PAT 1104 Sum of Number Segments (20)

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) (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 10^5^. 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

思路：确定了长度，便可以知道每个数出现的次数，查找规律

程序：

#include <iostream>
#include <cstdio>
using namespace std;
int main()
{
  //观察规律
  int n;
  scanf("%d",&n);
  double sum = 0;
  for(int i = 0; i < n; i++)
  {
    double num;
    scanf("%lf",&num);
    sum += num * (i + 1) * (n- i);
  }
  printf("%.2lf\n",sum);
  return 0;
}