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$ curl repovive.com/roadmaps/fundamental-algorithms/binary-search/example-capacity-to-ship-packages

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$ curl repovive.com/roadmaps/fundamental-algorithms/binary-search/example-capacity-to-ship-packages

Repovive

Example - Capacity to Ship Packages - Binary Search | Fundamental Algorithms | Repovive

Repovive.

Example - Capacity to Ship Packages

Another binary search on the answer problem.

min

Problem: Ship packages over $D$ D days. Find minimum capacity.

Approach: Binary search on capacity $[\max(weights), \sum(weights)]$ [max(weights),∑(weights)]. For each capacity, simulate loading and count days.

function shipWithinDays(weights, D):
    low = max(weights)
    high = sum(weights)
    while low < high:
        mid = (low + high) / 2
        if canShip(weights, mid, D):
            high = mid
        else:
            low = mid + 1
    return low

Time: $O(n \log(\sum weights))$ O(nlog(∑weights)). Space: $O(1)$ O(1).