Horizontal Pod Autoscaler Replica Count

Problem Statement

The Horizontal Pod Autoscaler reads one metric per pod — average CPU utilisation, or queue depth, or inference latency — compares it to a target, and rescales the Deployment. Implement its control loop.

Background

The HPA formula is:

desiredReplicas = ceil(currentReplicas * (currentMetric / targetMetric))

Two details keep it from oscillating and from running away:

Tolerance. If the ratio is within 10% of 1.0 — that is, abs(ratio - 1) <= 0.1 — the HPA does nothing and keeps currentReplicas. Without this, a service sitting at 51% against a 50% target would flap up and down forever.
Clamping. The result is clamped into [minReplicas, maxReplicas].

The ceiling matters: scaling to 7.2 pods means 8 pods, because under-provisioning is the expensive mistake.

Your Task

Implement:

def hpa_desired(current_replicas, current_metric, target_metric, min_replicas, max_replicas):

Return the replica count as an int.

Input Format

current_replicas: int, pods currently running.
current_metric: number, the observed average metric value per pod.
target_metric: number, the configured target.
min_replicas, max_replicas: ints, the autoscaler bounds.

Output Format

A single int.

Sample

print(hpa_desired(4, 90, 50, 1, 10))

Output:

The ratio is 1.8, well outside the tolerance band, so ceil(4 * 1.8) = 8 — within the [1, 10] bounds.

Example:

Input:

print(hpa_desired(4, 90, 50, 1, 10))

Output:

Reasoning:

ratio = 90 / 50 = 1.8. abs(1.8 - 1) = 0.8 > 0.1, so the tolerance band does not apply. ceil(4 * 1.8) = ceil(7.2) = 8, and 8 lies inside [1, 10], so the HPA scales the Deployment to 8 pods.

Constraints:

0 <= current_replicas <= 1000, 1 <= min_replicas <= max_replicas <= 1000
Metrics are non-negative numbers
Tolerance band: no change when abs(current_metric / target_metric - 1) <= 0.1
Otherwise ceil(current_replicas * ratio), then clamp into [min_replicas, max_replicas]
If current_replicas or target_metric is 0, return min_replicas
Return an int