Q3

Q3.js

var rule = /\(([^)(]+)\)/;

var map = {
	'*': 1,
	'/': 1,
	'+': 0,
	'-': 0
}

function getHighLow(str) {
	var l = str.length;
	var result = [];
	for (var i = 0; i < l; i++) {
		if (map[str[i]] !== undefined) {
			result.push(map[str[i]]);
		}
	}
	return result.reverse();
}

function detachQuote(eq, compare) {
	var times = compare.length - 1;
	var str = eq;
	var matchMap = {
		'[': '(',
		']': ')'
	};
	
	for (var j = 0; j < times; j++) {
		var noParen = rule.exec(str)[1];
		// Parentheses cannot be removed
		if (compare[j+1] > compare[j]) {
			var tmp = str.replace(rule, '[' + noParen + ']');
		} else { // can be removed
			var tmp = str.replace(rule, noParen);
		}
		str = tmp;
	}

	var finalAnswer = str.replace(/\[|\]/g, function(match) {
		return matchMap[match];
	})

	return finalAnswer;
}

function magic(str) {
	var compareRule = getHighLow(str);
	return detachQuote(str, compareRule);
}


var answer = magic("2*(2+(3*(4+5)))");
// will return 2*(2+3*(4+5))