#30 Medium Time O(n log m) Space O(1) Animated

Koko Eating Bananas

Find the minimum eating speed for Koko to finish all bananas in h hours.

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1 Predict
2 Trace
3 Explain
4 Implement

Pattern Binary search over a monotonic decision

Each comparison proves that half of the remaining search space cannot contain the answer.

Approach: Binary Search

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Core Insight

Each comparison proves that half of the remaining search space cannot contain the answer.

Common Pitfall

Choose inclusive or exclusive bounds once and update them consistently.

Description

Find the minimum eating speed for Koko to finish all bananas in h hours.

Constraints

Time Complexity: O(n log m)
Space Complexity: O(1)

Solution — Binary Search

TimeO(n log m) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Set the initial bounds.
Compute a midpoint.
Use the monotonic condition to discard one half.
Return when found or when the bounds cross.

def minEatingSpeed(piles, h):
    l, r = 1, max(piles)
    res = r
    
    while l <= r:
        k = (l + r) // 2
        
        totalTime = 0
        for p in piles:
            totalTime += math.ceil(float(p) / k)
            
        if totalTime <= h:
            res = min(res, k)
            r = k - 1
        else:
            l = k + 1
            
    return res

Search a 2D Matrix

Find Minimum in Rotated Sorted Array

Koko Eating Bananas

Steps

Description

Constraints

Tags

Solution — Binary Search