uva(11300)(spreading

链接:https://vjudge.net/problem/UVA-11300
思路:一道很巧妙的数学思路的贪心题,设xi为i到i-1的金币传递数量,可以推导出如下结论:
图片发自简书App

代码:

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#include<algorithm>
using namespace std;
int n;
int a[1000001];

int (){
while(~scanf("%d",&n)){
if(n==0){
printf("0n");
continue;
}
long long sum = 0;
for(int i=0;i<n;++i){
scanf("%d",&a[i]);
sum+=a[i];
}
sum/=n;
for(int i=0;i<n;i++){
a[i]=sum-a[i];
}
long long s;
for(int i=1;i<n-1;i++){
a[i]+=a[i-1];

}
a[n-1] = 0;
sort(a,a+n);
s=a[n/2];
long long res = 0;
for(int i=0;i<n;++i){
res+=labs(a[i]-s);
}
printf("%lldn",res);
}
return 0;
}