The Minimum Value in a Queue

[Question]
How to design a queue A, in addition to insert(), delete(), also has a function min() which returns the minimum element? Can you do all functions in O(1) time?

[Analysis]
Need an additional queue X to record each potential minimum elements along the way. Those are elements in queue A that are smaller than the last incoming element (the end of the queue). When adding a new element,  queue X will need to remove the elements that are larger than the new element.

The time complexity for min(), insert() and delete() is amortized O(1).

[Solution]

import java.util.*;

public class QueueWithWeights implements TestCaseRunner{

// -- interface of weights
public interface WeightedObject {
public int getWeight();
}

// -- class WeightedString is for testing purpose;
public class WeightedString implements WeightedObject {
String str;
int wgt;

WeightedString (String a, int w) {
str = a;
wgt = w;
}
public int getWeight() {
return wgt;
}
}

// -- members of the queue;
List<WeightedObject> oList;
List<Integer> wList;

// -- constructor;
QueueWithWeights() {
oList = new ArrayList<WeightedObject> ();
wList = new ArrayList<Integer>();
}

public  void insert(WeightedObject a) {
oList.add(a);
int i = wList.size()-1;
while (i>=0 && a.getWeight()<wList.get(i)) {
wList.remove(i--); //amortized O(1);
}
wList.add(a.getWeight());
}

public  WeightedObject delete() {
if (oList.size()>0) {
if (oList.get(0).getWeight() == wList.get(0)) {
wList.remove(0);
}
return oList.remove(0);
}
return null;
}

public  int min() {
if (oList.isEmpty()) return Integer.MIN_VALUE;
return wList.get(0);
}

public void runTestCases() {
int[] w = {3, 4, 5, 8, 5, 3, 2, 1, 2, 3, 9 , 10, 9, 8, 7, 6, 5, 4, 3, 6, 7};
QueueWithWeights que = new QueueWithWeights();
int j = 3;

for (int i: w) {
WeightedString s = new WeightedString(String.valueOf(i), i);
que.insert(s);
System.out.println("inserted " + i);
System.out.println("min " + que.min());
j--;
if (j==0) {
System.out.println("delete "+que.delete().getWeight());
System.out.println("min " + que.min());
System.out.println("delete "+que.delete().getWeight());
System.out.println("min " + que.min());
j=3;
}
}
}
}