1104 Sum of Number Segments (20分)

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

考察数学，我们需要在草稿纸上进行求和公式的计算。

#include<cstdio>
#include<vector>
using namespace std;
int main() {
    int N;
    scanf("%d", &N);
    vector<double> data(N, 0.0);
    for (int i = 0; i < N; i++)
        scanf("%lf", &data[i]);
    double result = 0.0;
    for (int i = 0; i < N; i++)
        result += data[i] * (N - i)*(i + 1);
    printf("%.2f", result);
}