See if an array contains another array

// function fullyContains(first: Array, second: Array): boolean;
//
// given two **already sorted** arrays with unique elements,
// first and second, return true if the first array contains
// all the elements found in the second array
//
// fullyContains([1, 2, 3], [1, 2, 3]) => true
// fullyContains([1, 2, 3], [2, 3]) => true
// fullyContains([1, 2, 3], [4]) => false
// fullyContains([], []) => true
// fullyContains([], [1, 2, 3]) => false
// fullyContains([1, 2, 3], []) => true





// [1, 2, 3] [2, 3]
// [0, 4, 6, 8] [4, 6, 8] => true
// [0, 4, 6, 8] [4, 8] => true



// [0, 4, 6, 8] [4, 8] => true
// newSecondArray = [8]
// newFirstArray = [6, 8]


function fullyContains(first, second) {

    for (let i = 0; i < first.length; i++) { // O(M)
        if (first[i] === second[0]) {
            second.shift()
        }
    }

    if (second.length > 0) return false; // TODO: fix me
    else return true;
}



function fullyContains(first /* len M */, second /* len N */) {
    for (let j = 0; j < second.length; j++) { // O(N)
        // if (!first.includes(second[j])) { // O(M)

        if (!binarySearch(first, second[j])) { // O(log M)
            return false;
        }
    }

    return true;
} // O(M)



// non-unique?

// fullyContains([1, 1, 2, 2, 3, 3], [1, 2, 3]) => true
// fullyContains([1, 1, 2, 2, 3, 3], [1, 1, 2, 3]) => true
// fullyContains([1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3]) => true
// fullyContains([1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3]) => false