Assignment 0

A rectangle with sides parallel to the X- and Y-axes is specified by four real numbers a, b, c, and d. Assume that a <= c and b <= d. The four corners of the rectangle are (a,b) [bottom left], (c,b) [bottom right], (a,d) [top left], and (c,d) [top right].

Read the values a₁, b₁, c₁, and d₁ from the user for a rectangle R₁. Subsequently, read the values a₂, b₂, c₂, and d₂ for another rectangle R₂. Your task is to determine whether the two rectangles R₁ and R₂ intersect.

To solve this problem, it suffices to check whether both the following conditions are satisfied:

• The interval [a₁, c₁] has an overlap with the interval [a₂, c₂].
• The interval [b₁, d₁] has an overlap with the interval [b₂, d₂].

Two real intervals I = [s,t] and J = [u,v] operlap if and only if I starts before J ends and J starts before I ends, that is, if and only if s <= v and u <= t.

Report the output of your program for the following four runs.

   a1,  b1,  c1,  d1        a2,  b2,  c2, d2
    1,   2,   3,   4         2,   3,   4,  5
    1,   2,   3,   4         3,   4,   5,  6
    1,   2,   3,   4         4,   5,   6,  7
    1,   2,   3,   4       1.5,   5, 2.5,  6

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