PAT甲级——1104 Sum of Number Segments (数学规律、自动转型)

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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

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
", sum);
    return 0;
}