# 0679. 24 Game

<https://leetcode.com/problems/24-game>

## Description

You are given an integer array `cards` of length `4`. You have four cards, each containing a number in the range `[1, 9]`. You should arrange the numbers on these cards in a mathematical expression using the operators `['+', '-', '*', '/']` and the parentheses `'('` and `')'` to get the value 24.

You are restricted with the following rules:

* The division operator `'/'` represents real division, not integer division.
  * For example, `4 / (1 - 2 / 3) = 4 / (1 / 3) = 12`.
* Every operation done is between two numbers. In particular, we cannot use `'-'` as a unary operator.
  * For example, if `cards = [1, 1, 1, 1]`, the expression `"-1 - 1 - 1 - 1"` is **not allowed**.
* You cannot concatenate numbers together
  * For example, if `cards = [1, 2, 1, 2]`, the expression `"12 + 12"` is not valid.

Return `true` if you can get such expression that evaluates to `24`, and `false` otherwise.

**Example 1:**

```
**Input:** cards = [4,1,8,7]
**Output:** true
**Explanation:** (8-4) * (7-1) = 24
```

**Example 2:**

```
**Input:** cards = [1,2,1,2]
**Output:** false
```

**Constraints:**

* `cards.length == 4`
* `1 <= cards[i] <= 9`

## ac

```java
class Solution {
    public boolean judgePoint24(int[] nums) {
        // edge cases

        List<Double> list = new ArrayList<>();
        for (int n : nums) list.add((double) n);

        return dfs(list);
    }

    private boolean dfs(List<Double> list) {
        int n = list.size();
        if (n == 1) return Math.abs(list.get(0) - 24.0) < 0.0001;

        // pick 2 numbers, calculate a new number
        for (int i = 0; i < n-1; i++) {
            for (int j = i + 1; j < n; j++) {
                List<Double> newVal = cal(list.get(i), list.get(j));
                // new list, pick remaining number from old list
                List<Double> newList = new ArrayList<>();
                for (int k = 0; k < n; k++) {
                    if (k != i && k != j) newList.add(list.get(k));
                }
                // backtracking, try new values
                int lastIdx = newList.size();
                for (double d : newVal) {
                    newList.add(d);
                    if (dfs(newList)) return true;
                    newList.remove(lastIdx);
                }
            }
        }

        return false;
    }

    private List<Double> cal(double n1, double n2) {
        List<Double> res = new ArrayList<>();
        res.add(n1 + n2);
        res.add(n1 - n2);
        res.add(n1 * n2);
        res.add(n1 / n2);
        res.add(n2 - n1);
        res.add(n2 / n1);
        return res;
    }
}

/*
1) pick 2 numbers, calculate a new number put back to array. 2) repeat, until only one number in array, check if it's 24.
*/
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/0679-24-game.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.