SolveTheEquation.java

package math;

/**
 * Created by gouthamvidyapradhan on 16/02/2018.
 * Solve a given equation and return the value of x in the form of string "x=#value". The equation contains only
 * '+', '-' operation, the variable x and its coefficient.

 If there is no solution for the equation, return "No solution".

 If there are infinite solutions for the equation, return "Infinite solutions".

 If there is exactly one solution for the equation, we ensure that the value of x is an integer.

 Example 1:
 Input: "x+5-3+x=6+x-2"
 Output: "x=2"
 Example 2:
 Input: "x=x"
 Output: "Infinite solutions"
 Example 3:
 Input: "2x=x"
 Output: "x=0"
 Example 4:
 Input: "2x+3x-6x=x+2"
 Output: "x=-1"
 Example 5:
 Input: "x=x+2"
 Output: "No solution"

 Solution: Solve the left and right part separately and then sum up the results.
 */

public class SolveTheEquation {

    int xL = 0, xR = 0, tL = 0, tR = 0;
    public static void main(String[] args) throws Exception{
        System.out.println(new SolveTheEquation().solveEquation("x=x+2"));
    }

    public String solveEquation(String equation) {
        String[] parts = equation.split("=");
        solve(parts[0], true);
        solve(parts[1], false);
        long right = (long)tR - tL;
        long left = (long)xL - xR;
        if(left == 0 && right == 0){
            return "Infinite solutions";
        } else if(left == 0){
            return "No solution";
        } else if(right == 0){
            return "x=0";
        } else{
            return "x=" + (right / left);
        }
    }

    private void solve(String s, boolean isLeft){
        String num = "";
        int xSum = 0;
        int rest = 0;
        boolean isNeg = false;
        for(int i = 0; i < s.length(); i ++){
            char c = s.charAt(i);
            if(c == '-'){
                if(!num.isEmpty()){
                    xSum = calculate(num, isNeg, xSum, rest)[0];
                    rest = calculate(num, isNeg, xSum, rest)[1];
                }
                isNeg = true;
                num = "";
            }else if(c == '+'){
                if(!num.isEmpty()){
                    xSum = calculate(num, isNeg, xSum, rest)[0];
                    rest = calculate(num, isNeg, xSum, rest)[1];
                }
                isNeg = false;
                num = "";
            } else{
                num += c;
            }
        }
        if(!num.isEmpty()){
            xSum = calculate(num, isNeg, xSum, rest)[0];
            rest = calculate(num, isNeg, xSum, rest)[1];
        }
        if(isLeft){
            xL = xSum;
            tL = rest;
        } else{
            xR = xSum;
            tR = rest;
        }
    }

    private int[] calculate(String num, boolean isNeg, int xSum, int rest){
        int[] A = new int[2];
        if(num.contains("x")){
            num = num.substring(0, num.length() - 1);
            if(isNeg){
                xSum -= num.isEmpty() ? 1 : Integer.parseInt(num);
            } else{
                xSum += num.isEmpty() ? 1 : Integer.parseInt(num);
            }

        } else{
            if(isNeg){
                rest -= Integer.parseInt(num);
            } else{
                rest += Integer.parseInt(num);
            }
        }
        A[0] = xSum;
        A[1] = rest;
        return A;
    }

}