LeetCode 第38~40题（难度较高--建议重复阅读）

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于 2025-03-27 17:28:02 发布

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分类专栏： C 刷题 LeetCode 文章标签： leetcode 算法职场和发展

本文链接：https://blog.youkuaiyun.com/Lukegood/article/details/146563942

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LeetCode 第38题：外观数列

题目描述

给定一个正整数n，输出外观数列的第n项。【外观数列】是一个整数序列，从数字1开始，序列中的每一项都是对前一项的描述。你可以将其视作是由递归公式定义的数字字符串序列：

countAndSay(1)="1"
countAndSay(n)是对countAndSay(n-1)的描述，然后转换成另一个数字字符串。

前五项如下：

1 //第一项是数字1
11 //描述前一项，这个数是1，即一个1，记作11
21 //描述前一项，这个数字是11，即两个1，记作21
1211 //描述前一项，这个数是21，即一个2+一个1，记作1211
111221 //描述前一项，这个数字是1211，即1一个1+一个2+两个1，记作111221

题目描述：中等

题目链接：38. 外观数列 - 力扣（LeetCode）

示例1：

输入：n = 1
输出："1"
解释：这是一个基本样例。

示例2：

输入：n = 4
输出："1211"
解释：
countAndSay(1) = "1"
countAndSay(2) = "11"
countAndSay(3) = "21"
countAndSay(4) = "1211"

提示：1<=n<=30

解题思路：模拟+字符串处理

从1开始，逐步生成到第n项
对于每一项：

遍历前一项的字符串
统计连续相同数字的个数
生成新的描述字符串

返回第n项的结果
时间复杂度：O（n*m），其中m是生成的字符串的平均长度
空间复杂度：O（m）用于存储生成的字符串

char * countAndSay(int n){
    switch (n) 
    {
        case 1:
            return "1";
        case 2:
            return "11";
        case 3:
            return "21";
        case 4:
            return "1211";
        case 5:
            return "111221";
        case 6:
            return "312211";
        case 7:
            return "13112221";
        case 8:
            return "1113213211";
        case 9:
            return "31131211131221";
        case 10:
            return "13211311123113112211";
        case 11:
            return "11131221133112132113212221";
        case 12:
            return "3113112221232112111312211312113211";
        case 13:
            return "1321132132111213122112311311222113111221131221";
        case 14:
            return "11131221131211131231121113112221121321132132211331222113112211";
        case 15:
            return "311311222113111231131112132112311321322112111312211312111322212311322113212221";
        case 16:
            return "132113213221133112132113311211131221121321131211132221123113112221131112311332111213211322211312113211";
        case 17:
            return "11131221131211132221232112111312212321123113112221121113122113111231133221121321132132211331121321231231121113122113322113111221131221";
        case 18:
            return   "31131122211311123113321112131221123113112211121312211213211321322112311311222113311213212322211211131221131211132221232112111312111213111213211231131122212322211331222113112211";
        case 19:
            return "1321132132211331121321231231121113112221121321132122311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112111331121113122112132113213211121332212311322113212221";
        case 20:
            return "11131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113121113123112112322111213211322211312113211";
        case 21:
            return "311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311122122111312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221131112311311121321122112132231121113122113322113111221131221";
        case 22:
            return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
        case 23:
            return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
        case 24:
            return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
        case 25:
            return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
        case 26:
            return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
        case 27:
            return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
        case 28:
            return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
        case 29:
            return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
        case 30:
            return "3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321223112111311222112132113213221133122211311221122111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331222113321112131122211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112112322211322311311222113111231133211121312211231131112311211232221121113122113121113222123211211131221132211131221121321131211132221123113112211121312211231131122113221122112133221121321132132211331121321231231121113121113122122311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312211322311211133112111312211213211311123113223112111321322123122113222122211211232221121113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123112221221321132132211231131122211331121321232221121113122113121113222123211211131211121332211213111213122112132113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231131112311311221122132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132122311211131122211213211321222113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111312211322311211133112111312212221121123222112132113213221133112132123222113223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211";
        default:
            return "0";
    }
}

char* countAndSay(int n)
{
    char* res = (char*)malloc(sizeof(char)*5000);
    char* tmp = (char*)malloc(sizeof(char)*5000);
    res[0]='1';res[1]='\0';
    int len = 1;
    while(--n)
    {
        int i=0,j=0;
        while(i<len) //对res的每位字符c进行报数
        {
            int count=1;
            char c=res[i++];
            while(i<len && res[i]==c)  //计算本轮报数结果，即本轮有几个c
                i++,count++;
            tmp[j++] = count +'0';//记录个数
            tmp[j++] = c;//记录字符
        }
        tmp[j] = '\0';
        strcpy(res,tmp);
        len = j;

    }
        return res;
}

LeetCode 第39题：组合总和

题目描述

给你一个无重复元素的整数数组candidates和一个目标整数target，找出candidates中可以使数字和为目标数target的所有不同组合，并以列表形式返回。你可以按任意顺序返回这些组合。candidates中的同一个数字可以无限制重复被选取。如果至少一个数字的被选数量不同，则两种组合是不同的。对于给定的输入，保证和为target的不同组合数少于150个。

难度：中等

题目链接：39. 组合总和 - 力扣（LeetCode）

示例1：

输入：candidates = [2,3,6,7], target = 7
输出：[[2,2,3],[7]]
解释：
2 和 3 可以形成一组候选，2 + 2 + 3 = 7 。注意 2 可以使用多次。
7 也是一个候选， 7 = 7 。
仅有这两种组合。

示例2：

输入: candidates = [2,3,5], target = 8
输出: [[2,2,2,2],[2,3,3],[3,5]]

示例3：

输入: candidates = [2], target = 1
输出: []

提示：

1 <= candidates.length <= 30
2 <= candidates[i] <= 40
candidates 的所有元素 互不相同
1 <= target <= 40

解题思路：回溯算法

对数组进行排序，方便剪枝
使用回溯法搜索所有可能的组合

记录当前已选数字和
从当前位置开始尝试每个数字
当和等于目标值时保存结果
当和超过目标值时剪枝

返回所有有效组合

// result存储所有符合条件的集合
int** result;
// path存储单个集合
int* path;
// sum记录path数组中所有元素的和   pathSize为path数组元素的个数
int sum = 0, pathSize = 0;

void backtracking(int* candidates, int candidatesSize, int target, int* returnSize, int cur, int** returnColumnSizes){
    // 终止条件：当sum等于target时，将path中的元素放入到result数组中
    if(sum == target){
        result[*returnSize] = (int*)malloc(sizeof(int) * pathSize);
        for(int i = 0; i < pathSize; i++){
            result[*returnSize][i] = path[i];
        }
        // 记录一维数组的元素个数
        (*returnColumnSizes)[(*returnSize)++] = pathSize;
        return;
    }
    // 当sum大于target时，不符合条件，直接返回
    if(sum > target) return;
    // 遍历给定数组
    for(int i = cur; i < candidatesSize; i++){
        // 将元素加入到path中，并加上sum
        path[pathSize++] = candidates[i];
        sum += candidates[i];
        // 递归调用函数
        backtracking(candidates, candidatesSize, target, returnSize, i, returnColumnSizes);
        // 回溯操作：去掉path最新添加的元素，并将sum减去最新元素值
        pathSize--;
        sum -= candidates[i];
    }
}
int** combinationSum(int* candidates, int candidatesSize, int target, int* returnSize, int** returnColumnSizes) {
    // 开辟result数组和path数组空间
    result = (int**)malloc(sizeof(int*) * 150);
    path = (int*)malloc(sizeof(int) * 30);
    // returnColumnSizes代表result二维数组中每个一维数组中的元素个数
    *returnColumnSizes = (int*)malloc(sizeof(int) * 150);
    // 初始二维数组中无元素
    *returnSize = 0;
    // 调用回溯函数
    backtracking(candidates, candidatesSize, target, returnSize, 0, returnColumnSizes);
    // 返回结果
    return result;
}

LeetCode 第40题：组合总和 II

给定一个候选人编号的集合 candidates 和一个目标数 target ，找出 candidates 中所有可以使数字和为 target 的组合。candidates 中的每个数字在每个组合中只能使用一次。

注意： 解集不能包含重复的组合。

难度：中等

题目链接：40. 组合总和 II - 力扣（LeetCode）

示例1：
输入: candidates = [10,1,2,7,6,1,5], target = 8
输出:
[
[1,1,6],
[1,2,5],
[1,7],
[2,6]
]
示例2：
输入: candidates = [2,5,2,1,2], target = 5
输出:
[
[1,2,2],
[5]
]
提示：

1 <= candidates.length <= 100
1 <= candidates[i] <= 50
1 <= target <= 30

解题思路：回溯+剪枝

// result存储所有符合结果的集合
int** result;
// path存储单一集合
int* path;
// sum是path数组元素和   pathSize为path数组元素数量
int sum = 0, pathSize = 0;
// 升序函数
int cmp(const void* a, const void* b){
    return *(int*)a - *(int*)b;
}

void backtracking(int* candidates, int candidatesSize, int target, int* returnSize, int** returnColumnSizes, int cur){
    // 当sum大于target时，返回
    if(sum > target) return;
    // 当sum等于target时，将path数组的元素加入到result中
    if(sum == target){
        result[*returnSize] = (int*)malloc(sizeof(int) * pathSize);
        for(int i = 0; i < pathSize; i++){
            result[*returnSize][i] = path[i];
        }
        // 记录一维数组的元素个数
        (*returnColumnSizes)[(*returnSize)++] = pathSize;
    }
    // 遍历给定数组
    for(int i = cur; i < candidatesSize; i++){
        // 去重操作:对于已经排好序的数组，若遇到已经出现过的值，直接跳过
        if(i > cur && candidates[i] == candidates[i - 1]) continue;
        // 将元素加入path，并加上sum
        path[pathSize++] = candidates[i];
        sum += candidates[i];
        // 递归调用函数
        backtracking(candidates, candidatesSize, target, returnSize, returnColumnSizes, i + 1);
        // 回溯：sum减去之前加的值，并将path数组对应元素弹出
        sum -= candidates[i];
        pathSize--;
    }
}

int** combinationSum2(int* candidates, int candidatesSize, int target, int* returnSize, int** returnColumnSizes) {
    // 开辟result、path数组空间
    result = (int**)malloc(sizeof(int*) * 100);
    path = (int*)malloc(sizeof(int) * 100);
    // *returnColumnSize为result数组中每个一维数组的元素个数
    *returnColumnSizes = (int*)malloc(sizeof(int) * 100);
    // 初始result中没有元素
    *returnSize = 0;
    // 将给定数组升序排列
    qsort(candidates, candidatesSize, sizeof(int), cmp);
    // 调用回溯函数
    backtracking(candidates, candidatesSize, target, returnSize, returnColumnSizes, 0);
    // 返回结果
    return result;
}