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数学·结合·enumeration 模式

12 道题目

模式页适合用来建立可复用解题框架。先识别题目特征,再按固定流程解释状态定义、转移和边界。

识别信号

  • Expect efficient palindrome generation without checking all products.
  • Look for correct handling of modulo 1337 to avoid integer overflow.
  • Can the candidate quickly recognize the mathematical pattern behind consecutive sums?

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

  • Checking every product of n-digit numbers instead of generating palindrome candidates first.
  • Forgetting that the starting number must be positive, which could lead to invalid sequences.
  • Failing to account for the fact that (a, b) and (b, a) represent the same triple, leading to double-counting.

推荐题单梯度

#题目难度
479

最大回文数乘积

Find the largest palindromic number from the product of two n-digit integers using math and enumeration efficiently.

困难
829

连续整数求和

Find the number of ways to express a number as the sum of consecutive positive integers.

困难
1925

统计平方和三元组的数目

Count Square Sum Triples asks to find the number of integer triples where a² + b² = c² for values between 1 and n.

简单
1952

三除数

Determine if a given integer has exactly three positive divisors.

简单
2081

k 镜像数字的和

This problem requires finding the sum of the n smallest k-mirror numbers by generating palindromes in base-k and base-10…

困难
2162

设置时间的最少代价

Calculate the minimum fatigue to set a microwave cooking time using digit moves and pushes efficiently.

中等
2240

买钢笔和铅笔的方案数

Calculate all distinct ways to spend a fixed total on pens and pencils using a straightforward enumeration strategy.

中等
2427

公因子的数目

The problem asks to find the number of common factors of two positive integers a and b.

简单
2443

反转之后的数字和

Determine if a non-negative integer can be expressed as the sum of a number and its reverse using enumeration and math r…

中等
2843

统计对称整数的数目

Count Symmetric Integers finds numbers where the sum of the first half of digits equals the sum of the second half withi…

简单
3001

捕获黑皇后需要的最少移动次数

Determine the fewest moves to capture the black queen using only white pieces with careful position analysis.

中等
3345

最小可整除数位乘积 I

Find the smallest number greater than or equal to n whose digit product is divisible by t.

简单

关联题型

LeetCode 数学·结合·enumeration模式题解:12题训练路线