278. First Bad Version

// You are a product manager and currently leading a team to develop a new product. Unfortunately, 
// the latest version of your product fails the quality check. Since each version is developed based on the 
// previous version, all the versions after a bad version are also bad.

// Suppose you have n versions [1, 2, ..., n] and you want to find out the first bad one, which 
// causes all the following ones to be bad.

// You are given an API bool isBadVersion(version) which returns whether version is bad. Implement a function 
// to find the first bad version. You should minimize the number of calls to the API.

var solution = function(isBadVersion) {
    /**
     * @param {integer} n Total versions
     * @return {integer} The first bad version
     */
    return function(n) {
        // binary search where we want to find the 
        // bad version start point
        let start = 1;
        let end = n
        while (start < end)
            {
                // create a midpoint
                let mid = Math.floor((start + end) / 2)
                // is our midpoint is bad then we know 
                // that the first bad version is either
                // that element or before it
                if(isBadVersion(mid))
                    {
                        // move our endpoint to mid to half
                        // our scope
                        end = mid
                    }
                // if our midpoint is fine, then we know 
                // that our first bad element is after it
                else
                    {
                        // move our startpoint to the mid to
                        // half our scope.  We add 1 because
                        // we alread know that the original 
                        // midpoint is fine
                        start = mid + 1
                    }
            }
        // we will eventually narrow our scope to the point where
        // the start of the bad versions is established.  We want 
        // to return that startpoint.
        return start
    };
};