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Linear Data Structures

This is putting your ducks in a row, Computer Science style. Some of the simplest but most useful data structures are linear. Dive in to build your foundational toolkit!

Array manipulation

Given a 2D \(N\times M\) matrix print it in spiral form. That is start from the top left corner and traverse clockwise.

Example

\[\begin{bmatrix} 3 & 5& 4& 1\\ 4& 10& 9 &2 \\ 5& 2& 8 &13 \\ 6& 1& 7& 18 \end{bmatrix}\]

When the above code is implemented it outputs 3, 5, 4, 1, 2, 13, 18, 7, 1, 6, 5, 4, 10, 9, 8, 2

What will the above function output when the following Matrix is inputted.

\[\begin{bmatrix} 1& 2& 11& 4& 6\\ 9& 2& 7& 8& 11\\ 3& 1& 13& 12 & 2\\ 8& 14& 11& 16& 4\\ 17& 19 & 17 & 7 & 8 \end{bmatrix}\]

Given a 2D square Array,write a method that finds the product of all elements in column \(x\). Also write a method that returns the sum of all elements in row \(x\).

In the \(10 \times 10\) matrix below, let \(S\) be the sum of all column products and let \(T\) be the sum of all row sums. What are the last three digits of \(S + T\)?

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{5, 10, 10, 1, 6, 4, 3, 9, 6, 4},
{2, 10, 9, 4, 9, 5, 1, 10, 1, 5},
{1, 3, 7, 3, 10, 7, 5, 1, 7, 5},
{5, 1, 2, 7, 3, 2, 4, 2, 1, 3},
{7, 6, 6, 6, 4, 10, 5, 1, 5, 5},
{3, 1, 10, 5, 8, 1, 9, 10, 2, 7},
{1, 7, 1, 10, 5, 10, 5, 3, 3, 3},
{6, 3, 10, 2, 5, 1, 6, 7, 10, 9},
{1, 7, 9, 6, 2, 7, 10, 1, 9, 6},
{10, 9, 6, 10, 4, 7, 6, 3, 4, 7}

Given an array and a number \(t\), write a function that determines if there exists a contiguous sub-array whose sum is \(t\).

Which of the below arrays contains a sub-array whose sum is \(316\)?

A. {61, 6, 39, 29, 30, 72, 98, 36, 42, 66, 24, 58, 13, 16, 73}

B. {87, 78, 4, 10, 48, 43, 33, 70, 21, 18, 75, 66, 39, 80, 87}

C. {82, 72, 39, 67, 65, 93, 28, 2, 89, 39, 68, 29, 61, 14, 98}

D. {45, 5, 14, 75, 100, 37, 98, 64, 90, 52, 66, 30, 18, 89, 19}

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