Given a string that contains only digits from 0 to 9, and an integer value, target. Find out how many expressions are possible which evaluate to target using binary operator +, – and * in given string of digits.
Input : "123", Target : 6
Output : {“1+2+3”, “1*2*3”}
Input : “125”, Target : 7
Output : {“1*2+5”, “12-5”}
This problem can be solved by putting all possible binary operator in mid between two digits and evaluating them and then check they evaluate to target or not.
- While writing the recursive code, we need to keep these variable as argument of recursive method – result vector, input string, current expression string, target value, position till which input is processed, current evaluated value and last value in evaluation.
- Last value is kept in recursion because of multiplication operation, while doing multiplication we need last value for correct evaluation.
See below example for better understanding –
Input is 125, suppose we have reached till 1+2 now, Input = “125”, current expression = “1+2”, position = 2, current val = 3, last = 2 Now when we go for multiplication, we need last value for evaluation as follows: current val = current val - last + last * current val First we subtract last and then add last * current val for evaluation, new last is last * current val. current val = 3 – 2 + 2*5 = 11 last = 2*5 = 10
Another thing to note in below code is, we have ignored all numbers which start from 0 by imposing a condition as first condition inside the loop so that we will not process number like 03, 05 etc.
See the use of c_str() function, this function converts the C++ string into C char array, this function is used in below code because atoi() function expects a character array as an argument not the string. It converts character array to number.
C++
// C++ program to find all possible expression which// evaluate to target#include <bits/stdc++.h>using namespace std;
// Utility recursive method to generate all possible// expressionsvoid getExprUtil(vector<string>& res, string curExp,
string input, int target, int pos,
int curVal, int last)
{ // true if whole input is processed with some
// operators
if (pos == input.length())
{
// if current value is equal to target
//then only add to final solution
// if question is : all possible o/p then just
//push_back without condition
if (curVal == target)
res.push_back(curExp);
return;
}
// loop to put operator at all positions
for (int i = pos; i < input.length(); i++)
{
// ignoring case which start with 0 as they
// are useless for evaluation
if (i != pos && input[pos] == '0')
break;
// take part of input from pos to i
string part = input.substr(pos, i + 1 - pos);
// take numeric value of part
int cur = atoi(part.c_str());
// if pos is 0 then just send numeric value
// for next recursion
if (pos == 0)
getExprUtil(res, curExp + part, input,
target, i + 1, cur, cur);
// try all given binary operator for evaluation
else
{
getExprUtil(res, curExp + "+" + part, input,
target, i + 1, curVal + cur, cur);
getExprUtil(res, curExp + "-" + part, input,
target, i + 1, curVal - cur, -cur);
getExprUtil(res, curExp + "*" + part, input,
target, i + 1, curVal - last + last * cur,
last * cur);
}
}
}// Below method returns all possible expression// evaluating to targetvector<string> getExprs(string input, int target)
{ vector<string> res;
getExprUtil(res, "", input, target, 0, 0, 0);
return res;
}// method to print resultvoid printResult(vector<string> res)
{ for (int i = 0; i < res.size(); i++)
cout << res[i] << " ";
cout << endl;
}// Driver code to test above methodsint main()
{ string input = "123";
int target = 6;
vector<string> res = getExprs(input, target);
printResult(res);
input = "125";
target = 7;
res = getExprs(input, target);
printResult(res);
return 0;
} |
Java
// Java program to find all possible expression which// evaluate to targetimport java.util.ArrayList;
class GFG {
// Utility recursive method to generate all possible
// expressions
static void getExprUtil(ArrayList<String> res,
String curExp, String input,
int target, int pos, int curVal,
int last)
{
// true if whole input is processed with some
// operators
if (pos == input.length()) {
// if current value is equal to target
// then only add to final solution
// if question is : all possible o/p then just
// push_back without condition
if (curVal == target)
res.add(curExp);
return;
}
// loop to put operator at all positions
for (int i = pos; i < input.length(); i++) {
// ignoring case which start with 0 as they
// are useless for evaluation
if (i != pos && input.charAt(pos) == '0')
break;
// take part of input from pos to i
String part = input.substring(pos, i + 1);
// take numeric value of part
int cur = Integer.parseInt(part);
// if pos is 0 then just send numeric value
// for next recursion
if (pos == 0)
getExprUtil(res, curExp + part, input,
target, i + 1, cur, cur);
// try all given binary operator for evaluation
else {
getExprUtil(res, curExp + "+" + part, input,
target, i + 1, curVal + cur,
cur);
getExprUtil(res, curExp + "-" + part, input,
target, i + 1, curVal - cur,
-cur);
getExprUtil(res, curExp + "*" + part, input,
target, i + 1,
curVal - last + last * cur,
last * cur);
}
}
}
// Below method returns all possible expression
// evaluating to target
static ArrayList<String> getExprs(String input,
int target)
{
ArrayList<String> res = new ArrayList<String>();
getExprUtil(res, "", input, target, 0, 0, 0);
return res;
}
// method to print result
static void printResult(ArrayList<String> res)
{
for (int i = 0; i < res.size(); i++)
System.out.print(res.get(i) + " ");
System.out.println();
}
// Driver code to test above methods
public static void main(String[] args)
{
String input = "123";
int target = 6;
ArrayList<String> res = getExprs(input, target);
printResult(res);
input = "125";
target = 7;
res = getExprs(input, target);
printResult(res);
}
}// This code is contributed by jainlovely450.o |
Python3
# Python3 program to find all possible expression which# evaluate to target# Utility recursive method to generate all possible# expressionsdef getExprUtil(res, curExp, _input, target, pos, curVal, last):
# true if whole input is processed with some
# operators
if (pos == len(_input)):
# if current value is equal to target
#then only add to final solution
# if question is : all possible o/p then just
#push_back without condition
if (curVal == target):
res.append(curExp)
return
# loop to put operator at all positions
for i in range(pos,len(_input)):
# ignoring case which start with 0 as they
# are useless for evaluation
if (i != pos and _input[pos] == '0'):
break
# take part of input from pos to i
part = _input[pos: i + 1].strip()
# take numeric value of part
cur = int(part)
# if pos is 0 then just send numeric value
# for next recursion
if (pos == 0):
getExprUtil(res, curExp + part, _input,
target, i + 1, cur, cur)
# try all given binary operator for evaluation
else:
getExprUtil(res, curExp + "+" + part, _input,
target, i + 1, curVal + cur, cur)
getExprUtil(res, curExp + "-" + part, _input,
target, i + 1, curVal - cur, -cur)
getExprUtil(res, curExp + "*" + part, _input,
target, i + 1, curVal - last + last * cur,
last * cur)
# Below method returns all possible expression# evaluating to targetdef getExprs(_input, target):
res=[]
getExprUtil(res, "", _input, target, 0, 0, 0)
return res
# method to print resultdef printResult(res):
for i in range(len(res)):
print(res[i],end=" ")
print()
# Driver code to test above methodsif __name__ == '__main__':
_input = "123"
target = 6
res = getExprs(_input, target)
printResult(res)
_input = "125"
target = 7
res = getExprs(_input, target)
printResult(res)
|
C#
// C# program to find all possible expression which// evaluate to targetusing System;
using System.Collections.Generic;
class GFG {
// Utility recursive method to generate all possible expressions
static void getExprUtil(List<string> res, string curExp,
string input, int target, int pos,
int curVal, int last)
{
// true if whole input is processed with some
// operators
if (pos == input.Length)
{
// if current value is equal to target
//then only add to final solution
// if question is : all possible o/p then just
//push_back without condition
if (curVal == target)
res.Add(curExp);
return;
}
// loop to put operator at all positions
for (int i = pos; i < input.Length; i++)
{
// ignoring case which start with 0 as they
// are useless for evaluation
if (i != pos && input[pos] == '0')
break;
// take part of input from pos to i
string part = input.Substring(pos, i + 1 - pos);
// take numeric value of part
int cur = Int32.Parse(part);
// if pos is 0 then just send numeric value
// for next recursion
if (pos == 0)
getExprUtil(res, curExp + part, input,
target, i + 1, cur, cur);
// try all given binary operator for evaluation
else
{
getExprUtil(res, curExp + "+" + part, input,
target, i + 1, curVal + cur, cur);
getExprUtil(res, curExp + "-" + part, input,
target, i + 1, curVal - cur, -cur);
getExprUtil(res, curExp + "*" + part, input,
target, i + 1, curVal - last + last * cur,
last * cur);
}
}
}
// Below method returns all possible expression
// evaluating to target
static List<string> getExprs(string input, int target)
{
List<string> res = new List<string>();
getExprUtil(res, "", input, target, 0, 0, 0);
return res;
}
// method to print result
static void printResult(List<string> res)
{
for (int i = 0; i < res.Count; i++)
Console.Write(res[i] + " ");
Console.WriteLine();
}
static void Main()
{
string input = "123";
int target = 6;
List<string> res = getExprs(input, target);
printResult(res);
input = "125";
target = 7;
res = getExprs(input, target);
printResult(res);
}
}// This code is contributed by divyesh072019. |
Javascript
<script> // Javascript program to find all possible expression which
// evaluate to target
// Utility recursive method to generate all possible
// expressions
function getExprUtil(res, curExp, input, target, pos, curVal, last)
{
// true if whole input is processed with some
// operators
if (pos == input.length)
{
// if current value is equal to target
//then only add to final solution
// if question is : all possible o/p then just
//push_back without condition
if (curVal == target)
res.push(curExp);
return;
}
// loop to put operator at all positions
for (let i = pos; i < input.length; i++)
{
// ignoring case which start with 0 as they
// are useless for evaluation
if (i != pos && input[pos] == '0')
break;
// take part of input from pos to i
let part = input.substr(pos, i + 1 - pos);
// take numeric value of part
let cur = parseInt(part, 10);
// if pos is 0 then just send numeric value
// for next recursion
if (pos == 0)
getExprUtil(res, curExp + part, input,
target, i + 1, cur, cur);
// try all given binary operator for evaluation
else
{
getExprUtil(res, curExp + "+" + part, input,
target, i + 1, curVal + cur, cur);
getExprUtil(res, curExp + "-" + part, input,
target, i + 1, curVal - cur, -cur);
getExprUtil(res, curExp + "*" + part, input,
target, i + 1, curVal - last + last * cur,
last * cur);
}
}
}
// Below method returns all possible expression
// evaluating to target
function getExprs(input, target)
{
let res = [];
getExprUtil(res, "", input, target, 0, 0, 0);
return res;
}
// method to print result
function printResult(res)
{
for (let i = 0; i < res.length; i++)
document.write(res[i] + " ");
document.write("</br>");
}
let input = "123";
let target = 6;
let res = getExprs(input, target);
printResult(res);
input = "125";
target = 7;
res = getExprs(input, target);
printResult(res);
// This code is contributed by decode2207.
</script> |
Output:
1+2+3 1*2*3 1*2+5 12-5
Time Complexity: O(
Auxiliary Space: O(N)
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