How to determine if a sequence is bitonic?

Question

A sequence is bitonic if it monotonically increases and then monotonically de- creases, or if it can be circularly shifted to monotonically increase and

Answer 1

Here is an efficient and simple implementation in Java. It traverses the array only once to determine whether the array is bitonic or not. It uses a variable reversal that counts the number of direction reversals of monotonicity in the array (including the circular wrapping around).

The variable trend can have three values:

• 0, if the values are the same;
• 1, if the array is monotonically increasing;
• -1, if the array is monotonically decreasing.

public static boolean bitonic(int[] arr) {
  int reversal = 0;
  int len = arr.length;
  int trend = 0; // 0 means any, 1 means increasing, -1 means decreasing 
  for (int i= 0; i < len ; i++) {
    if(arr[i%len] < arr[(i+1)%len]){
      if (trend == 0) trend = 1;
      else if ( trend == -1) {
        reversal ++;
        trend = 1;
      }
    }
    else if(arr[i%len] > arr[(i+1)%len]){
      if (trend == 0) trend = -1;
      else if ( trend == 1) {
        reversal ++;
        trend = -1;
      }
    }
    if(reversal > 2) return false;
  }
  return true;
}