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$ curl repovive.com/roadmaps/fundamental-algorithms/binary-search/template-find-minimum-valid

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$ curl repovive.com/roadmaps/fundamental-algorithms/binary-search/template-find-minimum-valid

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Template - Find Minimum Valid - Binary Search | Fundamental Algorithms | Repovive

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Fundamental Algorithms8 sections · 294 units2h total

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Template - Find Minimum Valid

Template for finding the first value satisfying a condition.

Problem type: Find the minimum $x$ such that isValid(x) is true, where validity is monotonic (once true, stays true for larger $x$ ).

function findMinValid(lo, hi):
    while lo < hi:
        mid = lo + (hi - lo) / 2
        if isValid(mid):
            hi = mid
        else:
            lo = mid + 1
    return lo

Invariant: hi is always a valid answer (or past the range). lo is the first potentially valid answer.

After loop: lo == hi is the minimum valid value.

Example uses:

Minimum speed to finish in time.
Minimum capacity to ship in days.
First version that is bad (git bisect).