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 -> []

Solution(Not mine)

public class Solution {
    public List<String> addOperators(String num, int target) {
        List<String> rst = new ArrayList<String>();
        if(num == null || num.length() == 0) return rst;
        helper(rst, "", num, target, 0, 0, 0);
        return rst;
    }
    public void helper(List<String> rst, String path, String num, int target, int pos, long eval, long multed){
        if(pos == num.length()){
            if(target == eval)
                rst.add(path);
            return;
        }
        for(int i = pos; i < num.length(); i++){
            if(i != pos && num.charAt(pos) == '0') break;
            long cur = Long.parseLong(num.substring(pos, i + 1));
            if(pos == 0){
                helper(rst, path + cur, num, target, i + 1, cur, cur);
            }
            else{
                helper(rst, path + "+" + cur, num, target, i + 1, eval + cur , cur);

                helper(rst, path + "-" + cur, num, target, i + 1, eval -cur, -cur);

                helper(rst, path + "*" + cur, num, target, i + 1, eval - multed + multed * cur, multed * cur );
            }
        }
    }
}

Solution

public class Solution {
    public List<String> addOperators(String num, int target) {
        List<String> ans = new ArrayList<String>();
        if(num.length() == 0) return ans;

        int[] oper = new int[num.length()];
        dfs(num.toCharArray(), 0, oper, ans, target);
        return ans;
    }

    public final int EMP = 0;
    public final int ADD = 1;
    public final int SUB = 2;
    public final int MUL = 3;

    public void dfs(char[] num, int idx, int[] oper, List<String> ans, int target) {
        if(idx == num.length - 1) {n
            if(eval(num, oper, target)) {
                ans.add(build(num, oper));
            }
            return;  
        } 

        for(int i = 0; i < 4; i++) {
            oper[idx] = i;
            dfs(num, idx + 1, oper, ans, target);
        }
    }

    public boolean eval(char[] num, int[] oper, int target) {
        int lastOp = ADD;
        Stack<Long> stack = new Stack<Long>();
        long current = 0;
        for(int i = 0; i < oper.length; i++) {

            if(current == 0 && num[i] == '0' && (i != oper.length-1 && oper[i] == EMP) ) return false;

            current = 10 * current + (num[i] - '0');
            if(i == oper.length - 1 || oper[i] == ADD || oper[i] == SUB || oper[i] == MUL) {
                if(lastOp == ADD) stack.push(current);
                else if(lastOp == SUB) stack.push(-current);
                else if(lastOp == MUL) {
                    stack.push(stack.pop() * current);
                }
                current = 0;
                lastOp = oper[i];
            } 
        }
        while(!stack.isEmpty()) {
            current += stack.pop();
        }
        return current == target;
    }

    public String build(char[] num, int[] oper) {
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < oper.length; i++) {
            sb.append(num[i]);
            if(i != oper.length - 1 && oper[i] != EMP) {
                sb.append(oper[i] == ADD ? '+' : (oper[i] == SUB ? '-' : '*') );
            }
        }
        return sb.toString();
    }
}