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Formatted question description: https://leetcode.ca/all/1284.html
1284. Minimum Number of Flips to Convert Binary Matrix to Zero Matrix (Hard)
Given a m x n binary matrix mat. In one step, you can choose one cell and flip it and all the four neighbours of it if they exist (Flip is changing 1 to 0 and 0 to 1). A pair of cells are called neighboors if they share one edge.
Return the minimum number of steps required to convert mat to a zero matrix or -1 if you cannot.
Binary matrix is a matrix with all cells equal to 0 or 1 only.
Zero matrix is a matrix with all cells equal to 0.
Example 1:
Input: mat = [[0,0],[0,1]] Output: 3 Explanation: One possible solution is to flip (1, 0) then (0, 1) and finally (1, 1) as shown.
Example 2:
Input: mat = [[0]] Output: 0 Explanation: Given matrix is a zero matrix. We don't need to change it.
Example 3:
Input: mat = [[1,1,1],[1,0,1],[0,0,0]] Output: 6
Example 4:
Input: mat = [[1,0,0],[1,0,0]] Output: -1 Explanation: Given matrix can't be a zero matrix
Constraints:
m == mat.lengthn == mat[0].length1 <= m <= 31 <= n <= 3mat[i][j]is 0 or 1.
Related Topics:
Breadth-first Search
Solution 1. Bit vector + BFS
// OJ: https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/
// Time: O(MN * 2^(MN))
// Space: O(2^(MN))
class Solution {
public:
int minFlips(vector<vector<int>>& A) {
int start = 0, M = A.size(), N = A[0].size(), step = 0, dirs[5] = {1,0,-1,0,1};
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
start |= (A[i][j] << (i * 3 + j));
}
}
queue<int> q;
unordered_set<int> s;
q.push(start);
s.insert(start);
while (q.size()) {
int cnt = q.size();
while (cnt--) {
int state = q.front();
q.pop();
if (state == 0) return step;
for (int i = 0; i < 9; ++i) {
int next = state, r = i / 3, c = i % 3;
next ^= (1 << (r * 3 + c));
for (int j = 0; j < 4; ++j) {
int x = r + dirs[j], y = c + dirs[j + 1];
if (x < 0 || x >= M || y < 0 || y >= N) continue;
next ^= (1 << (x * 3 + y));
}
if (s.count(next) == 0) {
q.push(next);
s.insert(next);
}
}
}
++step;
}
return -1;
}
};
-
class Solution { public int minFlips(int[][] mat) { int rows = mat.length, columns = mat[0].length; int[][] zeroMatrix = new int[rows][columns]; String zeroMatrixStr = matrixToString(zeroMatrix); final int WHITE = 0; final int GRAY = 1; final int BLACK = 2; Map<String, Integer> colorMap = new HashMap<String, Integer>(); Queue<int[][]> queue = new LinkedList<int[][]>(); queue.offer(mat); Queue<Integer> flipsQueue = new LinkedList<Integer>(); flipsQueue.offer(0); String matStr = matrixToString(mat); colorMap.put(matStr, GRAY); while (!queue.isEmpty()) { int[][] curMatrix = queue.poll(); int flip = flipsQueue.poll(); String curStr = matrixToString(curMatrix); if (zeroMatrixStr.equals(curStr)) return flip; for (int i = 0; i < rows; i++) { for (int j = 0; j < columns; j++) { int[][] flipMatrix = flip(curMatrix, i, j); String flipStr = matrixToString(flipMatrix); int color = colorMap.getOrDefault(flipStr, WHITE); if (color == WHITE) { queue.offer(flipMatrix); flipsQueue.offer(flip + 1); colorMap.put(flipStr, GRAY); } } } colorMap.put(curStr, BLACK); } return -1; } public String matrixToString(int[][] mat) { String str = "["; int rows = mat.length; for (int i = 0; i < rows; i++) { int[] row = mat[i]; String rowStr = Arrays.toString(row); if (i > 0) str += ", "; str += rowStr; } str += "]"; return str; } public int[][] flip(int[][] mat, int row, int column) { int rows = mat.length, columns = mat[0].length; int[][] flipMat = new int[rows][columns]; for (int i = 0; i < rows; i++) { for (int j = 0; j < columns; j++) flipMat[i][j] = mat[i][j]; } flipMat[row][column] = 1 - flipMat[row][column]; if (row > 0) flipMat[row - 1][column] = 1 - flipMat[row - 1][column]; if (row < rows - 1) flipMat[row + 1][column] = 1 - flipMat[row + 1][column]; if (column > 0) flipMat[row][column - 1] = 1 - flipMat[row][column - 1]; if (column < columns - 1) flipMat[row][column + 1] = 1 - flipMat[row][column + 1]; return flipMat; } } ############ class Solution { public int minFlips(int[][] mat) { int m = mat.length, n = mat[0].length; int state = 0; for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { if (mat[i][j] == 1) { state |= 1 << (i * n + j); } } } Deque<Integer> q = new ArrayDeque<>(); q.offer(state); Set<Integer> vis = new HashSet<>(); vis.add(state); int ans = 0; int[] dirs = {0, -1, 0, 1, 0, 0}; while (!q.isEmpty()) { for (int t = q.size(); t > 0; --t) { state = q.poll(); if (state == 0) { return ans; } for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { int nxt = state; for (int k = 0; k < 5; ++k) { int x = i + dirs[k], y = j + dirs[k + 1]; if (x < 0 || x >= m || y < 0 || y >= n) { continue; } if ((nxt & (1 << (x * n + y))) != 0) { nxt -= 1 << (x * n + y); } else { nxt |= 1 << (x * n + y); } } if (!vis.contains(nxt)) { vis.add(nxt); q.offer(nxt); } } } } ++ans; } return -1; } } -
// OJ: https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/ // Time: O(MN * 2^(MN)) // Space: O(2^(MN)) class Solution { public: int minFlips(vector<vector<int>>& A) { int M = A.size(), N = A[0].size(), init = 0, step = 0, dirs[4][2] = { {0,1},{0,-1},{1,0},{-1,0} }; for (int i = 0; i < M; ++i) { for (int j = 0; j < N; ++j) init |= A[i][j] << (i * N + j); } queue<int> q{ {init} }; unordered_set<int> seen{init}; auto flip = [&](int &state, int x, int y) { state ^= 1 << (x * N + y); }; while (q.size()) { int cnt = q.size(); while (cnt--) { int u = q.front(); q.pop(); if (u == 0) return step; for (int i = 0; i < M; ++i) { for (int j = 0; j < N; ++j) { int v = u; flip(v, i, j); for (auto &[dx, dy] : dirs) { int a = i + dx, b = j + dy; if (a < 0 || b < 0 || a >= M || b >= N) continue; flip(v, a, b); } if (seen.count(v)) continue; seen.insert(v); q.push(v); } } } ++step; } return -1; } }; -
class Solution: def minFlips(self, mat: List[List[int]]) -> int: m, n = len(mat), len(mat[0]) state = sum(1 << (i * n + j) for i in range(m) for j in range(n) if mat[i][j]) q = deque([state]) vis = {state} ans = 0 dirs = [0, -1, 0, 1, 0, 0] while q: for _ in range(len(q)): state = q.popleft() if state == 0: return ans for i in range(m): for j in range(n): nxt = state for k in range(5): x, y = i + dirs[k], j + dirs[k + 1] if not 0 <= x < m or not 0 <= y < n: continue if nxt & (1 << (x * n + y)): nxt -= 1 << (x * n + y) else: nxt |= 1 << (x * n + y) if nxt not in vis: vis.add(nxt) q.append(nxt) ans += 1 return -1 -
func minFlips(mat [][]int) int { m, n := len(mat), len(mat[0]) state := 0 for i, row := range mat { for j, v := range row { if v == 1 { state |= 1 << (i*n + j) } } } q := []int{state} vis := map[int]bool{state: true} ans := 0 dirs := []int{0, -1, 0, 1, 0, 0} for len(q) > 0 { for t := len(q); t > 0; t-- { state = q[0] if state == 0 { return ans } q = q[1:] for i := 0; i < m; i++ { for j := 0; j < n; j++ { nxt := state for k := 0; k < 5; k++ { x, y := i+dirs[k], j+dirs[k+1] if x < 0 || x >= m || y < 0 || y >= n { continue } if (nxt & (1 << (x*n + y))) != 0 { nxt -= 1 << (x*n + y) } else { nxt |= 1 << (x*n + y) } } if !vis[nxt] { vis[nxt] = true q = append(q, nxt) } } } } ans++ } return -1 }