## removeMin

Language/Type: Java Collections Stacks and Queues
Author: Stuart Reges (on 2014/02/13)

Write a method called removeMin that takes a stack of integers as a parameter and that removes and returns the smallest value from the stack. For example, if a variable called s stores the following sequence of values:

```        bottom [2, 8, 3, 19, 7, 3, 2, 42, 9, 3, 2, 7, 12, -8, 4] top
```

and you make the following call:

```        int n = removeMin(s);
```

the method removes and returns the value -8 from the stack, so that the variable n will be -8 after the call and s will store the following values:

```        bottom [2, 8, 3, 19, 7, 3, 2, 42, 9, 3, 2, 7, 12, 4] top
```

If the minimum value appears more than once, all occurrences of the minimum should be removed from the stack. For example, given the ending value of the stack above, if we again call removeMin(s), the method would return 2 and would leave the stack in the following state:

```        bottom [8, 3, 19, 7, 3, 42, 9, 3, 7, 12, 4] top
```

You are to use one queue as auxiliary storage to solve this problem. You may not use any other auxiliary data structures to solve this problem, although you can have as many simple variables as you like. You also may not solve the problem recursively. Your solution must run in O(n) time where n is the size of the stack. Use the Stack and Queue structures described in the cheat sheet and obey the restrictions described there.