数据结构：查找与排序

注：以下代码均为C++

查找

一、线性表的查找

1. 顺序查找

int search_seq(vector<int> s, int key){for(int i = 0; i < s.size(); i++){if(s[i] == key)return i;}return -1;
}

2. 折半查找

(1)非递归：循环

int search_bin1(vector<int> s, int key){int low = 0, high = s.size()-1, mid;while(low <= high){mid = (low + high) / 2;if(key == s[mid])return mid;else if(key < s[mid])high = mid - 1;elselow = mid + 1;}return -1;
}

(2)递归

int search_bin2(vector<int> s, int key, int low, int high){if(low > high)  return -1;int mid = (low + high)/2;if(key == s[mid])return mid;else if(key < s[mid])return search_bin2(s, key, low, mid-1);elsereturn search_bin2(s, key, mid+1, high);
}
int search_bin(vector<int> s, int key){int ans = search_bin2(s, key, 0, s.size()-1);return ans;
}

二、树表的查找

struct BSTree{int data;struct BSTree* lchild, *rchild;
};

1. 二叉排序树的查找

(1)非递归：循环

BSTree* searchBST1(BSTree* T, int key){if(T == NULL)   return NULL;while(T != NULL){if(key == T->data)return T;else if(key < T->data)T = T->lchild;elseT = T->rchild;}
}

(2)递归

BSTree* searchBST2(BSTree* T, int key){if(T == NULL)   return NULL;if(key == T->data)return T;else if(key < T->data)return searchBST2(T->lchild, key);elsereturn searchBST2(T->rchild, key);
}

排序

一、插入排序（从小到大排序）

1. 直接插入排序

void insertSort(vector<int>& s){if(s.size() <= 1)   return;for(int i = 1; i < s.size(); i++){if(s[i] < s[i-1]){  //待插入的元素为s[i]，若待插入元素比已排好序列的最后一位小，则开始插入排序，否则不用动它。int temp = s[i];  //暂存单元int j;for(j = i-1; j >=0 && temp < s[j]; j--){  //找到插入位置s[j+1] = s[j];}s[j+1] = temp;  //插入元素}}
}

2. 折半插入排序

void BinsertSort(vector<int>& s){if(s.size() <= 1)   return;int i, j, low, high, mid;for(i = 1; i < s.size(); i++){int temp = s[i];  //暂存单元//查找插入位置low = 0, high = i-1;while(low <= high){mid = (low + high)/2;if(temp < s[mid]){high = mid - 1;}elselow = mid + 1;}//移动元素for(j = i-1; j >= high+1; j--)s[j+1] = s[j];//插入正确位置s[high+1] = temp;}
}

3. 希尔排序：缩小增量的多遍插入排序，每个子表是直接插入排序

void shellInsert(vector<int>& s, int dk){if(s.size() <= 1)   return;for(int i = dk; i < s.size(); i++){if(s[i] < s[i-dk]){  //待插入的元素为s[i]，若待插入元素比已排好序列的最后一位小，则开始插入排序，否则不用动它。int temp = s[i];  //暂存单元int j;for(j = i - dk; j >= 0 && temp < s[j]; j = j - dk){  //找到插入位置s[j+dk] = s[j];}s[j+dk] = temp;  //插入元素}}
}
void shellSort(vector<int>& s, vector<int> dlta){  //dlta为增量数组for(int i = 0; i < dlta.size(); i++)shellInsert(s, dlta[i]);
}

二、交换排序

1. 冒泡排序

void bubbleSort(vector<int>& s){for(int i = 0; i < s.size() - 1; i++){  //n-1趟排序for(int j = 0; j < s.size() - i; j++){  //每趟排序比较n-i次if(s[i] > s[i+1]){int temp = s[i];s[i] = s[i+1];s[i+1] = temp;}}}
}
//改进的冒泡排序：一旦某一趟比较时不出现记录交换，说明已经排好序了，可以直接结束算法，不需要再进行后续比较。
void bubbleSort1(vector<int>& s){int flag = 1;for(int i = 0; i < s.size() - 1 && flag == 1; i++){  //n-1趟排序flag = 0;for(int j = 0; j < s.size() - i; j++){  //每趟排序比较n-i次if(s[i] > s[i+1]){flag = 1;int temp = s[i];s[i] = s[i+1];s[i+1] = temp;}}}
}

2. 快速排序

int partition(vector<int>& s, int low, int high){int temp = s[low];while(low < high){while(low < high && s[low] < temp)low++;s[low] = s[high];while(low < high && s[high] > temp)high--;s[high] = s[low];}s[low] = temp;return low;
}
void Qsort(vector<int>& s, int low, int high){if(low < high){int loc = partition(s, low, high);Qsort(s, low, loc-1);Qsort(s, loc+1, high);}
}

三、选择排序

1. 简单选择排序：每次从待排序的序列中选择最小的数，存放在待排序序列的起始位置

void selectSort(vector<int>& s){for(int i = 0; i < s.size()-1; i++){int min = i;for(int j = i+1; j < s.size(); j++){if(s[j] < s[min])min = j;}if(min != i){int temp = s[i];s[i] = s[min];s[min] = temp;}}}