Particle accelerator

#include <iostream>
#include <vector>
#include <climits>
using namespace std;
 
long long mass(const vector<long long>& prefix_sum, int i, int j) {
    return prefix_sum[j + 1] - prefix_sum[i];
}
 
long long min_energy_cost(int n, const vector<long long>& a) {
 
    vector<long long> prefix_sum(n + 1, 0);
    for (int i = 0; i < n; ++i) {
        prefix_sum[i + 1] = prefix_sum[i] + a[i];
    }
 
    vector<vector<long long>> dp(n, vector<long long>(n, LLONG_MAX));
 
    for (int i = 0; i < n; ++i) {
        dp[i][i] = 0;
    }
    
    for (int length = 2; length <= n; ++length) {  
        for (int i = 0; i <= n - length; ++i) {
            int j = i + length - 1;
    
            for (int k = i; k < j; ++k) {
                long long segment_mass = mass(prefix_sum, i, k) * mass(prefix_sum, k + 1, j);
                long long min_mass = min(mass(prefix_sum, i, k), mass(prefix_sum, k + 1, j));
                long long cost = dp[i][k] + dp[k + 1][j] + segment_mass - min_mass * min_mass;
                dp[i][j] = min(dp[i][j], cost);
            }
        }
    }
    
    return dp[0][n - 1];
}
 
int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    cout << min_energy_cost(n, a) << endl;
    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED

Test 71

Verdict: ACCEPTED

Test 72

Verdict: ACCEPTED

Test 73

Verdict: ACCEPTED

Test 74

Verdict: ACCEPTED

Test 75

Verdict: ACCEPTED

Test 76

Verdict: ACCEPTED

Test 77

Verdict: ACCEPTED

Test 78

Verdict: ACCEPTED

Test 79

Verdict: ACCEPTED

Test 80

Verdict: ACCEPTED

Test 81

Verdict: ACCEPTED

Test 82

Verdict: ACCEPTED

Test 83

Verdict: ACCEPTED

Test 84

Verdict: ACCEPTED

Test 85

Verdict: ACCEPTED

Test 86

Verdict: ACCEPTED

Test 87

Verdict: ACCEPTED

Test 88

Verdict: ACCEPTED

Test 89

Verdict: ACCEPTED

Test 90

Verdict: ACCEPTED

Test 91

Verdict: ACCEPTED