Find local extremums

extremums.js

function calculate(input) {
    "use strict";

    var len = input.length, extr, max, min, part;

    extr = input
        .reduce(function (pre, val, i, arr) { // find local extremums
            if ((!i && (val > arr[i + 1])) // check first element
                    || ((i === len - 1) && (val > arr[i - 1])) // check last element
                    || ((val > arr[i - 1]) && val > arr[i + 1]) // check rest
                    ) {
                pre.push({ val: val, i: i });
            }

            return pre;
        }, [])
        .reduce(function (pre, cur, i) { // find to largest extremums
            if (!i) { // first elem
                pre.first = cur;
            } else if (cur.val > pre.first.val) { // check greatest
                pre.last = pre.first;
                pre.first = cur;
            } else if ((cur.val > pre.last.val) || (-1 === pre.last.i)) { // check second greatest
                pre.last = cur.val;
            }

            return pre;
        }, {
            first: {val: null, i: -1},
            last: {val: null, i: -1}
        });

    min = Math.min(extr.first.i, extr.last.i);
    max = Math.max(extr.first.i, extr.last.i);

    part = input.slice(min + 1, max).reduce(function (pre, cur) { return pre + cur; }, 0);

    return Math.min(extr.first.val, extr.last.val) * (max - min - 1) - part;
}

console.log(calculate([2, 1, 1, 3, 4, 2, 3, 1, 2, 2, 4, 6, 5, 3])); // 10