POJ2231 Moo Volume [Simple DP]

Test instructions

A given n number.

Ask what the sum of the difference between any two numbers is.

Ideas:

Order from small to large first.

Then the DP transfer equation:

Dp[i]=dp[i-1] + (i-1) * (A[i]-a[i-1]);

The final result is ans=dp[n]*2; (because the noise calculation is bidirectional)

In fact, rather than DP, it is better to find the law.

Such time complexity is the time complexity O (NLOGN) of the sort.

#include <iostream>
#include <vector>
#include <string>
#include <queue>
# include<cmath>
#include <algorithm>
#define Llong Long
#define Min (A, B) (A<B?A:B)
#define MAX (A, B) (A>B?A:B)
#define ABS (a) ((a) >0? ( A):-(a)
#define MOD (a) ((a) -1+ (b))% (b) +1)
using namespace std;
int n,m,t;
const int n=10005;
const int m=105;
const int inf= (1<<30);
int a[n];
Llong Dp[n];
int main ()
{
	scanf ("%d", &n);
	for (int i=1;i<=n;i++)
		scanf ("%d", a+i);
	Sort (a+1,a+1+n);
	for (int i=2;i<=n;i++)
		dp[i]=dp[i-1]+ (i-1) *llong (a[i]-a[i-1]);
	Llong ans=0;
	for (int i=1;i<=n;i++)
		ans+=dp[i];
	printf ("%lld\n", ans*2);
	return 0;
}