Given two expressions in the form of strings. The task is to compare them and check if they are similar. Expressions consist of lowercase alphabets, '+', '-' and '( )'.
Examples:
Input : exp1 = "-(a+b+c)"
exp2 = "-a-b-c"
Output : Yes
Explanation : The first expression, when simplified by distributing the negative sign, matches the second expression, hence they are similar.Input : exp1 = "-(c+b+a)"
exp2 = "-c-b-a"
Output : Yes
Explanation : The order of terms inside parentheses does not affect the result, and distributing the negative sign yields a match, so the expressions are similar.Input : exp1 = "a-b-(c-d)"
exp2 = "a-b-c-d"
Output : No
Explanation : The negative sign distribution inside the parentheses leads to different signs for the terms, making the expressions not similar.
Approach - Sign Propagation - O(n) time and O(n) space
This approach tracks the global and local signs in an expression. The global sign affects operands within parentheses, while the local sign applies to each operand individually. The final sign of an operand is the product of its local and global signs.
For example, in
a + b - (c - d), the expression evaluates toa + b - c + d, where the global sign inside parentheses flips the signs ofcandd.A stack keeps track of global signs, and a count vector records operand counts. Both expressions are evaluated in opposite ways, and if the count vector ends with all zeros, the expressions are considered equivalent.
// CPP program to check if two expressions
// evaluate to same.
#include <bits/stdc++.h>
using namespace std;
const int MAX_CHAR = 26;
// Return local sign of the operand. For example,
// in the expr a-b-(c), local signs of the operands
// are +a, -b, +c
bool adjSign(string s, int i)
{
if (i == 0)
return true;
if (s[i - 1] == '-')
return false;
return true;
};
// Evaluate expressions into the count vector of
// the 26 alphabets.If add is true, then add count
// to the count vector of the alphabets, else remove
// count from the count vector.
void eval(string s, vector<int>& v, bool add)
{
// stack stores the global sign
// for operands.
stack<bool> stk;
stk.push(true);
// + means true
// global sign is positive initially
int i = 0;
while (s[i] != '\0') {
if (s[i] == '+' || s[i] == '-') {
i++;
continue;
}
if (s[i] == '(') {
// global sign for the bracket is
// pushed to the stack
if (adjSign(s, i))
stk.push(stk.top());
else
stk.push(!stk.top());
}
// global sign is popped out which
// was pushed in for the last bracket
else if (s[i] == ')')
stk.pop();
else {
// global sign is positive (we use different
// values in two calls of functions so that
// we finally check if all vector elements
// are 0.
if (stk.top())
v[s[i] - 'a'] += (adjSign(s, i) ? add ? 1 : -1 :
add ? -1 : 1);
// global sign is negative here
else
v[s[i] - 'a'] += (adjSign(s, i) ? add ? -1 : 1 :
add ? 1 : -1);
}
i++;
}
};
// Returns true if expr1 and expr2 represent
// same expressions
bool areSame(string expr1, string expr2)
{
// Create a vector for all operands and
// initialize the vector as 0.
vector<int> v(MAX_CHAR, 0);
// Put signs of all operands in expr1
eval(expr1, v, true);
// Subtract signs of operands in expr2
eval(expr2, v, false);
// If expressions are same, vector must
// be 0.
for (int i = 0; i < MAX_CHAR; i++)
if (v[i] != 0)
return false;
return true;
}
int main()
{
string expr1 = "-(a+b+c)", expr2 = "-a-b-c";
if (areSame(expr1, expr2))
cout << "Yes\n";
else
cout << "No\n";
return 0;
}
// Java program to check if two expressions
// evaluate to same.
import java.io.*;
import java.util.*;
class GFG
{
static final int MAX_CHAR = 26;
// Return local sign of the operand. For example,
// in the expr a-b-(c), local signs of the operands
// are +a, -b, +c
static boolean adjSign(String s, int i)
{
if (i == 0)
return true;
if (s.charAt(i - 1) == '-')
return false;
return true;
};
// Evaluate expressions into the count vector of
// the 26 alphabets.If add is true, then add count
// to the count vector of the alphabets, else remove
// count from the count vector.
static void eval(String s, int[] v, boolean add)
{
// stack stores the global sign
// for operands.
Stack<Boolean> stk = new Stack<>();
stk.push(true);
// + means true
// global sign is positive initially
int i = 0;
while (i < s.length())
{
if (s.charAt(i) == '+' || s.charAt(i) == '-')
{
i++;
continue;
}
if (s.charAt(i) == '(')
{
// global sign for the bracket is
// pushed to the stack
if (adjSign(s, i))
stk.push(stk.peek());
else
stk.push(!stk.peek());
}
// global sign is popped out which
// was pushed in for the last bracket
else if (s.charAt(i) == ')')
stk.pop();
else
{
// global sign is positive (we use different
// values in two calls of functions so that
// we finally check if all vector elements
// are 0.
if (stk.peek())
v[s.charAt(i) - 'a'] += (adjSign(s, i) ?
add ? 1 : -1 : add ? -1 : 1);
// global sign is negative here
else
v[s.charAt(i) - 'a'] += (adjSign(s, i) ?
add ? -1 : 1 : add ? 1 : -1);
}
i++;
}
};
// Returns true if expr1 and expr2 represent
// same expressions
static boolean areSame(String expr1, String expr2)
{
// Create a vector for all operands and
// initialize the vector as 0.
int[] v = new int[MAX_CHAR];
// Put signs of all operands in expr1
eval(expr1, v, true);
// Subtract signs of operands in expr2
eval(expr2, v, false);
// If expressions are same, vector must
// be 0.
for (int i = 0; i < MAX_CHAR; i++)
if (v[i] != 0)
return false;
return true;
}
// Driver Code
public static void main(String[] args)
{
String expr1 = "-(a+b+c)", expr2 = "-a-b-c";
if (areSame(expr1, expr2))
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by
// sanjeev2552
# Python3 program to check if two expressions
# evaluate to same.
MAX_CHAR = 26;
# Return local sign of the operand. For example,
# in the expr a-b-(c), local signs of the operands
# are +a, -b, +c
def adjSign(s, i):
if (i == 0):
return True;
if (s[i - 1] == '-'):
return False;
return True;
# Evaluate expressions into the count vector of
# the 26 alphabets.If add is True, then add count
# to the count vector of the alphabets, else remove
# count from the count vector.
def eval(s, v, add):
# stack stores the global sign
# for operands.
stk = []
stk.append(True);
# + means True
# global sign is positive initially
i = 0;
while (i < len(s)):
if (s[i] == '+' or s[i] == '-'):
i += 1
continue;
if (s[i] == '('):
# global sign for the bracket is
# pushed to the stack
if (adjSign(s, i)):
stk.append(stk[-1]);
else:
stk.append(not stk[-1]);
# global sign is popped out which
# was pushed in for the last bracket
elif (s[i] == ')'):
stk.pop();
else:
# global sign is positive (we use different
# values in two calls of functions so that
# we finally check if all vector elements
# are 0.
if (stk[-1]):
v[ord(s[i]) - ord('a')] += (1 if add else -1) if adjSign(s, i) else (-1 if add else 1)
# global sign is negative here
else:
v[ord(s[i]) - ord('a')] += (-1 if add else 1) if adjSign(s, i) else (1 if add else -1)
i += 1
# Returns True if expr1 and expr2 represent
# same expressions
def areSame(expr1, expr2):
# Create a vector for all operands and
# initialize the vector as 0.
v = [0 for i in range(MAX_CHAR)];
# Put signs of all operands in expr1
eval(expr1, v, True);
# Subtract signs of operands in expr2
eval(expr2, v, False);
# If expressions are same, vector must
# be 0.
for i in range(MAX_CHAR):
if (v[i] != 0):
return False;
return True;
# Driver Code
if __name__=='__main__':
expr1 = "-(a+b+c)"
expr2 = "-a-b-c";
if (areSame(expr1, expr2)):
print("Yes");
else:
print("No");
// C# program to check if two expressions
// evaluate to same.
using System;
using System.Collections.Generic;
public class GFG
{
static readonly int MAX_CHAR = 26;
// Return local sign of the operand. For example,
// in the expr a-b-(c), local signs of the operands
// are +a, -b, +c
static bool adjSign(String s, int i)
{
if (i == 0)
return true;
if (s[i-1] == '-')
return false;
return true;
}
// Evaluate expressions into the count vector of
// the 26 alphabets.If add is true, then add count
// to the count vector of the alphabets, else remove
// count from the count vector.
static void eval(String s, int[] v, bool add)
{
// stack stores the global sign
// for operands.
Stack<Boolean> stk = new Stack<Boolean>();
stk.Push(true);
// + means true
// global sign is positive initially
int i = 0;
while (i < s.Length)
{
if (s[i] == '+' || s[i] == '-')
{
i++;
continue;
}
if (s[i] == '(')
{
// global sign for the bracket is
// pushed to the stack
if (adjSign(s, i))
stk.Push(stk.Peek());
else
stk.Push(!stk.Peek());
}
// global sign is popped out which
// was pushed in for the last bracket
else if (s[i] == ')')
stk.Pop();
else
{
// global sign is positive (we use different
// values in two calls of functions so that
// we finally check if all vector elements
// are 0.
if (stk.Peek())
v[s[i] - 'a'] += (adjSign(s, i) ?
add ? 1 : -1 : add ? -1 : 1);
// global sign is negative here
else
v[s[i] - 'a'] += (adjSign(s, i) ?
add ? -1 : 1 : add ? 1 : -1);
}
i++;
}
}
// Returns true if expr1 and expr2 represent
// same expressions
static bool areSame(String expr1, String expr2)
{
// Create a vector for all operands and
// initialize the vector as 0.
int[] v = new int[MAX_CHAR];
// Put signs of all operands in expr1
eval(expr1, v, true);
// Subtract signs of operands in expr2
eval(expr2, v, false);
// If expressions are same, vector must
// be 0.
for (int i = 0; i < MAX_CHAR; i++)
if (v[i] != 0)
return false;
return true;
}
// Driver Code
public static void Main(String[] args)
{
String expr1 = "-(a+b+c)", expr2 = "-a-b-c";
if (areSame(expr1, expr2))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// Javascript program to check if two expressions
// evaluate to same.
let MAX_CHAR = 26;
// Return local sign of the operand. For example,
// in the expr a-b-(c), local signs of the operands
// are +a, -b, +c
function adjSign(s, i)
{
if (i == 0)
return true;
if (s[i - 1] == '-')
return false;
return true;
}
// Evaluate expressions into the count vector of
// the 26 alphabets.If add is true, then add count
// to the count vector of the alphabets, else remove
// count from the count vector.
function eval(s, v, add)
{
// stack stores the global sign
// for operands.
let stk = [];
stk.push(true);
// + means true
// global sign is positive initially
let i = 0;
while (i < s.length)
{
if (s[i] == '+' || s[i] == '-')
{
i++;
continue;
}
if (s[i] == '(')
{
// global sign for the bracket is
// pushed to the stack
if (adjSign(s, i))
stk.push(stk[stk.length - 1]);
else
stk.push(!stk[stk.length - 1]);
}
// global sign is popped out which
// was pushed in for the last bracket
else if (s[i] == ')')
stk.pop();
else
{
// global sign is positive (we use different
// values in two calls of functions so that
// we finally check if all vector elements
// are 0.
if (stk[stk.length - 1])
v[s[i] - 'a'] += (adjSign(s, i) ?
add ? 1 : -1 : add ? -1 : 1);
// global sign is negative here
else
v[s[i] - 'a'] += (adjSign(s, i) ?
add ? -1 : 1 : add ? 1 : -1);
}
i++;
}
};
// Returns true if expr1 and expr2 represent
// same expressions
function areSame(expr1, expr2)
{
// Create a vector for all operands and
// initialize the vector as 0.
let v = new Array(MAX_CHAR);
v.fill(0);
// Put signs of all operands in expr1
eval(expr1, v, true);
// Subtract signs of operands in expr2
eval(expr2, v, false);
// If expressions are same, vector must
// be 0.
for (let i = 0; i < MAX_CHAR; i++)
if (v[i] != 0)
return false;
return true;
}
let expr1 = "-(a+b+c)", expr2 = "-a-b-c";
if (areSame(expr1, expr2))
console.log("Yes");
else
console.log("No");
Output
Yes
