解题思路
中位数就是最优解
|x-a|+|x-b|>=|a-b|
相关题目
1.一维拓展到二维:[3167.星星还是树]
2.* 拓展到d维:需要用模拟退火算法
算法1
$O(nlogn)$
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 100010;
int n;
int a[N];
int main()
{
cin >> n;
for(int i = 0; i < n; i++) cin >> a[i];
sort(a, a + n);
int res = 0;
for(int i = 0; i < n; i++) res += abs(a[i] - a[n/2]);
cout << res << endl;
return 0;
}
算法2
$O(nlogn)$
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 100010;
int n;
int a[N];
int main()
{
cin >> n;
for(int i = 0; i < n; i++) cin >> a[i];
sort(a, a + n);
int res = 0;
for(int i = 0; i < n; i++) res += abs(a[i] - a[i/2]);
cout << res << endl;
return 0;
}
算法3
$O(n)$
```
include [HTML_REMOVED]
include [HTML_REMOVED]
using namespace std;
const int N = 100010;
int n;
int a[N];
int main()
{
cin >> n;
for(int i = 0; i < n; i) cin >> a[i];
nth_element(a, a + n / 2, a + n);
int res = 0;
for(int i = 0; i < n; i) res += abs(a[i] - a[n/2]);
cout << res << endl;
return 0;
}