LeetCode-in-Java

679. 24 Game

Hard

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

Solution

import java.util.Arrays;

public class Solution {
    private static final double EPS = 1e-6;

    private boolean backtrack(double[] list, int n) {
        if (n == 1) {
            return Math.abs(list[0] - 24) < EPS;
        }
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                double a = list[i];
                double b = list[j];
                list[j] = list[n - 1];
                list[i] = a + b;
                if (backtrack(list, n - 1)) {
                    return true;
                }
                list[i] = a - b;
                if (backtrack(list, n - 1)) {
                    return true;
                }
                list[i] = b - a;
                if (backtrack(list, n - 1)) {
                    return true;
                }
                list[i] = a * b;
                if (backtrack(list, n - 1)) {
                    return true;
                }
                if (Math.abs(b) > EPS) {
                    list[i] = a / b;
                    if (backtrack(list, n - 1)) {
                        return true;
                    }
                }
                if (Math.abs(a) > EPS) {
                    list[i] = b / a;
                    if (backtrack(list, n - 1)) {
                        return true;
                    }
                }
                list[i] = a;
                list[j] = b;
            }
        }
        return false;
    }

    public boolean judgePoint24(int[] nums) {
        double[] a = Arrays.stream(nums).asDoubleStream().toArray();
        return backtrack(a, a.length);
    }
}

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