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1. Use a stack implementation, to check that a given an arithmetic expression, that uses braces "{" & "}" or parenthesis "" &, ")" or brackets "[" & ")" as grouping symbols, is using them in a matching and balanced way. The book has an example function, called is Balance), that takes the input string as an argument and returns O if it is unbalanced or 1 if it is balanced. (Examples below are given only for illustrative purposes, you may come up with your own.) Examples, given for illustration of outcome Input: exp = "(0100101" Output: Balanced Input: exp = "[(1)" Output: Not Balanced Examples of other expressions 14* (6+5) A- (C+B)/(12*D] [8+ (38-14) -10)+12 {44 - [8+(38-14) -10] +12) -7 (9/5) * celsius +32 3+4+4+5(4+3)-1 (3+4*x)/5-10* (y-5) * (a+b+c) /x+9 (A*(x^2} + {B*y)) +C (4/X+9+x)/y) 2. Use your implementation to convert well-balanced arithmetic expressions in infix notation into their equivalent expressions in postfix. (Separate your operands in the postfix notation using a single space) Remember the example in the book (see the table on next page). Infix: A-(B/C+(D%E*F)/G)*H --->>> Postfix: ABC/DEF* %G/+H*. Infix Character Stack Postfix Expression KAS AB (-( (-( (-( (-( 1-(+1 (- (+ (% - (+ (% (- (+ (%* (- (+(%* AB ABC ABC/ ABC/ ABC/D ABC/D ABC/DE ABC/DE ABC/DEF ABC/DEF* % ABC/DEF* % ABC/DEF*%G ABC/DEF*% G/ + ABC/DEF* % G/+H ABC/DEF*% G/+H*