Get Target Number Using Number List and Arithmetic Operations

Given a list of numbers and a target number, write a program to determine whether the target number can be calculated by applying "+-*/" operations to the number list? You can assume () is automatically added when necessary. An operator should be put between each two consecutive numbers. So each number has to be used.

For example, given {1,2,3,4} and 21, return true. Because (1+2)*(3+4)=21

Java Solution

This is a partition problem which can be solved by using depth first search.

public boolean isReachable(ArrayList<Integer> list, int target) {
    if (list == null || list.size() == 0)
        return false;
    int i = 0;
    int j = list.size() - 1;
    ArrayList<Integer> results = getResults(list, i, j);
    for (int num : results) {
        if (num == target) {
            return true;
    return false;
public ArrayList<Integer> getResults(ArrayList<Integer> list,
                                            int left, int right) {
    ArrayList<Integer> result = new ArrayList<Integer>();
    if (left > right) {
        return result;
    } else if (left == right) {
        return result;
    for (int i = left; i < right; i++) {
        ArrayList<Integer> result1 = getResults(list, left, i);
        ArrayList<Integer> result2 = getResults(list, i + 1, right);
        for (int x : result1) {
            for (int y : result2) {
                result.add(x + y);
                result.add(x - y);
                result.add(x * y);
                if (y != 0)
                    result.add(x / y);
    return result;
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  • Pavel Petrenko

    What is time and space complexity of this solution?

  • alexwest11


    i would use exact words in formulation of task to avoid ambiguity

  • Bonsai

    The problem asks to put an operator between each two consecutive numbers. So each number has to be used.

  • alexwest11

    could we have more info

    1) DO i have use ALL NUMBERS?

    2) as known from 1d grade in school, any ‘*’ can be replaced by amount of ‘+’, so why do we need * in this case?

  • West

    O_o author is sick!

  • Thanks for sharing this.

  • Ankit Shah

    you don’t need to pass target in the second function:

    public static ArrayList getResults(ArrayList list,int left, int right) {