To determine if an array contains consecutive integers, first find the minimum and maximum values within the array. If the difference between the maximum and minimum values is not equal to n-1 (where n is the number of elements), the array cannot be consecutive. If this condition is met, you then need to verify that all numbers between the minimum and maximum are present exactly once. This can be efficiently done by using a hash set (or a boolean array if the range of numbers is known and manageable) to track the presence of each number. Iterate through the array, adding each element to the set. If you encounter a duplicate or a number outside the expected range, it's not consecutive. If you successfully add all elements and the set's size equals n, the array is consecutive.