hash table tracking efficiently.

中等
525

连续数组

Find the maximum length contiguous subarray with equal numbers of 0s and 1s using array scanning and hash lookup efficie…

中等
528

按权重随机选择

Random Pick with Weight requires implementing a probabilistic index picker using prefix sums and binary search efficient…

中等
560

和为 K 的子数组

Count the total number of contiguous subarrays in an integer array that sum exactly to a target value k using optimized …

中等
689

三个无重叠子数组的最大和

Maximize the sum of three non-overlapping subarrays with length k in an integer array using dynamic programming.

困难
713

乘积小于 K 的子数组

Count subarrays with a product strictly less than a given value k using efficient algorithms like binary search and slid…

中等
724

寻找数组的中心下标

Find the pivot index in an array where the sums of elements on both sides are equal using array and prefix sum technique…

简单
731

我的日程安排表 II

Implement a calendar that allows double bookings but prevents triple bookings, managing overlapping intervals efficientl…

中等
732

我的日程安排表 III

Implement My Calendar III to track maximum overlapping events efficiently using binary search and segment tree technique…

困难
798

得分最高的最小轮调

Find the smallest rotation index with the highest score using array and prefix sum techniques.

困难
813

最大平均值和的分组

Maximize the sum of averages by partitioning an integer array into at most k contiguous subarrays using dynamic programm…

中等
848

字母移位

Given a string and a shift array, shift the first i+1 letters of the string as specified in the array.

中等
862

和至少为 K 的最短子数组

Find the shortest subarray with a sum of at least k using binary search and sliding window techniques.

困难
903

DI 序列的有效排列

The problem asks to find the number of valid permutations for a given DI sequence string using dynamic programming and s…

困难
930

和相同的二元子数组

Count all contiguous subarrays in a binary array whose elements sum exactly to a given goal using prefix sums efficientl…

中等
974

和可被 K 整除的子数组

Count the number of subarrays whose sum is divisible by a given integer k using array scanning and hash lookup.

中等
995

K 连续位的最小翻转次数

Determine the minimum number of k-length consecutive bit flips needed to convert all zeros to ones in a binary array eff…

困难
1000

合并石头的最低成本

Minimize the cost to merge stones with k consecutive piles using dynamic programming to achieve the optimal solution.

困难
1004

最大连续1的个数 III

Find the longest consecutive ones in a binary array by optimally flipping at most k zeros using sliding window technique…

中等
1074

元素和为目标值的子矩阵数量

Count all non-empty submatrices in a given matrix whose elements sum exactly to the target using efficient scanning tech…

困难
1094

拼车

Determine if a car can handle multiple trips without exceeding its capacity using array sorting and event simulation tec…

中等
1109

航班预订统计

Solve Corporate Flight Bookings by marking range changes once, then building final seat totals with a single prefix sum …

中等
1124

表现良好的最长时间段

The Longest Well-Performing Interval problem challenges you to find the longest subarray where tiring days exceed non-ti…

中等
1140

石子游戏 II

Stone Game II is a dynamic programming problem where Alice and Bob alternate taking stones from piles to maximize their …

中等
1177

构建回文串检测

Given a string and queries, determine if a substring can be rearranged and modified to form a palindrome.

中等
1208

尽可能使字符串相等

Optimize substring transformations using a binary search approach to maximize the change within a budget.

中等
1248

统计「优美子数组」

The problem requires counting subarrays with exactly k odd numbers using an efficient array scanning approach.

中等
1292

元素和小于等于阈值的正方形的最大边长

This problem challenges you to find the largest square in a matrix with a sum below a given threshold using binary searc…

中等
1310

子数组异或查询

Compute XOR results for multiple subarray queries using efficient prefix XOR to reduce repeated computation overhead in …

中等
1314

矩阵区域和

Compute a matrix where each cell contains the sum of all elements within k-distance blocks using prefix sums efficiently…

中等
1352

最后 K 个数的乘积

Design a data structure to efficiently return the product of the last k numbers in a dynamic integer stream using prefix…

中等
1371

每个元音包含偶数次的最长子字符串

Find the longest substring with even counts of vowels using bitmasking and hash tables.

中等
1413

逐步求和得到正数的最小值

Find the minimum starting value to ensure the step-by-step sum of an array is always at least 1.

简单
1420

生成数组

This problem asks to build an array where the maximum element is found using exactly K comparisons, with dynamic program…

困难
1422

分割字符串的最大得分

Find the optimal split point in a binary string to maximize zeros on the left and ones on the right efficiently.

简单
1423

可获得的最大点数

Maximize your score by selecting k cards from the beginning or end of the array using a sliding window approach.

中等
1442

形成两个异或相等数组的三元组数目

Efficiently count all triplets in an array where two subarrays formed by splitting have equal XOR using array scanning a…

中等
1444

切披萨的方案数

This problem challenges you to determine the number of valid ways to cut a pizza into pieces with apples using dynamic p…

困难
1480

一维数组的动态和

Calculate the running sum of a given 1D array by updating each element to the sum of itself and all previous elements.

简单
1508

子数组和排序后的区间和

Compute the sum of sorted subarray sums efficiently using binary search over valid sum ranges and prefix sum accumulatio…

中等
1524

和为奇数的子数组数目

Count the number of subarrays with an odd sum using dynamic programming and prefix sum techniques.

中等
1546

和为目标值且不重叠的非空子数组的最大数目

Find the maximum number of non-overlapping subarrays that sum to a given target using efficient scanning and hash lookup…

中等
1588

所有奇数长度子数组的和

Calculate the sum of all odd-length subarrays in a given integer array using efficient array and math strategies.

简单
1589

所有排列中的最大和

Maximize the total sum of requests on nums by greedily assigning larger numbers to most frequently requested indices.

中等
1590

使数组和能被 P 整除

Determine the minimum-length subarray to remove so the remaining array sum is divisible by a given integer p efficiently…

中等
1658

将 x 减到 0 的最小操作数

Find the minimum number of operations to reduce a value x to zero by removing elements from an array.

中等
1664

生成平衡数组的方案数

Solve Ways to Make a Fair Array by tracking parity sums before and after each removal with prefix-sum style accounting.

中等
1674

使数组互补的最少操作次数

Find the minimum moves to make an array complementary by analyzing paired sums and using hash lookups for efficiency.

中等
1685

有序数组中差绝对值之和

Calculate the sum of absolute differences between each element and others in a sorted array efficiently.

中等
1687

从仓库到码头运输箱子

Optimize the minimum number of trips to deliver boxes to ports under strict ship constraints using dynamic programming t…

困难
1703

得到连续 K 个 1 的最少相邻交换次数

Find the minimum number of adjacent swaps to gather k consecutive ones in a binary array using sliding window logic.

困难
1712

将数组分成三个子数组的方案数

The problem requires finding the number of ways to split an array into three subarrays where each split meets a certain …

中等
1732

找到最高海拔

Find the highest altitude after a series of altitude changes during a road trip using prefix sum technique.

简单
1737

满足三条件之一需改变的最少字符数

This problem asks for the minimum operations to change two strings so that one of three conditions is met.

中等
1738

找出第 K 大的异或坐标值

Compute the kth largest XOR coordinate in a 2D matrix using prefix sums, bit manipulation, and optimized selection techn…

中等
1744

你能在你最喜欢的那天吃到你最喜欢的糖果吗?

Determine if you can eat a candy of your favorite type on a specific day, given daily limits and candy availability.

中等
1769

移动所有球到每个盒子所需的最小操作数

Solve the problem of finding the minimum operations to move balls to each box using an efficient approach with arrays an…

中等
1829

每个查询的最大异或值

Find the maximum XOR for each query based on a sorted array and bit manipulation.

中等
1838

最高频元素的频数

Maximize the frequency of an element in an array by incrementing at most `k` elements. Use binary search and greedy tech…

中等
1854

人口最多的年份

Find the earliest year with the highest population using an array plus counting approach.

简单
1856

子数组最小乘积的最大值

The problem asks to find the maximum min-product of any non-empty subarray of nums.

中等
1862

向下取整数对和

The problem asks to calculate the sum of floor divisions for all pairs in a given integer array, using an efficient meth…

困难
1871

跳跃游戏 VII

The problem asks to determine if we can reach the last index of a binary string, with a set range of jumps between indic…

中等
1872

石子游戏 VIII

Stone Game VIII requires calculating maximum score difference using state transition dynamic programming on prefix sums …

困难
1878

矩阵中最大的三个菱形和

Find the three largest distinct rhombus sums from a given grid using array and math techniques.

中等
1889

装包裹的最小浪费空间

Minimize the wasted space when packaging items into boxes, considering package and box size constraints.

困难
1893

检查是否区域内所有整数都被覆盖

Check if all integers in the range [left, right] are covered by intervals in a given set of ranges.

简单
1894

找到需要补充粉笔的学生编号

Identify the first student who will run out of chalk using a simulation with prefix sums and binary search.

中等
1895

最大的幻方

Find the side length of the largest magic square in a matrix where row, column, and diagonal sums are equal.

中等
1915

最美子字符串的数目

Count the number of wonderful non-empty substrings of a given string based on frequency conditions of characters.

中等
1930

长度为 3 的不同回文子序列

Count all unique length-3 palindromic subsequences in a string efficiently using hash tables and character positions.

中等
1943

描述绘画结果

Solve the problem of describing a painted segment with mixed colors using array scanning and hash table lookups.

中等
1991

找到数组的中间位置

Find the smallest middle index where the sum of elements on the left equals the sum on the right using prefix sums effic…

简单
2017

网格游戏

Solve the Grid Game problem by optimizing the movement of two robots on a 2D matrix grid.

中等
2024

考试的最大困扰度

Maximize the Confusion of an Exam requires adjusting at most k answers to create the longest consecutive true or false s…

中等
2025

分割数组的最多方案数

Determine the maximum number of ways to split an array into equal sums using at most one element change, leveraging pref…

困难
2055

蜡烛之间的盘子

Determine the number of plates between candles in a given substring using binary search and prefix sum techniques.

中等
2100

适合野炊的日子

Find good days to rob the bank by identifying days with non-increasing and non-decreasing guard counts using dynamic pro…

中等
2106

摘水果

Compute the maximum fruits collectable on an infinite line by moving at most k steps from a start position efficiently.

困难
2121

相同元素的间隔之和

Solve the problem of calculating intervals between identical elements using array scanning and hash lookup.

中等
2132

用邮票贴满网格图

Determine if a binary grid can be fully covered using fixed-size stamps by applying a greedy placement and validation st…

困难
2145

统计隐藏数组数目

Given a sequence of differences, count how many hidden sequences fit within a range using an array and prefix sum approa…

中等
2171

拿出最少数目的魔法豆

Determine the minimum beans to remove so all remaining non-empty bags have equal beans using a greedy approach.

中等
2207

字符串中最多数目的子序列

Maximize the number of subsequences by optimally adding a character to a given string to match a specified pattern.

中等
2209

用地毯覆盖后的最少白色砖块

Find the minimum number of white tiles visible after optimally placing carpets using state transition dynamic programmin…

困难
2218

从栈中取出 K 个硬币的最大面值和

Optimize coin selection across multiple piles using state transition dynamic programming to achieve the maximum wallet v…

困难
2222

选择建筑的方案数

Solve Number of Ways to Select Buildings by counting alternating 3-building patterns with state transitions over the bin…

中等
2234

花园的最大总美丽值

Determine the maximum total beauty of gardens by strategically planting flowers using binary search over achievable flow…

困难
2245

转角路径的乘积中最多能有几个尾随零

Find the maximum trailing zeros in the product of a cornered path within a 2D grid.

中等
2251

花期内花的数目

Find the number of flowers in full bloom at the given times for a list of people.

困难
2256

最小平均差

Find the index with the minimum average difference in an array using prefix sums.

中等
2270

分割数组的方案数

Count all valid ways to split a 0-indexed integer array into two non-empty parts using array plus prefix sum logic effic…

中等
2271

毯子覆盖的最多白色砖块数

Solve Maximum White Tiles Covered by a Carpet by sorting intervals, checking optimal carpet starts, and counting full pl…

中等
2281

巫师的总力量和

The Sum of Total Strength of Wizards problem asks for the sum of the total strengths of all contiguous subarrays of wiza…

困难
2302

统计得分小于 K 的子数组数目

Count all non-empty subarrays whose score, defined as sum times length, is strictly less than a given integer k efficien…

困难
2381

字母移位 II

Shift letters in a string using a sequence of range-based forward or backward operations efficiently with prefix sums.

中等
2382

删除操作后的最大子段和

Calculate the maximum segment sum after sequential removals using array plus union find for efficient merging of segment…

困难
2389

和有限的最长子序列

Find the maximum size of a subsequence from nums with a sum less than or equal to each query value.

简单
2391

收集垃圾的最少总时间

This problem asks you to find the minimum amount of time needed to collect all garbage in a city, focusing on array and …

中等
2398

预算内的最多机器人数目

Determine the maximum number of consecutive robots you can operate without exceeding a given budget using efficient bina…

困难
2406

将区间分为最少组数

Determine the minimum number of non-overlapping groups for a set of intervals using precise two-pointer scanning logic.

中等
2420

找到所有好下标

Identify all indices in an array where the k-length prefix is non-increasing and the k-length suffix is non-decreasing.

中等
2428

沙漏的最大总和

Calculate the maximum sum of an hourglass in a 2D matrix using array traversal and submatrix evaluation techniques effic…

中等
2438

二的幂数组中查询范围内的乘积

The Range Product Queries of Powers problem requires calculating the product of powers of 2 for a range of queries on a …

中等
2439

最小化数组中的最大值

Minimize Maximum of Array involves finding the smallest possible maximum value after applying a series of operations on …

中等
2448

使数组相等的最小开销

Find the minimum cost to make all elements of an array equal by using binary search over valid answers.

困难
2483

商店的最少代价

Determine the earliest closing hour of a shop to minimize penalty using a string of customer visits and prefix sums.

中等
2485

找出中枢整数

Find the Pivot Integer problem challenges you to identify an integer x that balances prefix sums on both sides.

简单
2488

统计中位数为 K 的子数组

Count the number of subarrays in a given array with median equal to a specified value k.

困难
2528

最大化城市的最小电量

Determine the maximum minimum power a city can achieve by strategically adding power stations using binary search and pr…

困难
2536

子矩阵元素加 1

Increment Submatrices by One focuses on efficiently updating submatrices using row-wise prefix sums in an n by n matrix.

中等
2552

统计上升四元组

Given a permutation of numbers, count the number of increasing quadruplets using dynamic programming.

困难
2559

统计范围内的元音字符串数

Count the number of strings that start and end with a vowel in given ranges within an array of words.

中等
2574

左右元素和的差值

Compute absolute differences between left and right cumulative sums for each element in an integer array efficiently.

简单
2587

重排数组以得到最大前缀分数

Maximize the number of positive prefix sums by rearranging an integer array using a greedy, order-focused strategy.

中等
2588

统计美丽子数组数目

Count the Number of Beautiful Subarrays is a Medium-level problem involving array scanning and hash table lookup to find…

中等
2602

使数组元素全部相等的最少操作次数

Find the minimum number of operations to make all elements in an array equal for each query.

中等
2615

等值距离和

In this problem, you calculate an array where each element is the sum of absolute differences of indices for equal value…

中等
2640

一个数组所有前缀的分数

Compute the score of each prefix in an array using conversion rules while tracking the maximum efficiently for prefix su…

中等
2680

最大或值

Maximize the bitwise OR of an array by applying at most k multiplication operations on selected elements.

中等
2681

英雄的力量

Calculate the total power of all non-empty hero groups using state transition dynamic programming efficiently with sorti…

困难
2731

移动机器人

Calculate total distances between robots moving on a number line while accounting for collisions using array plus braint…

中等
2772

使数组中的所有元素都等于零

Determine if all elements in a given array can be reduced to zero using repeated k-length prefix operations efficiently.

中等
2845

统计趣味子数组的数目

Count all subarrays where the number of elements satisfying a modulo condition equals a target k using efficient prefix …

中等
2848

与车相交的点

Count covered integer points by merging overlapping car intervals or marking visited positions on the number line.

简单
2875

无限数组的最短子数组

Find the shortest subarray in an infinite array that sums to a given target using array scanning and hash lookup.

中等
2906

构造乘积矩阵

Solve the "Construct Product Matrix" problem by calculating the product of elements in 2D matrices without division.

中等
2947

统计美丽子字符串 I

Given a string and a value k, count the number of beautiful substrings where vowels * consonants % k == 0.

中等
2949

统计美丽子字符串 II

Count Beautiful Substrings II focuses on finding beautiful substrings with hash tables and number theory techniques.

困难
2968

执行操作使频率分数最大

Maximize the frequency score by applying up to k operations on a sorted array using binary search over valid answer spac…

困难
2971

找到最大周长的多边形

Determine the largest perimeter polygon from a set of side lengths using a greedy approach with invariant validation che…

中等
2983

回文串重新排列查询

Given a string and queries, check if rearranging specified substrings can make the string a palindrome.

困难
3015

按距离统计房屋对数目 I

Determine the number of house pairs at each street distance using graph traversal and breadth-first search efficiently.

中等
3017

按距离统计房屋对数目 II

Count the Number of Houses at a Certain Distance II is a graph problem that requires efficient pair counting with an add…

困难
3026

最大好子数组和

Find the maximum sum of any subarray where the first and last elements differ by exactly k using efficient array scannin…

中等
3028

边界上的蚂蚁

Solve the problem of counting how often an ant returns to a boundary based on the steps described in the input array.

简单
3070

元素和小于等于 k 的子矩阵的数目

Count all submatrices including the top-left element with sum less than k using array and matrix prefix sum strategies.

中等
3077

K 个不相交子数组的最大能量值

Solve Maximum Strength of K Disjoint Subarrays with dynamic programming that tracks segment state, sign changes, and wei…

困难
3086

拾起 K 个 1 需要的最少行动次数

Find the minimum number of moves to pick exactly k ones from a binary array, considering a constraint on changes.

困难
3096

得到更多分数的最少关卡数目

Determine the minimum number of levels Alice must play in a binary game array to secure more points than Bob using prefi…

中等
3129

找出所有稳定的二进制数组 I

Find all stable binary arrays of a given number of 0's, 1's, and limit using dynamic programming and state transitions.

中等
3130

找出所有稳定的二进制数组 II

Compute the number of stable binary arrays using state transition dynamic programming with exact zero, one, and limit co…

困难
3147

从魔法师身上吸取的最大能量

Maximize your energy by strategically jumping through magicians using array and prefix sum techniques for optimal path c…

中等
3152

特殊数组 II

Determine whether each subarray meets the special condition of alternating parity for all adjacent elements efficiently …

中等
3179

K 秒后第 N 个元素的值

Solve for the N-th value after K seconds by simulating array updates and using prefix sum techniques.

中等
3191

使二进制数组全部等于 1 的最少操作次数 I

Find the minimum number of operations to make all elements of a binary array equal to one using sliding window and state…

中等
3212

统计 X 和 Y 频数相等的子矩阵数量

Count the number of submatrices with equal frequency of 'X' and 'Y' in a 2D character grid.

中等
3224

使差值相等的最少数组改动次数

Minimize changes to make array differences equal by replacing elements within a given range.

中等
3225

网格图操作后的最大分数

Maximize your score by choosing the optimal sequence of column operations on a grid using dynamic programming transition…

困难
3250

单调数组对的数目 I

Compute the number of monotonic pairs in an integer array using state transition dynamic programming efficiently.

困难
3251

单调数组对的数目 II

This problem involves finding the count of monotonic pairs in an array using dynamic programming and combinatorics techn…

困难
3261

统计满足 K 约束的子字符串数量 II

Count Substrings That Satisfy K-Constraint II requires finding valid substrings in a binary string based on a k-constrai…

困难
3312

查询排序后的最大公约数

Solve the Sorted GCD Pair Queries problem by efficiently counting and locating GCDs of all array pairs using hash mappin…

困难
3333

找到初始输入字符串 II

Calculate how many potential original strings Alice might have intended to type, considering her clumsy typing behavior.

困难
3346

执行操作后元素的最高频率 I

Maximize the frequency of an element in an array after performing a series of operations to find the best possible resul…

中等
3347

执行操作后元素的最高频率 II

Determine the maximum frequency of any element after performing limited operations using binary search and sliding windo…

困难
3354

使数组元素等于零

Learn how to transform an integer array to zeros using simulation and directional selection efficiently and reliably.

简单
3355

零数组变换 I

Transform the given integer array into a zero array using range operations, focusing on prefix sum optimization and care…

中等
3356

零数组变换 II

Zero Array Transformation II requires determining the minimum query sequence to convert all array elements to zero using…

中等
3361

两个字符串的切换距离

Find the minimum cost of transforming one string into another, considering operations between characters.

中等
3362

零数组变换 III

Zero Array Transformation III requires removing the minimum number of queries to make all elements zero using greedy val…

中等
3364

最小正和子数组

Find the minimum sum of any subarray of size between l and r with a positive total using efficient sliding window logic.

简单
3381

长度可被 K 整除的子数组的最大元素和

Find the maximum sum of a subarray where the length of the subarray is divisible by k.

中等
3413

收集连续 K 个袋子可以获得的最多硬币数量

Solve the problem of maximizing coins from selecting k consecutive bags, using binary search and sliding window techniqu…

中等
3425

最长特殊路径

Compute the longest downward path in a tree with unique node values using DFS, hash lookup, and careful array scanning.

困难
3427

变长子数组求和

Calculate the total sum of all elements in subarrays defined for each index in an array, using the array plus prefix sum…

简单
3432

统计元素和差值为偶数的分区方案

Count the number of partitions with an even sum difference from an array of integers.

简单
3434

子数组操作后的最大频率

Determine the maximum frequency of a target value k after applying one subarray addition operation efficiently using arr…

中等
3445

奇偶频次间的最大差值 II

Find the maximum difference between even and odd character frequencies in substrings using sliding window updates effici…

困难
3473

长度至少为 M 的 K 个子数组之和

Maximize the sum of k non-overlapping subarrays of at least length m using dynamic programming and prefix sums efficient…

中等
3480

删除一个冲突对后最大子数组数目

Maximize the count of subarrays after removing one conflicting pair using array traversal and segment tree logic efficie…

困难
3486

最长特殊路径 II

Find the longest downward path in a tree where node values are mostly distinct, allowing one repeat, using array scannin…

困难
3494

酿造药水需要的最少总时间

This problem involves calculating the minimum time required for wizards to brew potions based on their skills and mana u…

中等
3500

将数组分割为子数组的最小代价

Optimize array splits with dynamic programming to minimize costs for the Minimum Cost to Divide Array Into Subarrays pro…

困难
3538

合并得到最小旅行时间

Minimize the total travel time by merging road signs, using dynamic programming to manage state transitions efficiently.

困难
3546

等和矩阵分割 I

Determine if an m x n matrix grid can be split into two non-empty sections with equal sums by making a single horizontal…

中等
3548

等和矩阵分割 II

Determine if a matrix can be partitioned into two sections with an equal sum using a single cut.

困难
3578

统计极差最大为 K 的分割方式数

Count the number of valid ways to partition an array into contiguous segments where max-min difference is at most k.

中等
3599

划分数组得到最小 XOR

Partition an integer array into k subarrays to minimize the maximum XOR using state transition dynamic programming effic…

中等

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LeetCode 前缀和题型题解:186题训练路线