Finding the second smallest integer in array

Try this one. Second condition is used to catch an event when the smallest number is the first

    int[] elements = {-5, -4, 0, 2, 10, 3, -3};
    int smallest = Integer.MAX_VALUE;
    int secondSmallest = Integer.MAX_VALUE;
    for (int i = 0; i < elements.length; i++) {
        if(elements[i]==smallest){
          secondSmallest=smallest;
        } else if (elements[i] < smallest) {
            secondSmallest = smallest;
            smallest = elements[i];
        } else if (elements[i] < secondSmallest) {
            secondSmallest = elements[i];
        }

    }

UPD by @Axel

int[] elements = {-5, -4, 0, 2, 10, 3, -3};
int smallest = Integer.MAX_VALUE;
int secondSmallest = Integer.MAX_VALUE;
for (int i = 0; i < elements.length; i++) {
    if (elements[i] < smallest) {
        secondSmallest = smallest;
        smallest = elements[i];
    } else if (elements[i] < secondSmallest) {
        secondSmallest = elements[i];
    }
}

Here is TimeComlexity Linear O(N):

  public static int secondSmallest(int[] arr) {
    if(arr==null || arr.length < 2) {
        throw new IllegalArgumentException("Input array too small");
    }

    //implement
    int firstSmall = -1;
    int secondSmall = -1;

    //traverse to find 1st small integer on array
    for (int i = 0; i<arr.length;i++)
        if (firstSmall == -1 || arr[firstSmall]>arr[i])
            firstSmall = i;

     //traverse to array find 2 integer, and skip first small
    for (int i = 0;i<arr.length;i++) {
        if (i != firstSmall && (secondSmall == -1 || arr[secondSmall] > arr[i]))
            secondSmall = i;
    }

    return arr[secondSmall];
}

    int[] arr = { 4, 1, 2, 0, 6, 1, 2, 0 };

    int smallest = Integer.MAX_VALUE;
    int smaller = Integer.MAX_VALUE;
    int i = 0;

    if (arr.length > 2) {
        for (i = 0; i < arr.length; i++) {

            if (arr[i] < smallest) {
                smaller = smallest;
                smallest = arr[i];
            } else if (arr[i] < smaller && arr[i] > smallest) {
                smaller = arr[i];
            }
        }

        System.out.println("Smallest number is " + smallest);
        System.out.println("Smaller number is " + smaller);

    } else {
        System.out.println("Invalid array !");
    }
}