|
| 1 | +## 1. Brute Force |
| 2 | + |
| 3 | +::tabs-start |
| 4 | + |
| 5 | +```python |
| 6 | +class Solution: |
| 7 | + def leastBricks(self, wall: List[List[int]]) -> int: |
| 8 | + n = len(wall) |
| 9 | + m = 0 |
| 10 | + for brick in wall[0]: |
| 11 | + m += brick |
| 12 | + |
| 13 | + gaps = [[] for _ in range(n)] |
| 14 | + for i in range(n): |
| 15 | + gap = 0 |
| 16 | + for brick in wall[i]: |
| 17 | + gap += brick |
| 18 | + gaps[i].append(gap) |
| 19 | + |
| 20 | + res = n |
| 21 | + for line in range(1, m): |
| 22 | + cuts = 0 |
| 23 | + for i in range(n): |
| 24 | + if line not in gaps[i]: |
| 25 | + cuts += 1 |
| 26 | + |
| 27 | + res = min(res, cuts) |
| 28 | + return res |
| 29 | +``` |
| 30 | + |
| 31 | +```java |
| 32 | +public class Solution { |
| 33 | + public int leastBricks(List<List<Integer>> wall) { |
| 34 | + int n = wall.size(); |
| 35 | + int m = 0; |
| 36 | + for (int brick : wall.get(0)) { |
| 37 | + m += brick; |
| 38 | + } |
| 39 | + |
| 40 | + List<List<Integer>> gaps = new ArrayList<>(); |
| 41 | + for (int i = 0; i < n; i++) { |
| 42 | + gaps.add(new ArrayList<>()); |
| 43 | + int gap = 0; |
| 44 | + for (int brick : wall.get(i)) { |
| 45 | + gap += brick; |
| 46 | + gaps.get(i).add(gap); |
| 47 | + } |
| 48 | + } |
| 49 | + |
| 50 | + int res = n; |
| 51 | + for (int line = 1; line < m; line++) { |
| 52 | + int cuts = 0; |
| 53 | + for (int i = 0; i < n; i++) { |
| 54 | + if (!gaps.get(i).contains(line)) { |
| 55 | + cuts++; |
| 56 | + } |
| 57 | + } |
| 58 | + res = Math.min(res, cuts); |
| 59 | + } |
| 60 | + |
| 61 | + return res; |
| 62 | + } |
| 63 | +} |
| 64 | +``` |
| 65 | + |
| 66 | +```cpp |
| 67 | +class Solution { |
| 68 | +public: |
| 69 | + int leastBricks(vector<vector<int>>& wall) { |
| 70 | + int n = wall.size(); |
| 71 | + int m = 0; |
| 72 | + for (int brick : wall[0]) { |
| 73 | + m += brick; |
| 74 | + } |
| 75 | + |
| 76 | + vector<vector<int>> gaps(n); |
| 77 | + for (int i = 0; i < n; i++) { |
| 78 | + int gap = 0; |
| 79 | + for (int brick : wall[i]) { |
| 80 | + gap += brick; |
| 81 | + gaps[i].push_back(gap); |
| 82 | + } |
| 83 | + } |
| 84 | + |
| 85 | + int res = n; |
| 86 | + for (int line = 1; line < m; line++) { |
| 87 | + int cuts = 0; |
| 88 | + for (int i = 0; i < n; i++) { |
| 89 | + if (find(gaps[i].begin(), gaps[i].end(), line) == gaps[i].end()) { |
| 90 | + cuts++; |
| 91 | + } |
| 92 | + } |
| 93 | + res = min(res, cuts); |
| 94 | + } |
| 95 | + |
| 96 | + return res; |
| 97 | + } |
| 98 | +}; |
| 99 | +``` |
| 100 | + |
| 101 | +```javascript |
| 102 | +class Solution { |
| 103 | + /** |
| 104 | + * @param {number[][]} wall |
| 105 | + * @return {number} |
| 106 | + */ |
| 107 | + leastBricks(wall) { |
| 108 | + const n = wall.length; |
| 109 | + let m = 0; |
| 110 | + for (const brick of wall[0]) { |
| 111 | + m += brick; |
| 112 | + } |
| 113 | + |
| 114 | + const gaps = Array.from({ length: n }, () => []); |
| 115 | + for (let i = 0; i < n; i++) { |
| 116 | + let gap = 0; |
| 117 | + for (const brick of wall[i]) { |
| 118 | + gap += brick; |
| 119 | + gaps[i].push(gap); |
| 120 | + } |
| 121 | + } |
| 122 | + |
| 123 | + let res = n; |
| 124 | + for (let line = 1; line < m; line++) { |
| 125 | + let cuts = 0; |
| 126 | + for (let i = 0; i < n; i++) { |
| 127 | + if (!gaps[i].includes(line)) { |
| 128 | + cuts++; |
| 129 | + } |
| 130 | + } |
| 131 | + res = Math.min(res, cuts); |
| 132 | + } |
| 133 | + |
| 134 | + return res; |
| 135 | + } |
| 136 | +} |
| 137 | +``` |
| 138 | + |
| 139 | +::tabs-end |
| 140 | + |
| 141 | +### Time & Space Complexity |
| 142 | + |
| 143 | +* Time complexity: $O(m * n * g)$ |
| 144 | +* Space complexity: $O(n * g)$ |
| 145 | + |
| 146 | +> Where $m$ is the sum of widths of the bricks in the first row, $n$ is the number of rows and $g$ is the average number of gaps in each row. |
| 147 | +
|
| 148 | +--- |
| 149 | + |
| 150 | +## 2. Hash Map |
| 151 | + |
| 152 | +::tabs-start |
| 153 | + |
| 154 | +```python |
| 155 | +class Solution: |
| 156 | + def leastBricks(self, wall: List[List[int]]) -> int: |
| 157 | + countGap = {0: 0} |
| 158 | + |
| 159 | + for r in wall: |
| 160 | + total = 0 |
| 161 | + for i in range(len(r) - 1): |
| 162 | + total += r[i] |
| 163 | + countGap[total] = 1 + countGap.get(total, 0) |
| 164 | + |
| 165 | + return len(wall) - max(countGap.values()) |
| 166 | +``` |
| 167 | + |
| 168 | +```java |
| 169 | +public class Solution { |
| 170 | + public int leastBricks(List<List<Integer>> wall) { |
| 171 | + HashMap<Integer, Integer> countGap = new HashMap<>(); |
| 172 | + countGap.put(0, 0); |
| 173 | + |
| 174 | + for (List<Integer> row : wall) { |
| 175 | + int total = 0; |
| 176 | + for (int i = 0; i < row.size() - 1; i++) { |
| 177 | + total += row.get(i); |
| 178 | + countGap.put(total, countGap.getOrDefault(total, 0) + 1); |
| 179 | + } |
| 180 | + } |
| 181 | + |
| 182 | + int maxGaps = 0; |
| 183 | + for (int count : countGap.values()) { |
| 184 | + maxGaps = Math.max(maxGaps, count); |
| 185 | + } |
| 186 | + |
| 187 | + return wall.size() - maxGaps; |
| 188 | + } |
| 189 | +} |
| 190 | +``` |
| 191 | + |
| 192 | +```cpp |
| 193 | +class Solution { |
| 194 | +public: |
| 195 | + int leastBricks(vector<vector<int>>& wall) { |
| 196 | + unordered_map<int, int> countGap; |
| 197 | + countGap[0] = 0; |
| 198 | + |
| 199 | + for (const auto& row : wall) { |
| 200 | + int total = 0; |
| 201 | + for (size_t i = 0; i < row.size() - 1; ++i) { |
| 202 | + total += row[i]; |
| 203 | + countGap[total]++; |
| 204 | + } |
| 205 | + } |
| 206 | + |
| 207 | + int maxGaps = 0; |
| 208 | + for (const auto& [key, value] : countGap) { |
| 209 | + maxGaps = max(maxGaps, value); |
| 210 | + } |
| 211 | + |
| 212 | + return wall.size() - maxGaps; |
| 213 | + } |
| 214 | +}; |
| 215 | +``` |
| 216 | + |
| 217 | +```javascript |
| 218 | +class Solution { |
| 219 | + /** |
| 220 | + * @param {number[][]} wall |
| 221 | + * @return {number} |
| 222 | + */ |
| 223 | + leastBricks(wall) { |
| 224 | + const countGap = new Map(); |
| 225 | + countGap.set(0, 0); |
| 226 | + for (const row of wall) { |
| 227 | + let total = 0; |
| 228 | + for (let i = 0; i < row.length - 1; i++) { |
| 229 | + total += row[i]; |
| 230 | + countGap.set(total, (countGap.get(total) || 0) + 1); |
| 231 | + } |
| 232 | + } |
| 233 | + return wall.length - Math.max(...countGap.values()); |
| 234 | + } |
| 235 | +} |
| 236 | +``` |
| 237 | + |
| 238 | +::tabs-end |
| 239 | + |
| 240 | +### Time & Space Complexity |
| 241 | + |
| 242 | +* Time complexity: $O(N)$ |
| 243 | +* Space complexity: $O(g)$ |
| 244 | + |
| 245 | +> Where $N$ is the total number of bricks in the wall and $g$ is the total number of gaps in all the rows. |
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