|
| 1 | +##1. Depth First Search |
| 2 | + |
| 3 | +::tabs-start |
| 4 | + |
| 5 | +```python |
| 6 | +classSolution: |
| 7 | +defminimumFuelCost(self,roads: list[list[int]],seats:int) ->int: |
| 8 | + adj= defaultdict(list) |
| 9 | +for src, dstin roads: |
| 10 | + adj[src].append(dst) |
| 11 | + adj[dst].append(src) |
| 12 | + |
| 13 | + res=0 |
| 14 | +defdfs(node,parent): |
| 15 | +nonlocal res |
| 16 | + passengers=0 |
| 17 | +for childin adj[node]: |
| 18 | +if child!= parent: |
| 19 | + p= dfs(child, node) |
| 20 | + passengers+= p |
| 21 | + res+= ceil(p/ seats) |
| 22 | +return passengers+1 |
| 23 | + |
| 24 | + dfs(0,-1) |
| 25 | +return res |
| 26 | +``` |
| 27 | + |
| 28 | +```java |
| 29 | +publicclassSolution { |
| 30 | +privateList<Integer>[] adj; |
| 31 | +privatelong res=0; |
| 32 | + |
| 33 | +publiclongminimumFuelCost(int[][]roads,intseats) { |
| 34 | +int n= roads.length+1; |
| 35 | + adj=newArrayList[n]; |
| 36 | + |
| 37 | +for (int i=0; i< n; i++) { |
| 38 | + adj[i]=newArrayList<>(); |
| 39 | + } |
| 40 | + |
| 41 | +for (int[] road: roads) { |
| 42 | + adj[road[0]].add(road[1]); |
| 43 | + adj[road[1]].add(road[0]); |
| 44 | + } |
| 45 | + |
| 46 | + dfs(0,-1, seats); |
| 47 | +return res; |
| 48 | + } |
| 49 | + |
| 50 | +privateintdfs(intnode,intparent,intseats) { |
| 51 | +int passengers=0; |
| 52 | +for (int child: adj[node]) { |
| 53 | +if (child!= parent) { |
| 54 | +int p= dfs(child, node, seats); |
| 55 | + passengers+= p; |
| 56 | + res+=Math.ceil((double) p/ seats); |
| 57 | + } |
| 58 | + } |
| 59 | +return passengers+1; |
| 60 | + } |
| 61 | +} |
| 62 | +``` |
| 63 | + |
| 64 | +```cpp |
| 65 | +classSolution { |
| 66 | +private: |
| 67 | + vector<vector<int>> adj; |
| 68 | + long long res = 0; |
| 69 | + |
| 70 | +public: |
| 71 | + long long minimumFuelCost(vector<vector<int>>& roads, int seats) { |
| 72 | + int n = roads.size() + 1; |
| 73 | + adj.resize(n); |
| 74 | + |
| 75 | + for (auto& road : roads) { |
| 76 | + adj[road[0]].push_back(road[1]); |
| 77 | + adj[road[1]].push_back(road[0]); |
| 78 | + } |
| 79 | + |
| 80 | +dfs(0, -1, seats); |
| 81 | + return res; |
| 82 | + } |
| 83 | + |
| 84 | +private: |
| 85 | + int dfs(int node, int parent, int seats) { |
| 86 | + int passengers = 0; |
| 87 | + for (int child : adj[node]) { |
| 88 | + if (child != parent) { |
| 89 | + int p = dfs(child, node, seats); |
| 90 | + passengers += p; |
| 91 | + res += ceil((double) p / seats); |
| 92 | + } |
| 93 | + } |
| 94 | + return passengers + 1; |
| 95 | + } |
| 96 | +}; |
| 97 | +``` |
| 98 | +
|
| 99 | +```javascript |
| 100 | +class Solution { |
| 101 | + /** |
| 102 | + * @param {number[][]} roads |
| 103 | + * @param {number} seats |
| 104 | + * @return {number} |
| 105 | + */ |
| 106 | + minimumFuelCost(roads, seats) { |
| 107 | + const n = roads.length + 1; |
| 108 | + const adj = Array.from({ length: n }, () => []); |
| 109 | + let res = 0; |
| 110 | +
|
| 111 | + for (const [src, dst] of roads) { |
| 112 | + adj[src].push(dst); |
| 113 | + adj[dst].push(src); |
| 114 | + } |
| 115 | +
|
| 116 | + const dfs = (node, parent) => { |
| 117 | + let passengers = 0; |
| 118 | + for (const child of adj[node]) { |
| 119 | + if (child !== parent) { |
| 120 | + let p = dfs(child, node); |
| 121 | + passengers += p; |
| 122 | + res += Math.ceil(p / seats); |
| 123 | + } |
| 124 | + } |
| 125 | + return passengers + 1; |
| 126 | + }; |
| 127 | +
|
| 128 | + dfs(0, -1); |
| 129 | + return res; |
| 130 | + } |
| 131 | +} |
| 132 | +``` |
| 133 | + |
| 134 | +::tabs-end |
| 135 | + |
| 136 | +###Time & Space Complexity |
| 137 | + |
| 138 | +* Time complexity: $O(n)$ |
| 139 | +* Space complexity: $O(n)$ |
| 140 | + |
| 141 | +--- |
| 142 | + |
| 143 | +##2. Topological Sort (Kahn's Algorithm) |
| 144 | + |
| 145 | +::tabs-start |
| 146 | + |
| 147 | +```python |
| 148 | +classSolution: |
| 149 | +defminimumFuelCost(self,roads: list[list[int]],seats:int) ->int: |
| 150 | + n=len(roads)+1 |
| 151 | + adj= [[]for _inrange(n)] |
| 152 | + indegree= [0]* n |
| 153 | + passengers= [1]* n |
| 154 | + res=0 |
| 155 | + |
| 156 | +for src, dstin roads: |
| 157 | + adj[src].append(dst) |
| 158 | + adj[dst].append(src) |
| 159 | + indegree[src]+=1 |
| 160 | + indegree[dst]+=1 |
| 161 | + |
| 162 | + q= deque() |
| 163 | +for iinrange(1, n): |
| 164 | +if indegree[i]==1: |
| 165 | + q.append(i) |
| 166 | + |
| 167 | +while q: |
| 168 | + node= q.popleft() |
| 169 | + res+= math.ceil(passengers[node]/ seats) |
| 170 | +for parentin adj[node]: |
| 171 | + indegree[parent]-=1 |
| 172 | +if indegree[parent]==1and parent!=0: |
| 173 | + q.append(parent) |
| 174 | + passengers[parent]+= passengers[node] |
| 175 | + |
| 176 | +return res |
| 177 | +``` |
| 178 | + |
| 179 | +```java |
| 180 | +publicclassSolution { |
| 181 | +publiclongminimumFuelCost(int[][]roads,intseats) { |
| 182 | +int n= roads.length+1; |
| 183 | +List<Integer>[] adj=newArrayList[n]; |
| 184 | +int[] indegree=newint[n]; |
| 185 | +int[] passengers=newint[n]; |
| 186 | +Arrays.fill(passengers,1); |
| 187 | +long res=0; |
| 188 | + |
| 189 | +for (int i=0; i< n; i++) adj[i]=newArrayList<>(); |
| 190 | + |
| 191 | +for (int[] road: roads) { |
| 192 | +int src= road[0], dst= road[1]; |
| 193 | + adj[src].add(dst); |
| 194 | + adj[dst].add(src); |
| 195 | + indegree[src]++; |
| 196 | + indegree[dst]++; |
| 197 | + } |
| 198 | + |
| 199 | +Queue<Integer> q=newLinkedList<>(); |
| 200 | +for (int i=1; i< n; i++) { |
| 201 | +if (indegree[i]==1) q.offer(i); |
| 202 | + } |
| 203 | + |
| 204 | +while (!q.isEmpty()) { |
| 205 | +int node= q.poll(); |
| 206 | + res+= (int)Math.ceil((double) passengers[node]/ seats); |
| 207 | +for (int parent: adj[node]) { |
| 208 | +if (--indegree[parent]==1&& parent!=0) q.offer(parent); |
| 209 | + passengers[parent]+= passengers[node]; |
| 210 | + } |
| 211 | + } |
| 212 | + |
| 213 | +return res; |
| 214 | + } |
| 215 | +} |
| 216 | +``` |
| 217 | + |
| 218 | +```cpp |
| 219 | +classSolution { |
| 220 | +public: |
| 221 | + long long minimumFuelCost(vector<vector<int>>& roads, int seats) { |
| 222 | + int n = roads.size() + 1; |
| 223 | + vector<vector<int>> adj(n); |
| 224 | + vector<int> indegree(n, 0), passengers(n, 1); |
| 225 | + long long res = 0; |
| 226 | + |
| 227 | + for (auto& road : roads) { |
| 228 | + int src = road[0], dst = road[1]; |
| 229 | + adj[src].push_back(dst); |
| 230 | + adj[dst].push_back(src); |
| 231 | + indegree[src]++; |
| 232 | + indegree[dst]++; |
| 233 | + } |
| 234 | + |
| 235 | + queue<int> q; |
| 236 | +for (int i =1; i < n; i++) { |
| 237 | + if (indegree[i] == 1) q.push(i); |
| 238 | + } |
| 239 | + |
| 240 | + while (!q.empty()) { |
| 241 | + int node = q.front();q.pop(); |
| 242 | + res += ceil((double) passengers[node] / seats); |
| 243 | + for (int parent : adj[node]) { |
| 244 | + if (--indegree[parent] == 1 && parent != 0) q.push(parent); |
| 245 | + passengers[parent] += passengers[node]; |
| 246 | + } |
| 247 | + } |
| 248 | + |
| 249 | + return res; |
| 250 | +} |
| 251 | +}; |
| 252 | +``` |
| 253 | + |
| 254 | +```javascript |
| 255 | +classSolution { |
| 256 | +/** |
| 257 | + *@param{number[][]}roads |
| 258 | + *@param{number}seats |
| 259 | + *@return{number} |
| 260 | +*/ |
| 261 | +minimumFuelCost(roads,seats) { |
| 262 | +constn=roads.length+1; |
| 263 | +constadj=Array.from({ length: n }, ()=> []); |
| 264 | +constindegree=newArray(n).fill(0); |
| 265 | +constpassengers=newArray(n).fill(1); |
| 266 | +let res=0; |
| 267 | + |
| 268 | +for (const [src,dst]of roads) { |
| 269 | + adj[src].push(dst); |
| 270 | + adj[dst].push(src); |
| 271 | + indegree[src]+=1; |
| 272 | + indegree[dst]+=1; |
| 273 | + } |
| 274 | + |
| 275 | +constq=newQueue(); |
| 276 | +for (let i=1; i< n; i++) { |
| 277 | +if (indegree[i]===1)q.push(i); |
| 278 | + } |
| 279 | + |
| 280 | +while (!q.isEmpty()) { |
| 281 | +constnode=q.pop(); |
| 282 | + res+=Math.ceil(passengers[node]/ seats); |
| 283 | +for (constparentof adj[node]) { |
| 284 | +if (--indegree[parent]===1&& parent!==0)q.push(parent); |
| 285 | + passengers[parent]+= passengers[node]; |
| 286 | + } |
| 287 | + } |
| 288 | + |
| 289 | +return res; |
| 290 | + } |
| 291 | +} |
| 292 | +``` |
| 293 | + |
| 294 | +::tabs-end |
| 295 | + |
| 296 | +###Time & Space Complexity |
| 297 | + |
| 298 | +* Time complexity: $O(n)$ |
| 299 | +* Space complexity: $O(n)$ |