[LeetCode]679. 24 Game

Problem:

You have 4 cards each containing a number from 1 to 9. You need to judge whether they could operated through *, /, +, -, (, ) to get the value of 24.

Example 1:

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

Example 2:

Input: [1, 2, 1, 2]
Output: False

Note:

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

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Solution:

題意：模擬24點遊戲，給定一個只有4個元素的數組，且每個元素值在1~9之間，判斷是否能通過+，-，*，/得到24.

思路：回溯。

class Solution {
public:
    bool judgePoint24(vector<int>& nums) {
        vector<double> cards(nums.size(), 0);
        for (int i = 0; i < nums.size(); i++)
            cards[i] = (double)nums[i];
        return backTracking(cards);
    }
    bool backTracking(vector<double>& cards) {
        if (cards.size() == 0)
            return false;
        if (cards.size() == 1)
            return abs(cards[0] - 24) < 1e-6;
        
        for (int i = 0; i < cards.size(); i++) {
            for (int j = 0; j < cards.size(); j++) {
                if (i == j)
                    continue;
                
                vector<double> tempCards;
                for (int k = 0; k < cards.size(); k++)
                    if (k != i && k != j)
                        tempCards.push_back(cards[k]);
                
                // '+','*','-','/'
                for (int k = 0; k < 4; k++) {
                    if (k < 2 && j < i)
                        continue;
                    if (k == 0) tempCards.push_back(cards[i] + cards[j]);
                    else if (k == 1) tempCards.push_back(cards[i] * cards[j]);
                    else if (k == 2) tempCards.push_back(cards[i] - cards[j]);
                    else if (cards[j] == 0) continue;
                    else tempCards.push_back(cards[i] / cards[j]);
                    
                    if (backTracking(tempCards))
                        return true;
                    
                    tempCards.pop_back();
                }
            }
        }
        
        return false;
    }
};