UVA11300:Spreading the Wealth

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代数推导
题意：将所有人的硬币进行一次平均分配，这里要注意的是，每个人只能和左右相邻的人交换硬币，而且这些人组成的是一个环

解法：

首先求出平均数为M

每个人初始的硬币为Ai

那么对于1，他能给予4号x1个硬币，并从2号出得到x2个硬币，那么对于1可得Ai-x1+x2 = M

同理可得An-xn+x1 = M

对上述的式子进行转化，可得

1:x2 =x1-C1 (C1 = A1 - M)

2:x3 = M-A2+x2 = 2M-A1-A2+x1 = x1-x2

…

最后所求为

|x1| + |x1-C1|+…+|x1-Cn-1|,要求这个最小，那么就是要x1为这些数的中位数
骚操作1

#include<iostream>#include<cstdio>#include<cmath>#include<cstring>#include<string>#include<algorithm>#include<stack>#include<queue>#include<cctype>#include<functional>using namespace std;#define swap(a,b) {long long c=a;a=b;b=c;}const int MAX = 10e6+10;const double Eps = 1e-12;const double PI = acos(-1.0);int gcd(int x, int y){    return x%y == 0 ? y : gcd(y, x%y);}long long a[MAX], c[MAX];int main(){    int t;    int k = 1;    while (cin>>t &&t)    {        int i, j;        vector<long long> v1,v2;        long long ave = 0;        for (i = 1; i <= t; i++)        {            cin >> a[i];            v1.push_back(a[i]);            ave += a[i];        }        ave /= t;        c[0] = 0;        v2.push_back(a[0]);        //cout << v1.front() << endl;        //cout << c[0] << endl;        for (i = 1; i < v1.size(); i++)        {            c[i] = c[i - 1] + a[i] - ave;            v2.push_back(c[i]);        }        sort(c, c + v1.size());        long long x1 = c[v1.size() / 2];        long long ans = 0;        for (i = 0; i < v2.size(); i++)            ans += abs(x1 - c[i]);        cout << ans << endl;    }    return 0;}

骚操作2

#include<iostream>#include<cstdio>#include<cmath>#include<cstring>#include<string>#include<algorithm>#include<stack>#include<queue>#include<cctype>#include<functional>using namespace std;#define swap(a,b) {long long c=a;a=b;b=c;}const int MAX = 10e6+10;const double Eps = 1e-12;const double PI = acos(-1.0);int gcd(int x, int y){    return x%y == 0 ? y : gcd(y, x%y);}int main(){    int t;    int k = 1;    while (cin>>t &&t)    {        int i, j;        vector<long long> v1,v2;        long long ave = 0;        long long a, c;        for (i = 1; i <= t; i++)        {            cin >> a;            v1.push_back(a);            ave += a;        }        ave /= t;        //cout << v1.front() << endl;        //cout << c[0] << endl;        c = 0;        v2.push_back(c);        for (i = 1; i < v1.size(); i++)        {            c += v1[i] - ave;            v2.push_back(c);        }        //for (i = 0; i < v2.size(); i++)        //  cout << v2[i] << endl;        //puts("***********");        sort(v2.begin(),v2.end());        //for (i = 0; i < v2.size(); i++)    //      cout << v2[i] << endl;    long long x1 = v2[v1.size() / 2];        //cout << x1 << endl;    //  puts("_________");        long long ans = 0;        for (i = 0; i < v2.size(); i++)            ans += abs(x1 - v2[i]);        cout << ans << endl;    }    return 0;}

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