FastPrep

Description

Solutions

Circles Relationship

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Two circles on a Cartesian plane, A and B, are each defined by three descriptors:

x: the x-coordinate of the circle's center

y: the y-coordinate of the circle's center

R: the radius of the circle

Circles A and B will both be centered either on the X-axis (i.e., Y_A = 0 and Y_B = 0, or on the Y-axis (i.e., X_A = 0 and X_B = 0), but not both.

A pair of circles (A and B) will have one of the following relationship types:

Touching: they touch each other at a single point

Concentric: they have the same center point

Intersecting: they intersect each other (touching at two points)

Disjoint-Outside: disjoint with one not existing outside of the other

Disjoint-Inside: disjoint with one contained inside the other (but not concentric)

Function Description

Complete the function circles in the editor.

circles has the following parameter(s):

string circlePairs[n]: each string contains six space-separated integers. The first three integers are X, Y, and R for circle A, and the last three are X, Y, and R for circle B.

Returns

string[n]: each string is the relation between the circles described in circlePairs[i]

Example 1:

Input:  circlePairs = ["3 0 10 5 0 3", "0 1 4 0 1 5"]
Output: ["Disjoint-Inside", "Concentric"] 
Explanation:
1. The circles are Disjoint-Inside.
 
Circle A is centered at (3, 0) and extends 10 units along the x-axis from -7 to 13.
Circle B is centered at (5, 0) and extends 3 units along the x-axis from 2 to 8.

     
2. The circles are Concentric.

Circle A is centered at (0, 1) and extends 4 units along the y-axis from -3 to 5.
Circle B is centered at (0, 1) and extends 5 units along the y-axis from -4 to 6.

Constraints:

1 ≤ n ≤ 5000
0 ≤ X,Y,R ≤ 5000