C++算法20例

1、求两个数的最大公约数

int gcd(int a, int b) { 2 return b == 0 ? a : gcd(b, a % b); 3}

2、判断素数

bool isPrime(int n) 
{
    if (n <= 1) return false; 
    for (int i = 2; i * i <= n; i++) 
    {
        if (n % i == 0) return false;
    }

    return true;
}

3、冒泡排序

void bubbleSort(vector<int>& arr) {
    int n = arr.size();
    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < n - i - 1; j++) {
            if (arr[j] > arr[j + 1]) {
                swap(arr[j], arr[j + 1]);
            }
        }
    }
}

4、二分查找

int binarySearch(vector<int>& arr, int target) {
    int left = 0, right = arr.size() - 1;
    while (left <= right) {
        int mid = left + (right - left) / 2;
        if (arr[mid] == target) return mid;
        if (arr[mid] < target) left = mid + 1;
        else right = mid - 1;
    }
    return -1;
}

字符串算法

5、字符串反转

string reverseString(string s) {
    reverse(s.begin(), s.end());
    return s;
}

6、回文数判断

bool isPalindrome(int x) {
    string s = to_string(x);
    int left = 0, right = s.length() - 1;
    while (left < right) {
        if (s[left] != s[right]) return false;
        left++;
        right--;
    }
    return true;
}

7、最长公共前缀

string longestCommonPrefix(vector<string>& strs) {
    if (strs.empty()) return "";
    string prefix = strs[0];
    for (int i = 1; i < strs.size(); i++) {
        while (strs[i].find(prefix) != 0) {
            prefix = prefix.substr(0, prefix.length() - 1);
            if (prefix.empty()) return "";
        }
    }
    return prefix;
}

数组算法

8、找出数组中的重复元素

vector<int> findDuplicates(vector<int>& nums) {
    vector<int> result;
    for (int num : nums) {
        int index = abs(num) - 1;
        if (nums[index] < 0) {
            result.push_back(abs(num));
        }
        nums[index] = -nums[index];
    }
    return result;
}

9、数组中的第K个最大元素

int findKthLargest(vector<int>& nums, int k) {
    priority_queue<int, vector<int>, greater<int>> pq;
    for (int num : nums) {
        pq.push(num);
        if (pq.size() > k) {
            pq.pop();
        }
    }
    return pq.top();
}

10、合并两个有序数组

vector<int> mergeSortedArrays(vector<int>& arr1, vector<int>& arr2) {
    vector<int> result;
    int i = 0, j = 0;
    while (i < arr1.size() && j < arr2.size()) {
        if (arr1[i] < arr2[j]) {
            result.push_back(arr1[i++]);
        } else {
            result.push_back(arr2[j++]);
        }
    }
    while (i < arr1.size()) result.push_back(arr1[i++]);
    while (j < arr2.size()) result.push_back(arr2[j++]);
    return result;
}

递归算法

11、斐波那契数列

int fibonacci(int n) {
    if (n <= 1) return n;
    return fibonacci(n - 1) + fibonacci(n - 2);
}

12、汉诺塔问题

void hanoi(int n, char from, char aux, char to) {
    if (n == 1) {
        cout << "Move disk 1 from " << from << " to " << to << endl;
        return;
    }
    hanoi(n - 1, from, to, aux);
    cout << "Move disk " << n << " from " << from << " to " << to << endl;
    hanoi(n - 1, aux, from, to);
}

动态规划

13、最大子数组和

int maxSubArray(vector<int>& nums) {
    int maxSum = nums[0], currentSum = nums[0];
    for (int i = 1; i < nums.size(); i++) {
        currentSum = max(nums[i], currentSum + nums[i]);
        maxSum = max(maxSum, currentSum);
    }
    return maxSum;
}

14、爬楼梯问题

int climbStairs(int n) {
    if (n <= 2) return n;
    vector<int> dp(n + 1);
    dp[1] = 1;
    dp[2] = 2;
    for (int i = 3; i <= n; i++) {
        dp[i] = dp[i - 1] + dp[i - 2];
    }
    return dp[n];
}

图论算法

15、深度优先搜索(DFS)

void dfs(vector<vector<int>>& graph, int node, vector<bool>& visited) {
    visited[node] = true;
    cout << node << " ";
    for (int neighbor : graph[node]) {
        if (!visited[neighbor]) {
            dfs(graph, neighbor, visited);
        }
    }
}

16、广度优先搜索(BFS)

void bfs(vector<vector<int>>& graph, int start) {
    vector<bool> visited(graph.size(), false);
    queue<int> q;
    q.push(start);
    visited[start] = true;

    while (!q.empty()) {
        int node = q.front();
        q.pop();
        cout << node << " ";

        for (int neighbor : graph[node]) {
            if (!visited[neighbor]) {
                q.push(neighbor);
                visited[neighbor] = true;
            }
        }
    }
}

数学算法

17、水仙花数

bool isNarcissisticNumber(int num) {
    int original = num, sum = 0, digits = to_string(num).length();
    while (num > 0) {
        sum += pow(num % 10, digits);
        num /= 10;
    }
    return sum == original;
}

18、素数筛选(埃氏筛法)

vector<int> sieveOfEratosthenes(int n) {
    vector<bool> isPrime(n + 1, true);
    vector<int> primes;
    isPrime[0] = isPrime[1] = false;

    for (int i = 2; i <= n; i++) {
        if (isPrime[i]) {
            primes. push_back(i);
            for (int j = 2 * i; j <= n; j += i) {
                isPrime[j] = false;
            }
        }
    }
    return primes;
}

排序算法

19、选择排序

void selectionSort(vector<int>& arr) {
    int n = arr.size();
    for (int i = 0; i < n - 1; i++) {
        int minIndex = i;
        for (int j = i + 1; j < n; j++) {
            if (arr[j] < arr[minIndex]) {
                minIndex = j;
            }
        }
        swap(arr[i], arr[minIndex]);
    }
}

20、插入排序

void insertionSort(vector<int>& arr) {
    int n = arr.size();
    for (int i = 1; i < n; i++) {
        int key = arr[i];
        int j = i - 1;
        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];
            j--;
        }
        arr[j + 1] = key;
    }
}

后续补充其它算法