PAT Grade --A1104 Sum of Number Segments

Given a sequence of positive numbers, a segment is defined to be a consecutive subsequence. For example, given the sequence { 0.1, 0.2, 0.3, 0.4 }, we have 10 segments: (0.1) (0.1, 0.2) (0.1, 0.2, 0.3) (0.1, 0.2, 0.3, 0.4) (0.2) (0.2, 0.3) (0.2, 0.3, 0.4) (0.3) (0.3, 0.4) and (0.4).

Now given a sequence, you are supposed to find the sum of all the numbers in all the segments. For the previous example, the sum of all the 10 segments is 0.1 + 0.3 + 0.6 + 1.0 + 0.2 + 0.5 + 0.9 + 0.3 + 0.7 + 0.4 = 5.0.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N, the size of the sequence which is no more than 1. The next line contains N positive numbers in the sequence, each no more than 1.0, separated by a space.

Output Specification:

For each test case, print in one line the sum of all the numbers in all the segments, accurate up to 2 decimal places.

Sample Input:

4
0.1 0.2 0.3 0.4

Sample Output:

5.00

This is a problem to find the law 
many times each number appears as (i + 1) * (ni ) times

 1 #include <iostream>
 2 #include <vector>
 3 using namespace std;
 4 int n;
 5 double sum = 0.0;
 6 int main()
 7 {
 8     cin >> n;
 9     double *v = new double[n];
10     for (int i = 0; i < n; ++i)
11         cin >> v[i];
12     for (int i = 0; i < n; ++i)
13         sum += v[i] * (i + 1)*(n - i);
14     printf("%.2f\n", sum);
15     return 0;
16 }