Letter Combinations of a Phone Number

最新推荐文章于 2025-07-20 11:42:00 发布

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本文介绍了一个简单的算法问题：给定一个数字字符串，返回所有可能的字母组合。文章提供了基于分治策略的C++实现代码，并分析了其算法复杂度。

题目

Given a digit string, return all possible letter combinations that the number could represent.

A mapping of digit to letters (just like on the telephone buttons) is given below.

Input:Digit string "23"
Output: ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].

分析

本题较为简单，适用于分治算法求解。可将原字符串分成长度相近的两个子串，则原问题变成两个规模为原来一班的子问题，算法复杂度递推公式为

T(n)=2T(n/2)+O(n^7)

算法复杂度为O(n^7)

代码

#include <iostream>
#include <string>
#include <vector>
using namespace std;

class Solution {
public:
    vector<string> letterCombinations(string digits) {
        string grid[8] = {"abc","def","ghi","jkl","mno","pqrs","tuv","wxyz"};
        vector<string> result;
        int n = digits.size(); 
        if (!n) return result;
        if (n == 1)
        {
        	for (int i = 0;i < grid[digits[0]-'0'-2].size();i++)
        	{
        		string s = "";
        		s += grid[digits[0]-'0'-2][i];
        		result.push_back(s);
        	}
        	return result;
        }
        vector<string> r2 = letterCombinations(digits.substr(0,n/2));
        vector<string> r3 = letterCombinations(digits.substr(n/2));
        for (int i = 0;i < r2.size();i++)
        	for (int j = 0;j < r3.size();j++)
        		result.push_back(r2[i]+r3[j]);
        return result;
    }
};