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$ curl repovive.com/roadmaps/dynamic-programming/slope-trick/sonya-implementation

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$ curl repovive.com/roadmaps/dynamic-programming/slope-trick/sonya-implementation

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Sonya - Implementation - Slope Trick | Dynamic Programming | Repovive

Repovive.

Dynamic Programming21 sections · 918 units60h total

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Sonya - Implementation

Full solution

function solve(a)
    b[i] = a[i] - i for all i
    cost = 0
    maxHeap = empty

    for i from 1 to n:
        push b[i] to maxHeap
        if maxHeap.top() > b[i]:
            cost += maxHeap.top() - b[i]
            pop from maxHeap
            push b[i] to maxHeap

    return cost

Transform $a$ to $b$ with $b_i = a_i - i$ , then process with a heap. The heap tracks slope-change points.

Time: $O(n \log n)$ . Space: $O(n)$ .