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Mirrors

Statement

 Goal

When z units of light shine on any side of a mirror with reflectivity r, rz units of light are reflected, and the other (1-r)z units of light pass through the mirror.
There are n mirrors numbered 1...n arranged in a row. Mirror i has reflectivity r_i. Find the total amount of light reflected back to the source when 1 unit of light shines on the first mirror.
Note that light can be reflected multiple times.
----> | | | | |
light 1 2 3 4 5 ...
Input
Line 1: An integer n for the number of mirrors
Line 2: n space-separated floats r for the reflectivity of the mirrors
Output
Line 1: Total reflected light rounded to 4 decimal places
Constraints
1 ≤ n ≤ 10
0 ≤ r ≤ 1
Example
Input
2
0.5 0.500000
Output
0.6667

Tags
MathematicsSimulation

Difficulty
Easy

Test cases
Test 1 Test
Input
2 0.5 0.500000
Output
0.6667

Validator 1 Validator
Input
2 0.4 0.6
Output
0.6842

Test 2 Test
Input
1 0.011263
Output
0.0113

Validator 2 Validator
Input
1 0.95307
Output
0.9531

Test 3 Test
Input
3 0.313178 0.055436 0.998542
Output
0.9985

Validator 3 Validator
Input
3 0.293747 0.437975 0.666444
Output
0.7615

Test 4 Test
Input
4 0.756643 0.845056 0.439436 0.863778
Output
0.9401

Validator 4 Validator
Input
4 0.471017 0.515089 0.280896 0.247664
Output
0.7277

Test 5 Test
Input
10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Output
0.0000

Validator 5 Validator
Input
10 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
Output
1.0000

Test 6 Test
Input
8 0.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0
Output
1.0000

Validator 6 Validator
Input
9 1.0 1.0 1.0 1.0 1.0 1.0 0.9 1.0 1.0
Output
1.0000

Solution language

Solution

Stub generator input