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;}
}