Multiply Complexities

MultiplyComplexities.java

// Computers m binary searches
public static boolean containsElements(int[] seaches, int[] array)
{
  boolean hasElements = true;
  int m = searches.length;
  int n = array.length;
  // O(m) loop
  for(int i = 0; i < m; i++) {
    // Each Binary Search has O(lg n) complexity
    if(binarySearch(array, searches[i] == false)
       hasElements = false;
  }
  // Now for each O(m) we are performing a O(lg n) operation
  // Therefore we O(m * lg n)
  return hasElements;
}

// Brute force method to check if an array has unique elements
public static boolean containsUniqueElements(int[] array)
{
  int n = array.length;
  boolean hasUniqueElements = true;
  // O(n) Outer for loop.
  for(int i = 0; i < n; i++) {
    // O(n) Inner for loop.
    for(int j = 0; j < n; j++) {
      if(i != j && a[i] == a[j])
        hasUniqueElements = fasle;
    }
  }
  /* For each of the O(n) outer loop operations we are performing 
     another O(n) operations which makes this O(n * n) = O (n ^ 2)
  */
  return hasUniqueElements;
}