LeetCode 957: Prison Cells After N Days Solution

Master LeetCode problem 957 (Prison Cells After N Days), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

957. Prison Cells After N Days

Medium

Array Hash Table Math Bit Manipulation

Problem Explanation

Explanation

To solve this problem, we need to simulate the state changes of the prison cells for n days according to the given rules. We can optimize this process by observing that the state of the prison cells will start repeating after a certain number of days, which can help us avoid unnecessary iterations.

We can store the state of the prison cells after each day in a hashmap or a set.
If we encounter a state that we have seen before, it means we have reached a cycle and we can calculate the remaining days using modulo arithmetic.
After finding the cycle length, we can directly calculate the state of the prison cells after n days.

Time Complexity: O(2^N) - In the worst case, we might need to iterate through all possible states before finding a cycle, where N is the number of cells.

Space Complexity: O(2^N) - In the worst case, we might need to store all possible states before finding a cycle.

Solution Code

class Solution {
    public int[] prisonAfterNDays(int[] cells, int n) {
        Map<String, Integer> seen = new HashMap<>();
        boolean hasCycle = false;
        
        for (int i = 0; i < n; i++) {
            int[] next = new int[8];
            String cellStr = Arrays.toString(cells);
            if (seen.containsKey(cellStr)) {
                int cycleLength = i - seen.get(cellStr);
                int remainingDays = (n - i) % cycleLength;
                return prisonAfterNDays(cells, remainingDays);
            } else {
                seen.put(cellStr, i);
                for (int j = 1; j < 7; j++) {
                    next[j] = cells[j - 1] == cells[j + 1] ? 1 : 0;
                }
                cells = next;
            }
        }
        
        return cells;
    }
}

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