A palindrome is a string of characters (a word, phrase, or sentence) that is the same regardless of whether you read it forward or backward—assuming that you ignore spaces, punctuation, and case. For example, Race car is a palindrome. So is A man, a plan, a canal: Panama. Describe how you could use a stack to test whether a string is a palindrome.

Suppose that you read a binary string—that is, a string of 0s and 1s—one character at a time. Describe how you could use a stack but no arithmetic to see whether the number of 0s is equal to the number of 1s. When these counts are not equal, state how you could tell which character—0 or 1—occurs most frequently and by how much its count exceeds the other’s.