Overview

This is a problem of computing the dot product of 7-dimensional vectors.

Analysis

This problem asks us to compute the dot product \(\mathbf{a} \cdot \mathbf{b} = A_1 \times B_1 + A_2 \times B_2 + \cdots + A_7 \times B_7\) for two 7-dimensional vectors \(\mathbf{a} = (A_1, A_2, \ldots, A_7)\) and \(\mathbf{b} = (B_1, B_2, \ldots, B_7)\).

No particularly complex processing is needed — we simply multiply corresponding components and sum them up. Even a straightforward approach runs sufficiently fast, since the number of computations is only 7 and the constraints are very small.

For example, when \(\mathbf{a} = (1, 2, 3, 4, 5, 6, 7)\) and \(\mathbf{b} = (7, 6, 5, 4, 3, 2, 1)\):

\[ \mathbf{a} \cdot \mathbf{b} = 1 \times 7 + 2 \times 6 + 3 \times 5 + 4 \times 4 + 5 \times 3 + 6 \times 2 + 7 \times 1 = 7 + 12 + 15 + 16 + 15 + 12 + 7 = 84 \]

Algorithm

1. First, read two lines of input and store each as a list of integers.
2. Compute the product \(A_i \times B_i\) for each component and add it to a running total.
3. Output the final total.

Complexity

• Time complexity: \(O(7) = O(1)\) (constant time)
• Space complexity: \(O(7) = O(1)\) (constant space)

Implementation Notes

• Since the input consists of space-separated integers, you can easily convert it to a list using input().split() and map(int, ...).

• When accessing elements by index in a loop, be careful not to go out of bounds (in this case, there are always exactly 7 elements, so this is not an issue).

  Source Code

a = list(map(int, input().split()))
b = list(map(int, input().split()))

result = 0
for i in range(7):
    result += a[i] * b[i]

print(result)

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