Minimum Time to Bake All Cakes
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Minimum Time to Bake All Cakes
You are given an integer array speeds representing the baking speeds of some bakers. speeds[i] is the speed factor of the i-th baker. A baker with speed s can bake n cakes in: s×n² minutes. You are also given an integer cakes, representing the total number of cakes that need to be baked. Return the minimum time required to bake all the cakes. All bakers can bake cakes simultaneously.
Examples
speeds = [3, 1, 4, 2] cakes = 10
16
Explanation: Baker with speed 3 bakes 2 cakes: 3 × 2² = 12 minutes Baker with speed 1 bakes 4 cakes: 1 × 4² = 16 minutes Baker with speed 4 bakes 2 cakes: 4 × 2² = 16 minutes Baker with speed 2 bakes 2 cakes: 2 × 2² = 8 minutes Total cakes baked = 2 + 4 + 2 + 2 = 10 So, minimum time = 16.
Approach hint
use binary search on time
Common mistake
Skipping assumptions, edge cases, or trade-offs can make an otherwise good answer feel incomplete.