PAT甲级——1104 Sum of Number Segments (数学规律)

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 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

题目大意：给出N个数，按照要求找出所有的集合，将这些集合的数相加，输出结果。

思路：找出数学规律，总结公式，需要注意的是，系数k可能会超出int的范围，需要用long long int。（考察了自动转型的知识，题目是Google的人出的）

 

#include <iostream> #include <vector> using namespace std; int main() { int N; long long int k; scanf("%d", &N); vector <double> v(N); for (int i = 0; i < N; i++) scanf("%lf", &v[i]); double sum = 0; for (int i = 0; i < N; i++){ k = (i + 1); k *= N-i; sum += k * v[i]; } printf("%.2lf\n", sum); return 0; }