预备知识:二分查找基础知识

在列表A中查找B列表中元素是否存在，存在为1否则为0，结果存在result列表中。
递归实现：

#include <stdio.h>
#include <vector>bool binary_search(std::vector<int>& sort_array,int begin, int end, int target) {if (begin > end) {return false;}int mid = (begin + end) / 2;if (target == sort_array[mid]) {return true;}else if (target < sort_array[mid]) {return binary_search(sort_array, begin, mid - 1, target);}else if (target > sort_array[mid]) {return binary_search(sort_array, mid + 1, end, target);}
}std::vector<int> search_array(std::vector<int>& sort_array,std::vector<int>& random_array) {std::vector<int> result;for (int i = 0; i < random_array.size(); i++) {int res = binary_search(sort_array,0,sort_array.size() - 1,random_array[i]);result.push_back(res);}return result;
}//在列表A中查找B列表中元素
int main() {int A[] = { -1, 2, 5, 20, 90, 100, 207, 800 };int B[] = { 50, 90, 3, -1, 207, 80 };std::vector<int> sort_array;std::vector<int> random_array;std::vector<int> C;for (int i = 0; i < 8; i++) {sort_array.push_back(A[i]);}for (int i = 0; i < 6; i++) {random_array.push_back(B[i]);}C = search_array(sort_array, random_array);for (int i = 0; i < C.size(); i++) {printf("%d\n", C[i]);}return 0;
}

循环实现

#include <stdio.h>
#include <vector>bool binary_search(std::vector<int>& sort_array, int target) {int begin = 0;int end = sort_array.size() - 1;while (begin <= end) {int mid = (begin + end) / 2;if (target == sort_array[mid]) {return true;}else if (target < sort_array[mid]) {end = mid - 1;}else if (target > sort_array[mid]) {begin = mid + 1;}}return false;
}std::vector<int> search_array(std::vector<int>& sort_array,std::vector<int>& random_array) {std::vector<int> result;for (int i = 0; i < random_array.size(); i++) {int res = binary_search(sort_array, random_array[i]);result.push_back(res);}return result;
}int main() {int A[] = { -1, 2, 5, 20, 90, 100, 207, 800 };int B[] = { 50, 90, 3, -1, 207, 80 };std::vector<int> sort_array;std::vector<int> random_array;std::vector<int> C;for (int i = 0; i < 8; i++) {sort_array.push_back(A[i]);}for (int i = 0; i < 6; i++) {random_array.push_back(B[i]);}C = search_array(sort_array, random_array);for (int i = 0; i < C.size(); i++) {printf("%d\n", C[i]);}return 0;
}

例1:插入位置(easy) (二分查找)

class Solution {public:int searchInsert(vector<int>& nums, int target) {int index = -1;int begin = 0;int end = nums.size() - 1;while (index == -1) {int mid = (begin + end) / 2;if (target == nums[mid]) {index = mid;}else if (target < nums[mid]) {if (mid == 0 || target > nums[mid - 1]) {index = mid;}end = mid - 1;}else if (target > nums[mid]) {if (mid == nums.size() - 1 || target < nums[mid + 1]){index = mid + 1;}begin = mid + 1;}}return index;}
};

例2:区间查找(medium)(二分查找)

#include <vector>int left_bound(std::vector<int>& nums, int target) {int begin = 0;int end = nums.size() - 1;while (begin <= end) {int mid = (begin + end) / 2;if (target == nums[mid]) {if (mid == 0 || nums[mid - 1] < target) {return mid;}end = mid - 1;}else if (target < nums[mid]) {end = mid - 1;}else if (target > nums[mid]) {begin = mid + 1;}}return -1;
}int right_bound(std::vector<int>& nums, int target) {int begin = 0;int end = nums.size() - 1;while (begin <= end) {int mid = (begin + end) / 2;if (target == nums[mid]) {if (mid == nums.size()-1 || nums[mid + 1] > target) {return mid;}begin = mid + 1;}else if (target < nums[mid]) {end = mid - 1;}else if (target > nums[mid]) {begin = mid + 1;}}return -1;
}class Solution {public:std::vector<int> searchRange(std::vector<int>& nums, int target) {std::vector<int> result;result.push_back(left_bound(nums, target));result.push_back(right_bound(nums, target));return result;}
};

例3:旋转数组查找(medium)(二分查找)

class Solution {public:int search(vector<int>& nums, int target) {int begin = 0;int end = nums.size() - 1;while (begin <= end) {int mid = (begin + end) / 2;if (target == nums[mid]) {return mid;}else if (target < nums[mid]) {if (nums[begin] < nums[mid]) { //递增区间（正常做）if (target >= nums[begin]) {end = mid - 1;}else {begin = mid + 1;}}else if (nums[begin] > nums[mid]) {end = mid - 1;}else if (nums[begin] == nums[mid]) {begin = mid + 1;}}else if (target > nums[mid]) {if (nums[begin] < nums[mid]) {begin = mid + 1;}else if (nums[begin] > nums[mid]) {if (target >= nums[begin]) {end = mid - 1;}else {begin = mid + 1;}}else if (nums[begin] == nums[mid]) {begin = mid + 1;}}}return -1;}
};

预备知识:二叉查找(排序)树基础知识

#include <stdio.h>
#include <vector>struct TreeNode {int val;TreeNode *left;TreeNode *right;TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};void BST_insert(TreeNode *node, TreeNode *insert_node){if (insert_node->val < node->val){if (node->left){BST_insert(node->left, insert_node);}else{node->left = insert_node;}}else{if (node->right){BST_insert(node->right, insert_node);}else{node->right = insert_node;}}
}void preorder_print(TreeNode *node,int layer){if (!node){return;}for (int i = 0; i < layer; i++){printf("-----");}printf("[%d]\n", node->val);preorder_print(node->left, layer + 1);preorder_print(node->right, layer + 1);
}int main(){TreeNode root(8);std::vector<TreeNode *> node_vec;int test[] = {3, 10, 1, 6, 15};for (int i = 0; i < 5; i++){node_vec.push_back(new TreeNode(test[i]));}for (int i = 0; i < node_vec.size(); i++){BST_insert(&root, node_vec[i]);}preorder_print(&root, 0);return 0;
}

#include <stdio.h>
#include <vector>struct TreeNode {int val;TreeNode *left;TreeNode *right;TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};bool BST_search(TreeNode *node, int value){if (node->val == value){return true;}if (value < node->val){if (node->left){return BST_search(node->left, value);}else{return false;}}else{if (node->right){return BST_search(node->right, value);}else{return false;}}
}int main(){TreeNode a(8);TreeNode b(3);TreeNode c(10);TreeNode d(1);TreeNode e(6);TreeNode f(15);a.left = &b;a.right = &c;b.left = &d;b.right = &e;c.right = &f;for (int i = 0; i < 20; i++){if (BST_search(&a, i)){printf("%d is in the BST.\n", i);}else{printf("%d is not in the BST.\n", i);}}return 0;
}

例4:逆序数(hard)(二叉查找树应用)

#include <stdio.h>
#include <vector>struct BSTNode {int val;int count;BSTNode* left;BSTNode* right;BSTNode(int x) : val(x), left(NULL), right(NULL), count(0) {}
};void BST_insert(BSTNode* node, BSTNode* insert_node, int& count_small) {if (insert_node->val <= node->val) {node->count++;if (node->left) {BST_insert(node->left, insert_node, count_small);}else {node->left = insert_node;}}else {count_small += node->count + 1;if (node->right) {BST_insert(node->right, insert_node, count_small);}else {node->right = insert_node;}}
}class Solution {public:std::vector<int> countSmaller(std::vector<int>& nums) {std::vector<int> result;std::vector<BSTNode*> node_vec;std::vector<int> count;//将初始数组逆置for (int i = nums.size() - 1; i >= 0; i--) {node_vec.push_back(new BSTNode(nums[i]));}count.push_back(0);for (int i = 1; i < node_vec.size(); i++) {int count_small = 0;BST_insert(node_vec[0], node_vec[i], count_small);count.push_back(count_small);}for (int i = node_vec.size() - 1; i >= 0; i--) {delete node_vec[i];result.push_back(count[i]);}return result;}
};

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数据结构与算法——二分查找与二叉查找树汇总整理

目录

预备知识:二分查找基础知识

例1:插入位置(easy) (二分查找)

例2:区间查找(medium)(二分查找)

例3:旋转数组查找(medium)(二分查找)

预备知识:二叉查找(排序)树基础知识

例4:逆序数(hard)(二叉查找树应用)

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