烦恼的高考志愿（洛谷）已过加强测试点

烦恼的高考志愿

题目背景

计算机竞赛小组的神牛 V 神终于结束了高考，然而作为班长的他还不能闲下来，班主任老 t 给了他一个艰巨的任务：帮同学找出最合理的大学填报方案。可是 v 神太忙了，身后还有一群小姑娘等着和他约会，于是他想到了同为计算机竞赛小组的你，请你帮他完成这个艰巨的任务。

题目描述

现有 $m$ 所学校，每所学校预计分数线是 $a_i$。有 $n$ 位学生，估分分别为 $b_i$。

根据 $n$ 位学生的估分情况，分别给每位学生推荐一所学校，要求学校的预计分数线和学生的估分相差最小（可高可低，毕竟是估分嘛），这个最小值为不满意度。求所有学生不满意度和的最小值。

输入格式

第一行读入两个整数 $m,n$。$m$ 表示学校数，$n$ 表示学生数。

第二行共有 $m$ 个数，表示 $m$ 个学校的预计录取分数。第三行有 $n$ 个数，表示 $n$ 个学生的估分成绩。

输出格式

输出一行，为最小的不满度之和。

样例 #1

样例输入 #1

4 3
513 598 567 689
500 600 550

样例输出 #1

32

提示

数据范围：

对于 $30\%$ 的数据，$1\le n,m\le 1000$，估分和录取线 $\le 10000$；

对于 $100\%$ 的数据，$1\le n,m\le 100000$，估分和录取线 $\le 1000000$ 且均为非负整数。

#include<bits/stdc++.h> // 引入常用库，其中包括输入输出、数据结构等
using namespace std;

#define ll long long //这题不开long long过不了加强测试点 

// 定义两个全局数组，a 为学校的分数线，b 为学生的估分
ll a[1000000],b[1000000];

// 快速排序函数，用于对数组进行排序
void quick_sort(ll a[], ll l, ll r) {
    if(l >= r) return; // 递归基：当子数组长度为1时停止递归

    ll i = l - 1, j = r + 1;
    ll x = a[(l + r) >> 1]; // 选择中间点为基准
    while(i < j) {
        do i++; while(a[i] < x); // 找到左边第一个大于等于x的数
        do j--; while(a[j] > x); // 找到右边第一个小于等于x的数
        if(i < j) swap(a[i], a[j]); // 如果这两个数不是同一个数，则交换它们
    }

    quick_sort(a, l, j); // 对左半部分递归排序
    quick_sort(a, j + 1, r); // 对右半部分递归排序
}

// 归并排序函数，这个函数在代码中没有被调用
void merger_sort(ll a[], ll l, ll r) {
    if(l >= r) return;

    ll mid = (l + r) >> 1;
    merger_sort(a, l, mid);
    merger_sort(a, mid + 1, r);

    ll k = 0, i = l, j = mid + 1;
    while(i <= mid && j <= r) {
        if(a[i] < a[j]) tmp[k++] = a[i++];
        else tmp[k++] = a[j++];
    }
    while(i <= mid) tmp[k++] = a[i++];
    while(j <= r) tmp[k++] = a[j++];

    for(i = l, j = 0; i <= r; i++, j++) a[i] = tmp[j];
}

int main() {
    ll m, n; // m 是学校数量，n 是学生数量
    cin >> m >> n; // 输入学校数量和学生数量
    ll i, j;
    ll sum = 0; // 用于计算所有学生不满意度和的变量
    for(i = 0; i < m; i++) cin >> a[i]; // 输入每所学校的分数线
    quick_sort(a, 0, m - 1); // 对学校分数线进行快速排序
    //merger_sort(a, 0, m - 1); // 归并排序，这里被注释掉了，因为作者使用了快速排序

    for(i = 0; i < n; i++) {
        cin >> b[i]; // 输入每个学生的估分
        // 如果学生的估分比最低分数线还低，直接计算不满意度
        //因为下面二分查找的是左侧边界，但这里比最左侧边界还小，所以需要特派
        if(b[i] <= a[0]) {
            sum += a[0] - b[i];
            continue;
        }
        // 如果学生的估分比最高分数线还高，直接计算不满意度
        //该步与下面重复，因为下面一定会找到左边界，但放在这里是为了让代码速度更快
        if(b[i] >= a[m-1]) {
            sum += b[i] - a[m-1];
            continue;
        }
        // 使用二分查找算法找到学生估分在排序后的学校分数线数组中的位置，即左侧边界
        ll l = 0, r = m - 1;
        while(l < r) {
            ll mid = (l + r) >> 1;
            if(a[mid] >= b[i]) r = mid;
            else l = mid + 1;
        }
        // 计算不满意度，取左侧边界或者左侧边界前一个元素与学生估分的差值的最小值
        sum += min(abs(b[i] - a[l]), abs(b[i] - a[l - 1]));
    }
    cout << sum << endl; // 输出所有学生不满意度和的最小值
    return 0;
}

加强测试点

输入

1 100000
1000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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