C、C++、Java、Python、Go、Rust、Dart实现七大搜索算法
文章目录[隐藏]
本文为七种语言对比学习的第二十六篇,也是最后一篇:实现七大搜索算法。
搜索算法
查找或搜索是一类重要算法,查找既可以在原始数据上直接查找,也可以先排序再查找。查找算法其实有很多种情况,比如先排序再查找,而排序算法有很多种,比如字符串匹配也算查找算法,它们组合起来的查找算法就更多了。然而万变不离其宗,基本的查找思想就几种。
查找算法概念:
查找表,由同一类型的数据元素构成的集合查找,根据某个值,在查找表中确定关键字等于给定值的数据关键字,数据元素中某个数据项的值,又称为键值主键,可唯一的标识某个数据元素或记录的关键字查找表分为:
静态查找表,只做查找操作的查找表动态查找表,在查找的同时还会进行插入、删除等操作常见查找算法有七种:
序号查找算法最坏时间复杂度平均时间复杂度最好时间复杂度空间复杂度综合类别1顺序查找O(
n)O(
n/2)O(
1)O(1)无序遍历类2分块查找O(
log2n + k)O(
log2n + k/2)O(
1)O(k)有序插值遍历类3二分查找O(
log2n)O(
log2n)O(
1)O(1)有序插值类4插值查找O(
log2(log2n))O(
log2(log2n))O(
1)O(1)有序插值类5斐波那契查找O(
log2n)O(
log2n)O(
1)O(n)有序插值类7哈希查找O(
1)O(
1)O(
1)O(n)无序寻址类6树表查找O(
n)O(
log2n)O(
1)O(n)有序树查找类C实现七大查找算法
// 顺序查找
        int LinearSearch(int *arr, int size, int key) {
        for (int i = 0; i < size; i++) {
        if (arr[i] == key)
        return i;
        }
        return -1;
        }
        // 分块查找
        struct index {
        int key;
        int start;
        }newIndex[3];
        int DisSearch(int *arr, int key) {
        int i = 0, start;
        while (i < 3 && key > newIndex[i].key)
        i++;
        if (i >= 3)
        return -1;
        start = newIndex[i].start;
        while (start <= start + 5 && arr[start] != key)
        start++;
        if (start > start + 5)
        return -1;
        return start;
        }
        // 二分查找,数据需已排序
        int BinarySearch(int *arr, int size, int key) {
        int mid, low = 0, high = size - 1;
        while (low <= high) {
        mid = (low + high) / 2;
        if (arr[mid] == key)
        return mid;
        else if (arr[mid] < key)
        low = mid + 1;
        else
        high = mid - 1;
        }
        return -1;
        }
        // 插值查找,数据需已排序
        int InsertSearch(int *arr, int size, int key) {
        int mid, low = 0, high = size - 1;
        while (low <= high) {
        mid = low + (key - arr[low]) * (high - low) / (arr[high] - arr[low]);
        if (arr[mid] == key)
        return mid;
        else if (arr[mid] > key)
        high = mid - 1;
        else
        low = mid + 1;
        }
        return -1;
        }
        void Fibonacci(int *f, int size) {
        f[0] = 1;
        f[1] = 1;
        for ( int i = 2; i < size; i++)
        f[i] = f[i-1] + f[i-1];
        }
        // 斐波那契查找
        int FibonacciSearch(int *arr, int size, int key) {
        int mid = 0, low = 0, high = size - 1;
        int k = 0;
        int F[size];
        Fibonacci(F, size);
        while ( size > F[k] - 1)
        ++k;
        for (int i = size; i < F[k] - 1; ++i)
        arr[i] = arr[high];
        while (low <= high) {
        mid = low + F[k-1] - 1;
        if (arr[mid] > key) {
        high = mid - 1;
        k--;
        } else if (arr[mid] < key) {
        low = mid + 1;
        k -= 2;
        } else {
        if (mid <= high)
        return mid;
        else
        return -1;
        }
        }
        return -1;
        }
        // 树表查找
        /*file:biTree.h*/
        #ifndef CHIYX_BITREE
        #define CHIYX_BITREE
        #ifndef NULL
        #define NULL 0
        #endif
        
        typedef int DataType;
        //二叉树的节点结构
        typedef struct BiTreeNode {
        DataType data;
        struct BiTreeNode *parent;
        struct BiTreeNode *left;
        struct BiTreeNode *right;
        }BiTreeNode, *BiTree;
        //查找:返回第一个等于data域等于key的节点,不存在返回NULL
        BiTreeNode *search(BiTree *biTree, DataType key);
        //返回二叉树的最小节点,空树返回NULL
        BiTreeNode *minImum(BiTree *biTree);
        //返回二叉树的最大节点,空树返回NULL
        BiTreeNode *maxImum(BiTree *biTree);
        //返回节点x的后继节点,不存在后继(节点x为最大节点)返回NULL
        BiTreeNode *successor(BiTreeNode *x);
        //返回节点x的前驱节点,不存在前驱(节点x为最小节点)返回NULL
        BiTreeNode *predecessor(BiTreeNode *x);
        //将值data插入到二叉树中(生成一个值为data的节点)
        void insertNode(BiTree *biTree, DataType data);
        //删除一个值为data的节点
        void deleteNode(BiTree *biTree, DataType data);
        //中序遍历二叉树
        void inorderTraversal(BiTree *biTree, void (*visitor)(BiTreeNode *node));
        #endif
        
        /*file:biTree.c*/
        #include <stdlib.h>#include "biTree.h"
        //查找:返回第一个等于data域等于key的节点,不存在返回NULL
        BiTreeNode *search(BiTree *biTree, DataType key) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->data != key) {
        if (key < curNode->data)
        curNode = curNode->left;
        else
        curNode = curNode->right;
        }
        return curNode;
        }
        //返回二叉树的最小节点,空树返回NULL
        BiTreeNode *minImum(BiTree *biTree) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->left != NULL)
        curNode = curNode->left;
        return curNode;
        }
        //返回二叉树的最大节点,空树返回NULL
        BiTreeNode *maxImum(BiTree *biTree) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->right != NULL)
        curNode = curNode->right;
        return curNode;
        }
        //返回节点x的后继节点,不存在后继(节点x为最大节点)返回NULL
        BiTreeNode *successor(BiTreeNode *x) {
        if (x == NULL)
        return NULL;
        //存在右子树,则后继节点为其右子树中最小的节点
         if (x != NULL && x->right != NULL)
        return minImum(&(x->right));
        while (x->parent != NULL && x->parent->right == x)
        x = x->parent;
        return x->parent; //错误版本为 x, 此处应该返回父结点
        }
        //返回节点x的前驱节点,不存在前驱(节点x为最小节点)返回NULL
        BiTreeNode *predecessor(BiTreeNode *x) {
        if (x == NULL)
        return NULL;
        //存在左子树,则后继节点为其左子树中最大的节点
         if (x != NULL && x->left != NULL)
        return maxImum(&(x->left));
        while (x->parent != NULL && x->parent->left == x)
        x = x->parent;
        return x->parent; //错误版本为 x, 此处应该返回父结点
        
        }
        void insertNode(BiTree *biTree, DataType data) {
        //创建节点
         BiTreeNode *targetNode;
        targetNode = (BiTreeNode *)malloc(sizeof(BiTreeNode));
        //没有足够内存
         if (targetNode == NULL) return;
        targetNode->data = data;
        targetNode->parent = NULL;
        targetNode->left = NULL;
        targetNode->right = NULL;
        BiTreeNode *p, *y;
        p = *biTree;
        y = NULL;
        while (p != NULL ) {
        y = p;
        if (targetNode->data < p->data)
        p = p->left;
        else
        p = p->right;
        }
        //空树,将新节点置为树根
         if (y == NULL) {
        *biTree = targetNode;
        } else {
        if (targetNode->data < y->data)
        y->left = targetNode;
        else
        y->right = targetNode;
        }
        targetNode->parent = y;
        }
        //删除一个值为data的节点
        void deleteNode(BiTree *biTree, DataType data) {
        //查找待删除的节点
         BiTreeNode *targetNode, *x, *y;
        targetNode = search(biTree, data);
        if (targetNode == NULL) return;
        //找出真正的删除节点,如果目标节点最多只有一个子树,则其为真正删除的节点
         //否则其后继节点(最多只有一个子树,想想为什么)为真正删除的节点,然后将后继节点的值赋给目标节点
         if (targetNode->left == NULL || targetNode->right == NULL)
        y = targetNode;
        else
        y = successor(targetNode);
        if (y->left != NULL)
        x = y->left;
        else
        x = y->right;
        if (x != NULL)
        x->parent = y->parent;
        //如果y是根节点, 则根节点变为x
         if (y->parent == NULL)
        *biTree = x;
        else
        if (y->parent->right == y)
        y->parent->right = x;
        else
        y->parent->left = x;
        if (y != targetNode)
        targetNode->data = y->data;
        //释放y占有的空间
         free(y);
        }
        //中序遍历二叉树
        void inorderTraversal(BiTree *biTree, void (*visitor)(BiTreeNode *node)) {
        BiTreeNode *curNode;
        curNode = *biTree;
        if (curNode != NULL) {
        inorderTraversal(&(curNode->left), visitor); //遍历左子树
         visitor(curNode); //访问节点
         inorderTraversal(&(curNode->right), visitor); //遍历右子树
         }
        }
        // 哈希查找
        #include <stdlib.h>#include <io.h>#include <math.h>#include <time.h>
        #define HASHSIZE 100
        #define NULLKEY -32768
        
        int L;
        typedef struct {
        int *elem;
        int count;
        } HashTable;
        bool initHashTable(HashTable *hashTable) {
        L = HASHSIZE;
        hashTable->elem = (int *) malloc(L*sizeof(int));
        hashTable->count = L;
        for (int i = 0; i < L; i++)
        hashTable->elem[i] = NULLKEY;
        return true;
        }
        int HashCalc(int key) {
        return key % L;
        }
        void insert(HashTable *hashTable, int key) {
        int addr = HashCalc(key);
        while (hashTable->elem[addr] != NULLKEY)
        addr = (addr + 1) % L;
        hashTable->elem[addr] = key;
        }
        int HashSearch(HashTable *hashTable, int key) {
        int addr = HashCalc(key);
        while (hashTable->elem[addr] != key) {
        add = (addr + 1) % L;
        if (hashTable->elem[addr] == NULLKEY || add == Hash(key))
        return 0;
        }
        return addr;
        }
    
    C++实现七大查找算法
// 顺序查找
        template <typename T>
        int LinearSearch(T *arr, int size, T key) {
        for (int i = 0; i < size; i++) {
        if (arr[i] == key)
        return i;
        }
        return -1;
        }
        // 分块查找
        struct index {
        T key;
        int start;
        }newIndex[3];
        int DisSearch(T *arr, T key) {
        int i = 0, start;
        while (i < 3 && key > newIndex[i].key)
        i++;
        if (i >= 3)
        return -1;
        start = newIndex[i].start;
        while (start <= start + 5 && arr[start] != key)
        start++;
        if (start > start + 5)
        return -1;
        return start;
        }
        // 二分查找,数据需已排序
        template<typename T>
        int BinarySearch(T *arr, int size, T key) {
        int mid, low = 0, high = size - 1;
        while (low <= high) {
        mid = (low + high) / 2;
        if (arr[mid] == key)
        return mid;
        else if (arr[mid] < key)
        low = mid + 1;
        else
        high = mid - 1;
        }
        return -1;
        }
        // 插值查找,数据需已排序
        template <typename T>
        int InsertSearch(T *arr, int size, T key) {
        int mid, low = 0, high = size - 1;
        while (low <= high) {
        mid = low + (key - arr[low]) * (high - low) / (int) (arr[high] - arr[low]);
        if (arr[mid] == key)
        return mid;
        else if (arr[mid] > key)
        high = mid - 1;
        else
        low = mid + 1;
        }
        return -1;
        }
        void Fibonacci(int *f, int size) {
        f[0] = 1;
        f[1] = 1;
        for ( int i = 2; i < size; i++)
        f[i] = f[i-1] + f[i-1];
        }
        // 斐波那契查找
        template <typename T>
        int FibonacciSearch(T *arr, int size, T key) {
        int mid = 0, low = 0, high = size - 1;
        int k = 0;
        int F[size];
        Fibonacci(F, size);
        while ( size > F[k] - 1)
        ++k;
        for (int i = size; i < F[k] - 1; ++i)
        arr[i] = arr[high];
        while (low <= high) {
        mid = low + F[k-1] - 1;
        if (arr[mid] > key) {
        high = mid - 1;
        k--;
        } else if (arr[mid] < key) {
        low = mid + 1;
        k -= 2;
        } else {
        if (mid <= high)
        return mid;
        else
        return -1;
        }
        }
        return -1;
        }
        // 树表查找
        /*file:biTree.h*/
        #ifndef CHIYX_BITREE
        #define CHIYX_BITREE
        #ifndef NULL
        #define NULL 0
        #endif
        
        typedef int DataType;
        //二叉树的节点结构
        typedef struct BiTreeNode {
        DataType data;
        struct BiTreeNode *parent;
        struct BiTreeNode *left;
        struct BiTreeNode *right;
        }BiTreeNode, *BiTree;
        //查找:返回第一个等于data域等于key的节点,不存在返回NULL
        BiTreeNode *search(BiTree *biTree, DataType key);
        //返回二叉树的最小节点,空树返回NULL
        BiTreeNode *minImum(BiTree *biTree);
        //返回二叉树的最大节点,空树返回NULL
        BiTreeNode *maxImum(BiTree *biTree);
        //返回节点x的后继节点,不存在后继(节点x为最大节点)返回NULL
        BiTreeNode *successor(BiTreeNode *x);
        //返回节点x的前驱节点,不存在前驱(节点x为最小节点)返回NULL
        BiTreeNode *predecessor(BiTreeNode *x);
        //将值data插入到二叉树中(生成一个值为data的节点)
        void insertNode(BiTree *biTree, DataType data);
        //删除一个值为data的节点
        void deleteNode(BiTree *biTree, DataType data);
        //中序遍历二叉树
        void inorderTraversal(BiTree *biTree, void (*visitor)(BiTreeNode *node));
        #endif
        
        /*file:biTree.c*/
        #include <stdlib.h>#include "biTree.h"
        //查找:返回第一个等于data域等于key的节点,不存在返回NULL
        BiTreeNode *search(BiTree *biTree, DataType key) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->data != key) {
        if (key < curNode->data)
        curNode = curNode->left;
        else
        curNode = curNode->right;
        }
        return curNode;
        }
        //返回二叉树的最小节点,空树返回NULL
        BiTreeNode *minImum(BiTree *biTree) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->left != NULL)
        curNode = curNode->left;
        return curNode;
        }
        //返回二叉树的最大节点,空树返回NULL
        BiTreeNode *maxImum(BiTree *biTree) {
        BiTreeNode *curNode = *biTree;
        while (curNode != NULL && curNode->right != NULL)
        curNode = curNode->right;
        return curNode;
        }
        //返回节点x的后继节点,不存在后继(节点x为最大节点)返回NULL
        BiTreeNode *successor(BiTreeNode *x) {
        if (x == NULL) return NULL;
        //存在右子树,则后继节点为其右子树中最小的节点
         if (x != NULL && x->right != NULL)
        return minImum(&(x->right));
        while (x->parent != NULL && x->parent->right == x)
        x = x->parent;
        return x->parent; //错误版本为 x, 此处应该返回父结点
        }
        //返回节点x的前驱节点,不存在前驱(节点x为最小节点)返回NULL
        BiTreeNode *predecessor(BiTreeNode *x) {
        if (x == NULL)
        return NULL;
        //存在左子树,则后继节点为其左子树中最大的节点
         if (x != NULL && x->left != NULL)
        return maxImum(&(x->left));
        while (x->parent != NULL && x->parent->left == x)
        x = x->parent;
        return x->parent; //错误版本为 x, 此处应该返回父结点
        
        }
        void insertNode(BiTree *biTree, DataType data) {
        //创建节点
         BiTreeNode *targetNode;
        targetNode = (BiTreeNode *)malloc(sizeof(BiTreeNode));
        //没有足够内存
         if (targetNode == NULL) return;
        targetNode->data = data;
        targetNode->parent = NULL;
        targetNode->left = NULL;
        targetNode->right = NULL;
        BiTreeNode *p, *y;
        p = *biTree;
        y = NULL;
        while (p != NULL ) {
        y = p;
        if (targetNode->data < p->data)
        p = p->left;
        else
        p = p->right;
        }
        //空树,将新节点置为树根
         if (y == NULL)
        *biTree = targetNode;
        else {
        if (targetNode->data < y->data)
        y->left = targetNode;
        else
        y->right = targetNode;
        }
        targetNode->parent = y;
        }
        //删除一个值为data的节点
        void deleteNode(BiTree *biTree, DataType data) {
        //查找待删除的节点
         BiTreeNode *targetNode, *x, *y;
        targetNode = search(biTree, data);
        if (targetNode == NULL)
        return;
        //找出真正的删除节点,如果目标节点最多只有一个子树,则其为真正删除的节点
         //否则其后继节点(最多只有一个子树,想想为什么)为真正删除的节点,然后将后继节点的值赋给目标节点
         if (targetNode->left == NULL || targetNode->right == NULL)
        y = targetNode;
        else
        y = successor(targetNode);
        if (y->left != NULL)
        x = y->left;
        else
        x = y->right;
        if (x != NULL)
        x->parent = y->parent;
        //如果y是根节点, 则根节点变为x
         if (y->parent == NULL)
        *biTree = x;
        else {
        if (y->parent->right == y)
        y->parent->right = x;
        else
        y->parent->left = x;
        }
        if (y != targetNode)
        targetNode->data = y->data;
        //释放y占有的空间
         free(y);
        }
        //中序遍历二叉树
        void inorderTraversal(BiTree *biTree, void (*visitor)(BiTreeNode *node)) {
        BiTreeNode *curNode;
        curNode = *biTree;
        if (curNode != NULL) {
        inorderTraversal(&(curNode->left), visitor); //遍历左子树
         visitor(curNode); //访问节点
         inorderTraversal(&(curNode->right), visitor); //遍历右子树
         }
        }
        // 哈希查找
        #include <stdlib.h>#include <io.h>#include <math.h>#include <time.h>
        #define HASHSIZE 100
        #define NULLKEY -32768
        
        int L;
        typedef struct {
        T *elem;
        int count;
        } HashTable;
        template <typename T>
        bool initHashTable(HashTable *hashTable)
        L = HASHSIZE;
        hashTable->elem = (T *) new(L*sizeof(T));
        hashTable->count = L;
        for (int i = 0; i < L; i++)
        hashTable->elem[i] = NULLKEY;
        return true;
        }
        template <typename T>
        int HashCalc(T key) {
        return int (key % L);
        }
        template <typename T>
        void insert(HashTable *hashTable, T key) {
        int addr = HashCalc(key);
        while (hashTable->elem[addr] != NULLKEY)
        addr = (addr + 1) % L;
        hashTable->elem[addr] = key;
        }
        template <typename T>
        int HashSearch(HashTable *hashTable, T key) {
        int addr = HashCalc(key);
        while (hashTable->elem[addr] != key) {
        add = (addr + 1) % L;
        if (hashTable->elem[addr] == NULLKEY || add == Hash(key))
        return 0;
        }
        return addr;
        }
    
    Java实现七大查找算法
public class Search {
        public static void main(String[] args) {
        int[10] arr = {100,80,10,5,3,2,1,0,13,9};
        // xxxSearch(arr);
         System.out.print(arr.toString());
        }
        // 顺序查找
         public static int <T extends Comparable<? super T>> linearSearch(T[] arr, T key) {
        for (int i = 0; i < arr.length; i++) {
        if (key == arr[i])
        return i;
        }
        return -1;
        }
        // 二分查找
         public static int <T extends Comparable<? super T>> binarySearch(T[] arr, T key) {
        int mid;
        int low = 0;
        int high = arr.length - 1;
        while (low <= high) {
        mid = (low + high) / 2;
        if (key == arr[mid]) {
        return mid;
        } else if (key < arr[mid]) {
        high = mid - 1;
        } else {
        low = mid + 1;
        }
        }
        return -1;
        }
        // 插值查找
         public static int <T extends Comparable<? super T>> insertSearch(T[] arr, T key) {
        int mid;
        int low = 0;
        int high = arr.length - 1;
        while (low <= high) {
        mid = low + (key - arr[low]) * (high - low) / (arr[high] - arr[low]);
        if (arr[mid] == key) {
        return mid;
        } else if (arr[mid] > key) {
        high = mid - 1;
        } else {
        low = mid + 1;
        }
        }
        return -1;
        }
        // 斐波那契查找
         public static int fibonacciSearch(int[] arr, int key) {
        int[arr.length] F;
        F[0] = 1;
        F[1] = 1;
        for (int i = 2; i < arr.length; i++)
        F[i] = F[i-1] + F[i-1];
        int k = 0;
        while (arr.length > F[k] - 1)
        k++;
        for (int i = 0; i < arr.length, F[k] - 1)
        arr[i] = arr[high];
        int mid;
        int low = 0;
        int high = arr.length - 1;
        while (low <= high) {
        mid = low + F[k-1] - 1;
        if (arr[mid] > key) {
        high = mid - 1;
        k--;
        } else if (arr[mid] < key) {
        low = mid + 1;
        k -= 2;
        } else {
        if (mid <= high)
        return mid;
        else
        return -1;
        }
        }
        return -1;
        }
        }
    
    Python实现七大查找算法
# 顺序查找
        def LinearSearch(arr, key):
        for i in range(len(arr)):
        if key == arr[i]:
        return i
        return None
        # 二分查找
        def BinSearch(arr, key):
        low, high = 0, len(arr) - 1
        while low <= high:
        mid = (low + high) / 2
        if key == arr[mid]:
        return mid
        elif key < arr[mid]:
        high = mid - 1
        else:
        low = mid + 1
        return None
        # 插值查找
        def InsertSearch(arr, key):
        low, high = 0, len(arr) - 1
        while low <= high:
        mid = low + (key - arr[low]) * (high - low) / (arr[high] - arr[low])
        if arr[mid] == key:
        return mid
        elif arr[mid] > key:
        high = mid - 1;
        else:
        low = mid + 1;
        return -1
        # 斐波那契查找
        def FibonacciSearch(arr, key):
        #初始化斐波那契数列
        F = [0]* len(arr)
        F[0], F[1] = 1, 1
        for i in range(2, len(arr)):
        F[i] = F[i-1] + F[i-1]
        k = 0
        while len(arr) > F[k] - 1:
        k += 1
        for i in range(len(arr), F[k] - 1):
        arr[i] = arr[high]
        low, high = 0, len(arr) - 1
        while low <= high:
        mid = low + F[k-1] - 1
        if arr[mid] > key:
        high = mid - 1
        k -= 1
        elif arr[mid] < key:
        low = mid + 1
        k -= 2
        else:
        if mid <= high:
        return mid
        else:
        return None
        return None
        # 哈希查找
        class HashStruct:
        def __init__(self):
        self.elem = HashStruct
        self.count = 0
        def HashSearch(hashTable, key):
        addr = key % len(hashTable)
        while hashTable.elem[addr] != key:
        addr = (addr + 1) % L
        if hashTable.elem[addr] == None || addr == (key % len(hashTable)):
        return None;
        return addr
    
    Go实现七大查找算法
// 顺序查找
        func LinearSearch(arr []int, key int) {
        for i, v := range arr {
        if key == v {
        return i
        }
        }
        return -1
        }
        // 二分查找
        func BinSearch(arr []int, key int) {
        mid, low , high := 0, 0, len(arr) - 1
        for low <= high {
        mid = (low + high) / 2
        if key == arr[mid] {
        return mid
        } else if key < arr[mid] {
        high = mid - 1
        } else {
        low = mid + 1
        }
        }
        return -1
        }
        // 插值查找
        func InsertSearch(arr, key) {
        mid, low, high := 0, 0, len(arr) - 1
        for low <= high {
        mid = low + (key - arr[low]) * (high - low) / (arr[high] - arr[low])
        if arr[mid] == key {
        return mid
        } else if arr[mid] > key {
        high = mid - 1
        } else{
        low = mid + 1
        }
        }
        return -1
        }
        // 斐波那契查找
        func FibonacciSearch(arr, key){
        var F [len(arr)]int
        F[0], F[1] = 1, 1
        for i := 2; i < len(arr); i++ {
        F[i] = F[i-1] + F[i-1]
        }
        k, low, high := 0, 0, len(arr) - 1
        for len(arr) > F[k] - 1 {
        k++
        }
        for i := len(arr); i < F[k] - 1; i++ {
        arr[i] = arr[high]
        }
        for low <= high {
        mid = low + F[k-1] - 1
        if arr[mid] > key {
        high = mid - 1
        k--
        } else if arr[mid] < key {
        low = mid + 1
        k -= 2
        } else {
        if mid <= high {
        return mid
        } else {
        return -1
        }
        }
        }
        return -1
        }
        // 哈希查找
        type HashTable struct {
        elem *HashTable
        count int
        }
        func HashSearch(hashTable, key) {
        addr := key % len(hashTable)
        for hashTable.elem[addr] != key {
        addr = (addr + 1) % len(hashTable)
        if hashTable.elem[addr] == "" || addr == (key % len(hashTable)) {
        return -1
        }
        }
        return addr
        }
    
    Rust实现七大查找算法
usestd::cmp::{PartialEq,PartialOrd};// 顺序查找
        fn LinearSearch<T:PartialEq>(arr: &[T],key: &T)-> Option<usize>{for(i,data)inarr.iter().enumerate(){ifkey==data{Some(i)}}None}// 二分查找
        fn BinarySearch<T:PartialEq +PartialOrd>(arr: &[T],key: &T)-> Option<usize>{ifarr.is_empty(){None}letmutmid: usize;letmut(low,high)=(0,arr.len()-1);while(low<=high){mid=low+(high-low)/2;ifkey<&arr[mid]{high=mid-1;}elseifkey>arr[mid]{low=mid+1;}else{Some(mid)}}None}// 插值查找
        fn InsertSearch<T:PartialEq +PartialOrd>(arr: &[T],key: &T)-> Option<usize>{letmutmid: usize;letmut(low,high)=(0,arr.len()-1);whilelow<=high{mid=low+(key-arr[low])*(high-low)/(arr[high]-arr[low]);ifkey==&arr[mid]{Some(mid)}elseifkey<&arr[mid]{high=mid-1;}else{low=mid+1;}}None}// 斐波那契查找
        fn FibonacciSearch<T:PartialEq +PartialOrd>(arr: &[T],key: &T)-> Option<usize>{letmutF: [usize;arr.len()];F[0]=1;F[1]=1;foriin2..arr.len(){F[i]=F[i-1]+F[i-1];}letmutk=0;letmutmidusize;letmut(low,high)=(0,arr.len()-1);whilehigh>F[k]-1{k+=1;}foriinarr.len()..F[k]-1{arr[i]=arr[high];}whilelow<=high{mid=low+F[k-1]-1;ifkey<&arr[mid]{high=mid-1;k-=1;}elseifkey>&arr[mid]{low=mid+1;k-=2;}else{ifmid<=high{Some(mid)}else{None}}}None}// 哈希查找
        fn HashSearch<T:PartialEq>(hashTable: &HashTable<T>,key: &T)-> Option<usize>{letmutaddr:usize;addr=key%len(hashTable);while&hashTable.elem[addr]!=key{addr=(addr+1)%&hashTable.len()if&hashTable.elem[addr]==""||addr==(key%&hashTable.len()){None}}Some(addr)}
    Dart实现七大查找算法
// 线性查找
        int LinearSearch(List<int> arr, int key) {
        for (int i = 0; i < arr.length; i++) {
        if (arr[i] == key) {
        return i;
        }
        }
        return -1;
        }
        // 二分查找
        int BinarySearch(List<int> arr, int key) {
        if arr.length == 0 {
        return -1;
        }
        int low = 0;
        int high = arr.length - 1;
        int mid;
        while (low <= high) {
        mid = (low + high) ~/ 2;
        if (key == arr[mid]) {
        return mid;
        } else if (key < arr[mid]) {
        high = mid - 1;
        } else {
        low = mid + 1;
        }
        }
        return -1;
        }
        // 插值查找
        int InsertSearch(List<int> arr, int key) {
        int mid;
        int low = 0;
        int high = arr.length - 1;
        while (low <= high) {
        mid = low + (key - arr[low]) * (high - low) ~/ (arr[high] - arr[low]);
        if (key == arr[mid]) {
        return mid;
        } else if (key < arr[mid]) {
        high = mid - 1;
        } else {
        low = mid + 1;
        }
        }
        return -1;
        }
        // 斐波那契查找
        int FibonacciSearch(List<int> arr, int key) {
        List<int> F = List();
        F[0] = 1;
        F[1] = 1;
        for (int i = 2; i < arr.length; i++) {
        F.add(F[i-1] + F[i-1]);
        }
        int k = 0;
        while ( arr.length > F[k] - 1) {
        k++;
        }
        int mid = 0;
        int low = 0;
        int high = arr.length - 1;
        for (int i = arr.length; i < F[k] - 1; i++) {
        arr[i] = arr[high];
        }
        while (low <= high) {
        mid = low + F[k-1] - 1;
        if (key < arr[mid]) {
        high = mid - 1;
        k--;
        } else if (arr[mid] < key) {
        low = mid + 1;
        k -= 2;
        } else {
        if (mid <= high) {
        return mid;
        }
        else {
        return -1;
        }
        }
        }
        return -1;
        }
    
                
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