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Formatted question description: https://leetcode.ca/all/770.html

# 770. Basic Calculator IV (Hard)

Given an expression such as expression = "e + 8 - a + 5" and an evaluation map such as {"e": 1} (given in terms of evalvars = ["e"] and evalints = [1]), return a list of tokens representing the simplified expression, such as ["-1*a","14"]

• An expression alternates chunks and symbols, with a space separating each chunk and symbol.
• A chunk is either an expression in parentheses, a variable, or a non-negative integer.
• A variable is a string of lowercase letters (not including digits.) Note that variables can be multiple letters, and note that variables never have a leading coefficient or unary operator like "2x" or "-x".

Expressions are evaluated in the usual order: brackets first, then multiplication, then addition and subtraction. For example, expression = "1 + 2 * 3" has an answer of ["7"].

The format of the output is as follows:

• For each term of free variables with non-zero coefficient, we write the free variables within a term in sorted order lexicographically. For example, we would never write a term like "b*a*c", only "a*b*c".
• Terms have degree equal to the number of free variables being multiplied, counting multiplicity. (For example, "a*a*b*c" has degree 4.) We write the largest degree terms of our answer first, breaking ties by lexicographic order ignoring the leading coefficient of the term.
• The leading coefficient of the term is placed directly to the left with an asterisk separating it from the variables (if they exist.)  A leading coefficient of 1 is still printed.
• An example of a well formatted answer is ["-2*a*a*a", "3*a*a*b", "3*b*b", "4*a", "5*c", "-6"]
• Terms (including constant terms) with coefficient 0 are not included.  For example, an expression of "0" has an output of [].

Examples:

Input: expression = "e + 8 - a + 5", evalvars = ["e"], evalints = [1]
Output: ["-1*a","14"]

Input: expression = "e - 8 + temperature - pressure",
evalvars = ["e", "temperature"], evalints = [1, 12]
Output: ["-1*pressure","5"]

Input: expression = "(e + 8) * (e - 8)", evalvars = [], evalints = []
Output: ["1*e*e","-64"]

Input: expression = "7 - 7", evalvars = [], evalints = []
Output: []

Input: expression = "a * b * c + b * a * c * 4", evalvars = [], evalints = []
Output: ["5*a*b*c"]

Input: expression = "((a - b) * (b - c) + (c - a)) * ((a - b) + (b - c) * (c - a))",
evalvars = [], evalints = []
Output: ["-1*a*a*b*b","2*a*a*b*c","-1*a*a*c*c","1*a*b*b*b","-1*a*b*b*c","-1*a*b*c*c","1*a*c*c*c","-1*b*b*b*c","2*b*b*c*c","-1*b*c*c*c","2*a*a*b","-2*a*a*c","-2*a*b*b","2*a*c*c","1*b*b*b","-1*b*b*c","1*b*c*c","-1*c*c*c","-1*a*a","1*a*b","1*a*c","-1*b*c"]


Note:

1. expression will have length in range [1, 250].
2. evalvars, evalints will have equal lengths in range [0, 100].

Companies:
Intuit, Pinterest, Roblox

Related Topics:
Hash Table, String, Stack

Similar Questions:

## Solution 1.

• class Solution {
public List<String> basicCalculatorIV(String expression, String[] evalvars, int[] evalints) {
Polynomial polynomial = parse(expression);
Map<String, Integer> evaluateMap = new HashMap<String, Integer>();
int length = evalvars.length;
for (int i = 0; i < length; i++)
evaluateMap.put(evalvars[i], evalints[i]);
Polynomial evaluation = polynomial.evaluate(evaluateMap);
List<String> list = evaluation.toList();
return list;
}

public Polynomial parse(String expression) {
List<Polynomial> bucket = new ArrayList<Polynomial>();
List<Character> operators = new ArrayList<Character>();
int index = 0, length = expression.length();
while (index < length) {
if (expression.charAt(index) == '(') {
int balance = 0;
int curIndex = index;
while (curIndex < length) {
if (expression.charAt(curIndex) == '(')
balance++;
else if (expression.charAt(curIndex) == ')')
balance--;
if (balance == 0)
break;
curIndex++;
}
Polynomial curPolynomial = parse(expression.substring(index + 1, curIndex));
index = curIndex;
} else if (Character.isLetterOrDigit(expression.charAt(index))) {
boolean flag = true;
int curIndex = index;
while (curIndex < length) {
if (expression.charAt(curIndex) == ' ') {
Polynomial curPolynomial = make(expression.substring(index, curIndex));
flag = false;
break;
}
curIndex++;
}
if (flag) {
Polynomial polynomial = make(expression.substring(index));
}
index = curIndex;
} else if (expression.charAt(index) != ' ')
index++;
}
for (int i = operators.size() - 1; i >= 0; i--) {
if (operators.get(i) == '*') {
Polynomial newPolynomial = combine(bucket.get(i), bucket.remove(i + 1), operators.remove(i));
bucket.set(i, newPolynomial);
}
}
if (bucket.isEmpty())
return new Polynomial();
Polynomial polynomial = bucket.get(0);
int size = operators.size();
for (int i = 0; i < size; i++)
polynomial = combine(polynomial, bucket.get(i + 1), operators.get(i));
return polynomial;
}

public Polynomial make(String expression) {
Polynomial polynomial = new Polynomial();
List<String> list = new ArrayList<String>();
if (Character.isDigit(expression.charAt(0)))
polynomial.update(list, Integer.valueOf(expression));
else {
polynomial.update(list, 1);
}
return polynomial;
}

public Polynomial combine(Polynomial polynomial1, Polynomial polynomial2, char operator) {
if (operator == '+')
else if (operator == '-')
return polynomial1.subtract(polynomial2);
else if (operator == '*')
return polynomial1.multiply(polynomial2);
else
return null;
}
}

class Polynomial {
Map<List<String>, Integer> countMap;

public Polynomial() {
countMap = new HashMap<List<String>, Integer>();
}

public void update(List<String> key, int count) {
int newCount = countMap.getOrDefault(key, 0) + count;
countMap.put(key, newCount);
}

Polynomial sum = new Polynomial();
Set<List<String>> keySet1 = countMap.keySet();
for (List<String> list : keySet1)
sum.update(list, countMap.get(list));
Set<List<String>> keySet2 = polynomial2.countMap.keySet();
for (List<String> list : keySet2)
sum.update(list, polynomial2.countMap.get(list));
return sum;
}

public Polynomial subtract(Polynomial polynomial2) {
Polynomial difference = new Polynomial();
Set<List<String>> keySet1 = countMap.keySet();
for (List<String> list : keySet1)
difference.update(list, countMap.get(list));
Set<List<String>> keySet2 = polynomial2.countMap.keySet();
for (List<String> list : keySet2)
difference.update(list, -polynomial2.countMap.get(list));
return difference;
}

public Polynomial multiply(Polynomial polynomial2) {
Polynomial product = new Polynomial();
Set<List<String>> keySet1 = countMap.keySet();
Set<List<String>> keySet2 = polynomial2.countMap.keySet();
for (List<String> list1 : keySet1) {
for (List<String> list2 : keySet2) {
List<String> newList = new ArrayList<String>();
for (String str : list1)
for (String str : list2)
Collections.sort(newList);
product.update(newList, countMap.get(list1) * polynomial2.countMap.get(list2));
}
}
return product;
}

public Polynomial evaluate(Map<String, Integer> evaluateMap) {
Polynomial polynomial = new Polynomial();
Set<List<String>> keySet = countMap.keySet();
for (List<String> list : keySet) {
int count = countMap.get(list);
List<String> freeList = new ArrayList<String>();
for (String str : list) {
if (evaluateMap.containsKey(str))
count *= evaluateMap.get(str);
else
}
polynomial.update(freeList, count);
}
return polynomial;
}

public int compareList(List<String> list1, List<String> list2) {
int size1 = list1.size(), size2 = list2.size();
if (size1 != size2)
return size2 - size1;
else {
for (int i = 0; i < size1; i++) {
String str1 = list1.get(i), str2 = list2.get(i);
if (!str1.equals(str2))
return str1.compareTo(str2);
}
return 0;
}
}

public List<String> toList() {
List<String> list = new ArrayList<String>();
List<List<String>> keyList = new ArrayList<List<String>>(countMap.keySet());
Collections.sort(keyList, new Comparator<List<String>>() {
public int compare(List<String> list1, List<String> list2) {
return compareList(list1, list2);
}
});
for (List<String> key : keyList) {
int count = countMap.get(key);
if (count != 0) {
StringBuffer sb = new StringBuffer();
sb.append(count);
for (String str : key) {
sb.append('*');
sb.append(str);
}
}
}
return list;
}
}

• // OJ: https://leetcode.com/problems/basic-calculator-iv
class Solution {
private:
vector<string> tokenize(string &expression) {
vector<string> tokens;
for (int i = 0; i < expression.size();) {
string token;
if (isalnum(expression[i])) {
while (i < expression.size() && isalnum(expression[i])) {
token += expression[i++];
}
} else token += expression[i++];
tokens.push_back(token);
while (i < expression.size() && expression[i] == ' ') ++i;
}
}
vector<string> inject(vector<string> &tokens, unordered_map<string, string> &m) {
for (auto &token : tokens) {
if (m.find(token) != m.end()) token = m[token];
}
}
vector<string> toRPN(vector<string> &tokens) {
stack<string> ops;
vector<string> ans;
for (auto &token : tokens) {
switch(token.back()) {
case '+':
case '-':
while (ops.size() && ops.top() != "(") {
ans.push_back(ops.top());
ops.pop();
}
ops.push(token);
break;
case '*':
if (ops.size() && ops.top() == "*") {
ans.push_back(ops.top());
ops.pop();
}
ops.push(token);
break;
case '(':
ops.push(token);
break;
case ')':
while (ops.size() && ops.top() != "(") {
ans.push_back(ops.top());
ops.pop();
}
if (ops.size()) ops.pop();
break;
default:
ans.push_back(token);
break;
}
}
while (ops.size()) {
ans.push_back(ops.top());
ops.pop();
}
return ans;
}
vector<string> splitSymbols(string exp) {
istringstream s(exp);
vector<string> ans;
string symbol;
while (getline(s, symbol, '*')) ans.push_back(symbol);
return ans;
}
vector<string> evaluate(vector<string> &tokens) {
stack<map<string, int>> s;
for (auto &token : tokens) {
switch(token.back()) {
case '+':
case '-': {
int sign = token[0] == '+' ? 1 : -1;
auto b = s.top(); s.pop();
auto a = s.top(); s.pop();
map<string, int> m;
for (auto &p : a) {
m[p.first] += p.second;
}
for (auto &p : b) {
m[p.first] += sign * p.second;
}
s.push(m);
break;
}
case '*': {
auto b = s.top(); s.pop();
auto a = s.top(); s.pop();
map<string, int> m;
for (auto &p : a) {
auto symbol1 = splitSymbols(p.first);
for (auto &q : b) {
istringstream sb(q.first);
auto symbol2 = splitSymbols(q.first);
string symbol;
if (symbol1.size() == 1 && symbol1[0] == "1") {
symbol = q.first;
} else if (symbol2.size() == 1 && symbol2[0] == "1") {
symbol = p.first;
} else {
for (int i = 0, j = 0; i < symbol1.size() || j < symbol2.size();) {
if (symbol.size()) symbol += "*";
if (i >= symbol1.size()) {
symbol += symbol2[j++];
} else if (j >= symbol2.size()) {
symbol += symbol1[i++];
} else if (symbol1[i] < symbol2[j]){
symbol += symbol1[i++];
} else {
symbol += symbol2[j++];
}
}
}
m[symbol] += p.second * q.second;
}
}
s.push(m);
break;
}
default: {
map<string, int> m;
if (isdigit(token.back())) {
m["1"] = stoi(token);
} else {
m[token] = 1;
}
s.push(m);
break;
}
}
}
vector<string> ans;
for (auto &p : s.top()) {
if (!p.second) continue;
ans.push_back(to_string(p.second) + (p.first == "1" ? "" : "*" + p.first));
}
stable_sort(ans.begin(), ans.end(), [&](string a, string b) {
return count(a.begin(), a.end(), '*') > count(b.begin(), b.end(), '*');
});
return ans;
}
public:
vector<string> basicCalculatorIV(string expression, vector<string>& evalvars, vector<int>& evalints) {
unordered_map<string, string> m;
for (int i = 0; i < evalvars.size(); ++i) {
m[evalvars[i]] = to_string(evalints[i]);
}
auto tokens = tokenize(expression);
tokens = inject(tokens, m);
tokens = toRPN(tokens);
tokens = evaluate(tokens);