Virus Memory Consumption Timing | Dataford Interview Questions

A monitoring simulation for KeyValue infrastructure models a virus that consumes t bits during the first second, t + 1 bits during the second, and one additional bit more each subsequent second. Given the available RAM and the initial consumption t, return the maximum number of complete seconds the virus can run.

The virus may consume memory only when the full amount required for that second is available. Do not simulate one second at a time, and do not use floating-point arithmetic.

Formal Specification

Implement max_survival_time(memory, t).

memory is a non-negative integer representing available RAM bits.
t is a positive integer representing first-second consumption.
Return an integer k, where k is the largest value satisfying: t + (t + 1) + ... + (t + k - 1) <= memory.

Constraints

0 <= memory <= 10^18
1 <= t <= 10^9
The answer must not be computed by simulating every second
Floating-point arithmetic is not reliable for boundary decisions

Function Signature

def max_survival_time(memory, t):

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