查找学习笔记

1、静态查找表

以下查找的索引均从1开始

（1）顺序查找（带哨兵）

#include
#include

using namespace std;

int search(vector arr, int key) {
    arr[0] = key;
    int i;
    for (i = arr.size() - 1; arr[i] != key; i--);
    return i;
}

int main()
{
    int n;
    cin >> n;
    vector list(n+1);
    for (auto i = list.begin() + 1; i != list.end(); i++) {
        cin >> *i;
    }
    int t;
    cin >> t;
    while (t--) {
        int key;
        cin >> key;
        int check = search(list, key);
        if (check != 0) {
            cout << check << endl;
        }
        else {
            cout << "error" << endl;
        }
    }
    return 0;
}

（2）折半查找（二分查找）

#include
#include
#include
using namespace std;

int search(vector arr, int key) {
    int beg = 1, end = arr.size() - 1;
    int mid;
    while (beg <= end) {
        mid = (end + beg) / 2 ;
        if (arr[mid] == key) break;
        else if (arr[mid] < key) {
            beg = mid + 1;
        }
        else end = mid - 1;
    }
    if (arr[mid] == key)return mid;
    else return 0;
}

int main()
{
    int n;
    cin >> n;
    vector list(n+1);
    for (auto i = list.begin() + 1; i != list.end(); i++) {
        cin >> *i;
    }
    int t;
    cin >> t;
    while (t--) {
        int key;
        cin >> key;
        int check = search(list, key);
        if (check != 0) {
            cout << check << endl;
        }
        else {
            cout << "error" << endl;
        }
    }
    return 0;
}

扩展：次优查找树

考虑每个元素被查询的概率不同，概率高的元素应尽早被查询

转载：查找算法 | 静态树表（次优查找树）详细分析-CSDN博客

（3）索引顺序查找（分块查找）

#include
#include
#include
using namespace std;

struct Ind {
    int maxnum;
    int start;
};

int search(vector list, vector ind, int key, int &time){ 
    int i;
    for (i = 0; i != ind.size(); i++) {
        time++;
        if (key <= ind[i].maxnum) break;
    }
    if (i == ind.size()) return -1;
    int j = ind[i].start;
    for (; j <= list.size() - 1 && list[j] <= ind[i].maxnum; j++) {
        time++;
        if (list[j] == key)break;
    }
    if (j > list.size() - 1 || list[j] != key) return -1;
    else return j;
}

int main()
{
    int n;
    cin >> n;
    vector list(n + 1);
    for (auto i = list.begin() + 1; i != list.end(); i++) {
        cin >> *i;
    }

    // 构建索引表
    int m;
    cin >>  m;
    vector ind(m);
    int tmp = 1;
    for (auto& i : ind) {
        cin >> i.maxnum;
        i.start = tmp;
        tmp += n / m;
    }

    int t;
    cin >> t;
    while (t--) {
        int key;
        cin >> key;
        int time = 0; // time记录查询次数
        int check = search(list, ind, key, time);
        if (check == -1) {
            cout << "error" << endl;
        }
        else {
            cout << check << "-" << time << endl;
        }
    }
    return 0;
}

应用：美团外卖订单中，按同一时刻来对订单分块，但同一时刻中的订单间是无序的。