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数学·driven模式

模式页更适合建立可迁移的解题框架。先抓识别信号,再反复练状态定义、更新规则和边界解释,能比零散刷题更快形成稳定手感。

database43 道题tune29/11/3 难度梯度category1 个关联题型

模式摘要

先识别什么

题目里常出现可以复用的状态更新节奏。

解法节奏

先口述状态和不变量,再解释每一步如何更新,最后用反例验证边界。

高频失分点

状态定义说不清,写出来也难以稳定维护。

识别信号

  • 题目里常出现可以复用的状态更新节奏。
  • 暴力枚举太慢,但结构上存在可维护的不变量。
  • 面试追问通常会盯住边界、状态变更和复杂度。

解题流程

  1. 1. 明确窗口/状态定义
  2. 2. 更新状态并维护约束
  3. 3. 用边界样例验证

常见失分点

  • 状态定义说不清,写出来也难以稳定维护。
  • 只会背模板,解释不了为什么这样更新。
  • 样例能过,但边界和复杂度追问容易崩。

推荐题单梯度

题库

数学·driven模式题库

这里更适合先按关键词或难度找题,再按关联题型切入。题库会在容器内继续滚动时慢慢续载,避免模式页被长列表一下子拉穿。

慢加载模式题库

适合先建模式理解,再扩展到完整题单。

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当前展示 24 / 43 道题目

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#题目难度
7

整数反转

Reverse Integer challenges you to invert the digits of a signed 32-bit integer, handling overflow and negative values ca…

中等
9

回文数

Determine if a given integer reads the same forward and backward using a math-driven solution strategy without convertin…

简单
172

阶乘后的零

Given a number n, find how many trailing zeroes are in n! using a math-driven approach.

中等
263

丑数

The Ugly Number problem asks you to determine if a number is divisible only by 2, 3, or 5.

简单
492

构造矩形

Given an area, design a rectangle with integer length and width optimizing L >= W and minimal difference, using math.

简单
507

完美数

Check if a given number is a perfect number by verifying if it's equal to the sum of its divisors, excluding itself.

简单
728

自除数

Identify self-dividing numbers in a given range by verifying divisibility against their digits.

简单
780

到达终点

Determine whether it is possible to reach a target point from a start point using repeated additive moves following stri…

困难
1017

负二进制转换

Convert any non-negative integer into its base -2 representation using a math-driven iterative remainder strategy.

中等
1175

质数排列

Calculate the number of valid permutations of 1 to n where prime numbers occupy prime indices using math-driven logic.

简单
1185

一周中的第几天

Given a date, calculate the corresponding weekday using a math-based strategy, focusing on modular arithmetic.

简单
1276

不浪费原料的汉堡制作方案

Determine the exact counts of jumbo and small burgers using all tomato and cheese slices without leftovers, applying mat…

中等
1281

整数的各位积和之差

Calculate the difference between the product and sum of an integer's digits using a simple math-driven approach for effi…

简单
1317

将整数转换为两个无零整数的和

Find two positive integers whose sum equals n and neither contains the digit zero, using a direct math-driven approach.

简单
1344

时钟指针的夹角

Calculate the smaller angle between the hour and minute hands of a clock based on given time inputs.

中等
1362

最接近的因数

Find the closest divisors of num + 1 and num + 2 with minimal absolute difference in this math-driven problem.

中等
1523

在区间范围内统计奇数数目

Count Odd Numbers in an Interval Range efficiently using a math-driven formula that avoids unnecessary iteration over la…

简单
1551

使数组中所有元素相等的最小操作数

Compute the minimum number of operations to equalize a sequential odd-number array using a precise math-driven approach.

中等
1716

计算力扣银行的钱

Calculate the total amount of money in the Leetcode bank at the end of the nth day, based on a weekly increasing deposit…

简单
1780

判断一个数字是否可以表示成三的幂的和

Determine if a number can be expressed as the sum of distinct powers of three using a math-driven strategy.

中等
1837

K 进制表示下的各位数字总和

Calculate the sum of digits of a number after converting it from base 10 to any given base using a math-driven approach.

简单
2117

一个区间内所有数乘积的缩写

Calculate the abbreviated product of integers in a range efficiently using math-driven analysis of trailing zeros and si…

困难
2119

反转两次的数字

Determine if reversing a number twice returns the original integer by analyzing trailing zeros and digit placement.

简单
2235

两整数相加

This problem asks to return the sum of two integers within a specific range, focusing on math-driven solution strategy.

简单

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按题型继续深入

模式学会之后,最好回到具体题型里做迁移训练。这样更容易分清楚“模式本身”和“场景变化”分别在哪里。

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LeetCode 数学·driven模式题解:43题训练路线