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672. Bulb Switcher II

Description

There is a room with n bulbs labeled from 1 to n that all are turned on initially, and four buttons on the wall. Each of the four buttons has a different functionality where:

  • Button 1: Flips the status of all the bulbs.
  • Button 2: Flips the status of all the bulbs with even labels (i.e., 2, 4, ...).
  • Button 3: Flips the status of all the bulbs with odd labels (i.e., 1, 3, ...).
  • Button 4: Flips the status of all the bulbs with a label j = 3k + 1 where k = 0, 1, 2, ... (i.e., 1, 4, 7, 10, ...).

You must make exactly presses button presses in total. For each press, you may pick any of the four buttons to press.

Given the two integers n and presses, return the number of different possible statuses after performing all presses button presses.

 

Example 1:

Input: n = 1, presses = 1
Output: 2
Explanation: Status can be:
- [off] by pressing button 1
- [on] by pressing button 2

Example 2:

Input: n = 2, presses = 1
Output: 3
Explanation: Status can be:
- [off, off] by pressing button 1
- [on, off] by pressing button 2
- [off, on] by pressing button 3

Example 3:

Input: n = 3, presses = 1
Output: 4
Explanation: Status can be:
- [off, off, off] by pressing button 1
- [off, on, off] by pressing button 2
- [on, off, on] by pressing button 3
- [off, on, on] by pressing button 4

 

Constraints:

  • 1 <= n <= 1000
  • 0 <= presses <= 1000

Solutions

Solution 1

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class Solution:
    def flipLights(self, n: int, presses: int) -> int:
        ops = (0b111111, 0b010101, 0b101010, 0b100100)
        n = min(n, 6)
        vis = set()
        for mask in range(1 << 4):
            cnt = mask.bit_count()
            if cnt <= presses and cnt % 2 == presses % 2:
                t = 0
                for i, op in enumerate(ops):
                    if (mask >> i) & 1:
                        t ^= op
                t &= (1 << 6) - 1
                t >>= 6 - n
                vis.add(t)
        return len(vis)

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class Solution {
    public int flipLights(int n, int presses) {
        int[] ops = new int[] {0b111111, 0b010101, 0b101010, 0b100100};
        Set<Integer> vis = new HashSet<>();
        n = Math.min(n, 6);
        for (int mask = 0; mask < 1 << 4; ++mask) {
            int cnt = Integer.bitCount(mask);
            if (cnt <= presses && cnt % 2 == presses % 2) {
                int t = 0;
                for (int i = 0; i < 4; ++i) {
                    if (((mask >> i) & 1) == 1) {
                        t ^= ops[i];
                    }
                }
                t &= ((1 << 6) - 1);
                t >>= (6 - n);
                vis.add(t);
            }
        }
        return vis.size();
    }
}

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class Solution {
public:
    int flipLights(int n, int presses) {
        n = min(n, 6);
        vector<int> ops = {0b111111, 0b010101, 0b101010, 0b100100};
        unordered_set<int> vis;
        for (int mask = 0; mask < 1 << 4; ++mask) {
            int cnt = __builtin_popcount(mask);
            if (cnt > presses || cnt % 2 != presses % 2) continue;
            int t = 0;
            for (int i = 0; i < 4; ++i) {
                if (mask >> i & 1) {
                    t ^= ops[i];
                }
            }
            t &= (1 << 6) - 1;
            t >>= (6 - n);
            vis.insert(t);
        }
        return vis.size();
    }
};

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func flipLights(n int, presses int) int {
    if n > 6 {
        n = 6
    }
    ops := []int{0b111111, 0b010101, 0b101010, 0b100100}
    vis := map[int]bool{}
    for mask := 0; mask < 1<<4; mask++ {
        cnt := bits.OnesCount(uint(mask))
        if cnt <= presses && cnt%2 == presses%2 {
            t := 0
            for i, op := range ops {
                if mask>>i&1 == 1 {
                    t ^= op
                }
            }
            t &= 1<<6 - 1
            t >>= (6 - n)
            vis[t] = true
        }
    }
    return len(vis)
}

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