tricky question, the reasoning is far longer than the algorithm

O(n)

int cost(vector<int> B) {
    pair<int, int> Q = {0, 0};
    for (int i=1; i < B.size(); i++) Q = {max(Q.first, Q.second + B[i-1] - 1), max(Q.first + B[i] - 1, Q.second + abs(B[i]- B[i-1]))};
    return max(Q.first, Q.second);
}

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js

function cost(B) {
    let high = 0;
    let low = 0;
    let [last, ...rest] = B;
    for (const cur of rest) {
        [
            high,
            low,
            last
        ] = [
                Math.max(
                    high + Math.abs(cur - last),
                    low + Math.abs(cur - 1)
                ),
                Math.max(
                    high + Math.abs(1 - last),
                    low
                ),
                cur
            ];
    }

    return Math.max(high, low);
}