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Description

Editorial

Interval Normalization Transform

EASY10 pts

Interval normalization is a fundamental data preprocessing technique that rescales numerical values from their original range to a specified target interval. This transformation is essential in machine learning, data visualization, and signal processing, where features often need to be brought to a common scale for optimal algorithm performance.

Given a NumPy array x with values naturally spanning from a (minimum) to b (maximum), the goal is to linearly map all values to a new interval [c, d] where c is the target minimum and d is the target maximum.

Mathematical Foundation

The linear mapping formula that transforms any value xᵢ from the original range [a, b] to the target range [c, d] is:

$$f(x_i) = c + \frac{(d - c)}{(b - a)} \cdot (x_i - a)$$

Where:

a = min(x) is the minimum value in the input array
b = max(x) is the maximum value in the input array
c is the desired minimum value (target lower bound)
d is the desired maximum value (target upper bound)

Geometric Interpretation

This transformation can be understood as a two-step process:

Shift and normalize: Subtract the minimum a and divide by the range (b - a) to map values to [0, 1]
Scale and shift: Multiply by the target range (d - c) and add the target minimum c to achieve the final mapping

Your Task

Implement a Python function that performs interval normalization on a NumPy array. The function should:

Accept both 1D and 2D arrays and preserve the original shape
Calculate the array's natural minimum and maximum values
Apply the linear mapping formula to transform all values to the target interval
Return floating-point results with appropriate precision

Example

Input

x = np.array([0, 5, 10])
target_min = 2
target_max = 4

Output

[2.0, 3.0, 4.0]

Explanation

The input array has: • Minimum (a) = 0 • Maximum (b) = 10 • Range = 10 - 0 = 10

Applying the formula f(x) = 2 + (4-2)/(10-0) × (x - 0) = 2 + 0.2x: • f(0) = 2 + 0.2 × 0 = 2.0 • f(5) = 2 + 0.2 × 5 = 3.0 • f(10) = 2 + 0.2 × 10 = 4.0

The values are evenly distributed in the target interval [2, 4].

Example

Input

x = np.array([-10, 0, 10])
target_min = 0
target_max = 1

Output

[0.0, 0.5, 1.0]

Explanation

The input spans from -10 to 10 (range = 20). Normalizing to [0, 1]: • Minimum (-10) maps to 0.0 • Middle value (0) maps to 0.5 • Maximum (10) maps to 1.0

This is the standard min-max normalization to the unit interval, commonly used before feeding data into neural networks.

Example

Input

x = np.array([[1, 2], [3, 4]])
target_min = 0
target_max = 100

Output

[[0.0, 33.3333], [66.6667, 100.0]]

Explanation

For this 2×2 matrix with global min = 1 and max = 4 (range = 3): • f(1) = 0 + (100-0)/(4-1) × (1-1) = 0.0 • f(2) = 0 + (100/3) × (2-1) = 33.3333 • f(3) = 0 + (100/3) × (3-1) = 66.6667 • f(4) = 0 + (100/3) × (4-1) = 100.0

The 2D structure is preserved while all values are mapped to the [0, 100] range.

Accepted0/0·0% Acceptance

Constraints

The input array x will be a valid NumPy array (1D or 2D)
x will contain at least 2 distinct values (min ≠ max to avoid division by zero)
-10⁹ ≤ x[i] ≤ 10⁹ for all elements
-10⁹ ≤ target_min < target_max ≤ 10⁹
Array dimensions: 1 ≤ rows × columns ≤ 10⁶
The output should be floating-point values rounded to 4 decimal places

Code

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Solutions

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Test Cases3

Results

Submissions

c =

d =

x =

[0,5,10]

Mathematical Foundation

The linear mapping formula that transforms any value xᵢ from the original range [a, b] to the target range [c, d] is:

$$f(x_i) = c + \frac{(d - c)}{(b - a)} \cdot (x_i - a)$$

Where:

a = min(x) is the minimum value in the input array

b = max(x) is the maximum value in the input array

c is the desired minimum value (target lower bound)

d is the desired maximum value (target upper bound)

Your Task

Implement a Python function that performs interval normalization on a NumPy array. The function should:

Accept both 1D and 2D arrays and preserve the original shape

Calculate the array's natural minimum and maximum values

Apply the linear mapping formula to transform all values to the target interval

Return floating-point results with appropriate precision

Interval Normalization Transform

Mathematical Foundation

Geometric Interpretation

Your Task

Hints

Interval Normalization Transform

Mathematical Foundation

Geometric Interpretation

Your Task

Hints