ExpressionAddOperators.java

package com.fishercoder.solutions;

import java.util.ArrayList;
import java.util.List;

/**
 * Given a string that contains only digits 0-9 and a target value, return all possibilities to add binary operators (not unary) +, -, or * between the digits so they evaluate to the target value.

 Examples:
 "123", 6 -> ["1+2+3", "1*2*3"]
 "232", 8 -> ["2*3+2", "2+3*2"]
 "105", 5 -> ["1*0+5","10-5"]
 "00", 0 -> ["0+0", "0-0", "0*0"]
 "3456237490", 9191 -> []
 */
public class ExpressionAddOperators {

    public List<String> addOperators(String num, int target) {
        List<String> res = new ArrayList<String>();
        StringBuilder sb = new StringBuilder();
        dfs(res, sb, num, 0, target, 0, 0);
        return res;

    }

    private void dfs(List<String> res, StringBuilder sb, String num, int pos, int target, long prev, long multi) {
        if(pos == num.length()){
            if(target == prev) res.add(sb.toString());
            return;
        }
        for(int i = pos; i < num.length(); i++){
            if(num.charAt(pos) == '0' && i != pos) break;
            long curr = Long.parseLong(num.substring(pos, i+1));
            int len = sb.length();
            if(pos == 0){
                dfs(res, sb.append(curr), num, i+1, target, curr, curr);
                sb.setLength(len);
            } else {
                dfs(res, sb.append("+").append(curr), num, i+1, target, prev+curr, curr);
                sb.setLength(len);

                dfs(res, sb.append("-").append(curr), num, i+1, target, prev-curr, -curr);
                sb.setLength(len);

                dfs(res, sb.append("*").append(curr), num, i+1, target, prev - multi + multi*curr, multi*curr);
                sb.setLength(len);
            }
        }
    }

}