Question

672. Bulb Switcher II

中文文档

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

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)

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();
  }
}

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();
  }
};

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)
}