PAT (Advanced Level) 1104 Sum of Number Segments （20 分）

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最新推荐文章于 2023-05-27 22:26:46 发布

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本文解析了1104题目的算法，该题目要求计算给定正数序列所有连续子序列（段）的总和。通过观察序列中每个数出现的频率，推导出计算公式，实现高效求解。

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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 10⁵. 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

Code:

#include <iostream>
#pragma warning(disable:4996)

using namespace std;

int main()
{
	int n;
	cin >> n;
	double sum = 0.0, temp;
	for (int i = 1; i <= n; i++)
	{
		cin >> temp;
		sum += temp * i * (n - i + 1);
	}
	printf("%.2f\n", sum);
	return 0;
}

思路：

当n=5时有：
0.1，0.1 0.2，0.1 0.2 0.3，0.1 0.2 0.3 0.4，0.1 0.2 0.3 0.4 0.5
0.2，0.2 0.3，0.2 0.3 0.4，0.2 0.3 0.4 0.5
0.3，0.3 0.4，0.3 0.4 0.5
0.4，0.4 0.5
0.5
序列中第i个数的个数a = 1/2(n(n + 1) - (n - i + 1)(n - i) - i(i - 1)) = i * (n - i + 1)
比如当i=3时，a = 9 就是 0.3 的个数