Arith_Geo

/***************************************************************************************
*                                                                                      *
*                  CODERBYTE BEGINNER CHALLENGE                                        *
*                                                                                      *
*  Arith Geo                                                                            *
*  Using the JavaScript language, have the function ArithGeo(arr) take the array of    *
*  numbers stored in arr and return the string "Arithmetic" if the sequence follows    *
*  an arithmetic pattern or return "Geometric" if it follows a geometric pattern. If   *
*  the sequence doesn't follow either pattern return -1. An arithmetic sequence is     *
*  one where the difference between each of the numbers is consistent, where as in a   *
*  geometric sequence, each term after the first is multiplied by some constant or     *
*  common ratio. Arithmetic example: [2, 4, 6, 8] and Geometric                        *
*  example: [2, 6, 18, 54]. Negative numbers may be entered as parameters, 0 will not  *
*  be entered, and no array will contain all the same elements.                        *
*                                                                                      *
*  SOLUTION                                                                            *
*  To check for arithmetic pattern, start by getting the difference between the first  *
*  two number. Then loop thru array starting in position 2 and subtract the previous   *
*  number. If the difference is equal to the initial difference then you have an       *
*  arithmetic pattern so return arithmetic. Next repeat by getting initial difference  *
*  by dividing the first and second numbers. Loop through array starting in position   *
*  2 and compare the current number divided by previous number. If difference is       *
*  equal to the initial number then you have a geometric pattern. Else return -1.      *
*                                                                                      *
*  Steps for solution                                                                  *
*    1) set flags for both patterns to True                                            *
*    2) Loop thru array starting in position 2 and compare difference between current  *
*       number and the previous number to see if it is equal to initial difference     *
*    3) If aritimetic pattern exists return arithmetic else check for geometric        *
*    4) Get difference between second numvber divided by first number                  *
*    5) Loop thru array starting in position 2 and compare difference between current  *
*       number and the previous to see if it is equal to the intial difference         *
*    6) If geometric pattern exists return geometric                                   *
*    7) Else return -1                                                                 *
*                                                                                      *
***************************************************************************************/

function ArithGeo(arr) { 

  var arithFlag = true, geoFlag = true;
  var diff = arr[1] - arr[0];
  
  for (var i = 2; i < arr.length; i++) {
    if ((arr[i] - arr[i-1]) !== diff) {
      arithFlag = false;
    }
  }
  if (arithFlag) {
    return "Arithmetic";
  }
  else { // check for geometric pattern
    diff = arr[1] / arr[0];
    for (var i = 2; i < arr.length; i++) {
      if ((arr[i] / arr[i-1]) !== diff) { 
        geoFlag = false;
      }
    }
    if (geoFlag) {
      return "Geometric";
    }
    else {
      return "-1"
    }
  }
  
}