Incremental Memory Leak

Incremental Memory Leak - Problem

Math Simulation Medium

You are given two integers memory1 and memory2 representing the available memory in bits on two memory sticks. There is currently a faulty program running that consumes an increasing amount of memory every second.

At the i-th second (starting from 1), i bits of memory are allocated to the stick with more available memory (or from the first memory stick if both have the same available memory). If neither stick has at least i bits of available memory, the program crashes.

Return an array containing [crashTime, memory1crash, memory2crash], where crashTime is the time (in seconds) when the program crashed and memory1crash and memory2crash are the available bits of memory in the first and second sticks respectively.

Input & Output

Example 1 — Basic Case

$ Input: memory1 = 2, memory2 = 2

› Output: [3,1,0]

💡 Note: Second 1: allocate 1 bit to memory1 (both equal, choose first) → [1,2]. Second 2: allocate 2 bits to memory2 (2 > 1) → [1,0]. Second 3: need 3 bits but memory1 has only 1, memory2 has 0 → crash at second 3 with remaining [1,0]

Example 2 — Unequal Memory

$ Input: memory1 = 8, memory2 = 11

› Output: [6,0,4]

💡 Note: Allocation sequence: [8,11] → [7,11] → [7,9] → [4,9] → [4,5] → [4,0] → crash at second 6 when need 6 bits but max available is 4

Example 3 — Single Large Memory

$ Input: memory1 = 1, memory2 = 8

› Output: [4,0,6]

💡 Note: Second 1: [0,8], Second 2: [0,6], Second 3: [0,3], Second 4 needs 4 bits but only 3 available → crash

Constraints

0 ≤ memory1, memory2 ≤ 2³¹ - 1

Visualization

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Asked in

a Amazon 15 M Microsoft 12 G Google 8

The key insight is to simulate the memory allocation process second by second, always choosing the memory stick with more available memory. The simulation approach is straightforward and efficient for this problem. Time: O(√n), Space: O(1)

Common Approaches

✓ Memoization

⏱️ Time: N/A Space: N/A

Sliding Window

⏱️ Time: N/A Space: N/A

Dp 1d

⏱️ Time: N/A Space: N/A

Mathematical Optimization

⏱️ Time: O(log n) Space: O(1)

Instead of simulating each second, calculate how many seconds each memory stick can sustain based on arithmetic progression formulas. Find the optimal distribution and determine crash point mathematically.

Simulation Approach

⏱️ Time: O(√n) Space: O(1)

Start from second 1 and simulate the memory allocation process. At each second i, allocate i bits to the memory stick with more available memory. Continue until neither stick can handle the required allocation.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Input & Output

Constraints

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Common Approaches

Algorithm Steps — Algorithm Steps

Code -

Time & Space Complexity

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