[HAOI2008] 糖果传递

A1 + X1 - X2 = G

A2 + X2 - X3 = G

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.

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An + Xn - X1 = G

解得

X1 = X1

X2 = A1 - G + X1

X3 = A1 + A2 - G - G + X1

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Xn = sigma(1, n)A - n * G + X1

注意到ans = abs (X1 - lamda1) + abs (X2 - lamda2) + ... + abs (Xn - lamdan)

于是sort 取中位数

#include <cstdio>
#include <cstdlib>
#include <algorithm>
using namespace std;
const long long N = 2001000;
long long a[N], s[N], tar[N], n;
int main ()
{
    scanf ("%d", &n);
    for (long long i = 1; i <= n; i ++)
        scanf ("%d", &a[i]), s[i] = s[i - 1] + a[i];
    long long g = s[n] / n;
    for (long long i = 1; i <= n; i ++)
        tar[i] = i * g - s[i];
    sort (tar + 1, tar + 1 + n);
    long long x = n >> 1, z (0);
    for (long long i = 1; i <= n; i ++)
        z += abs (tar[i] - tar[x]);
    printf ("%lld\n", z);
    return 0;
}