In the previous exercise you also profiled the performance of adding new elements at the beginning of a LinkedList. Based on our analysis, we expect each add to take constant time, because in a linked list, we don’t have to shift the existing elements; we can just add a new node at the beginning. So we expect the total time for n adds to be linear.

Here’s a solution:

public static void profileLinkedListAddBeginning() {
Timeable timeable = new Timeable() {
List<String> list;

public void setup(int n) {
}

public void timeMe(int n) {
for (int i=0; i<n; i++) {
}
}
};
int startN = 128000;
int endMillis = 2000;
}


We only had a make a few changes, replacing ArrayList with LinkedList and adjusting startN and endMillis to get a good range of data. The measurements were noisier than the previous batch; here are the results:

128000, 16
256000, 19
512000, 28
1024000, 77
2048000, 330
4096000, 892
8192000, 1047
16384000, 4755


Figure 5.3.1 shows the graph of these results.

It’s not a very straight line, and the slope is not exactly 1; the slope of the least squares fit is 1.23. But these results indicate that the total time for n adds is at least approximately $$O(n)$$, so each add is constant time.