// Returns an array that has every element in arr mulitplied by two
public int[] timesTwo(int[] arr) {
    int[] result = new int[arr.length];
    for (int i = 0; i < arr.length; i++) {
        result[i] = arr[i] * 2;
    }
}

// Returns an array that has every element in arr plus  one
public int[] plusOne(int[] arr) {
    int[] result = new int[arr.length];
    for (int i = 0; i < arr.length; i++) {
        result[i] = arr[i] + 1;
    }
}

// In pseduo code, we could imagine factoring out this redundancy by thinking about these in terms of maps
// where you pass in the array to process and the thing you want to perform on each element
public int[] timesTwo(int[] arr) {
    map(arr, *2);  // multiple each element by two
}

public int[] plusOne(int[] arr) {
    map(arr, +1); // add one to every element
}

/* Why is it helpful to think about code in terms of maps?
 *
 * One possible answer: Easier to reason about code at a higher level and can get parallelism for free!
 *
 * What are examples of some other maps? What is an example of an algorithm that is not a map?
 *
 * map(arr, is even)
 * mapp(arr, divide by 5);
 *
 * An example of something that can't be a map is sorting an array, it requires swapping things around and
 *  global knowledge of the array; you would be hard pressed to write a function that took an element and
 *  returned the right element for that spot.
 */

// Reductions are the same idea but they take an array and collapse it down to one value
public int findMax(int[] arr) {
    int max = -Integer.MIN_VALUE;
    for (int i = 0; i < arr.length; i++) {
        if (arr[i] > max) {
            maxx = arr[i];
        }
    }
    return max;
}

// In pseudocode could be written something like this
reduce(arr, MAX); // collapse the array down the the max value

/* What are examples of some other reductions you can perform on an array?
 *
 * Some possible answers: Min, average, all odd, leftmost even
 *
 *
 * What is an example of something that can't be written as a reduction.
 *
 * One possible answer is median.
 */