数据结构-图-总结
Is Graph Bipartite?
Description
Given an undirected graph, return true if and only if it is bipartite.
Recall that a graph is bipartite if we can split it's set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node in B.
The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists. Each node is an integer between 0 and graph.length - 1. There are no self edges or parallel edges: graph[i] does not contain i, and it doesn't contain any element twice.
graphwill have length in range[1, 100].graph[i]will contain integers in range[0, graph.length - 1].graph[i]will not containior duplicate values.- The graph is undirected: if any element
jis ingraph[i], theniwill be ingraph[j].
Have you met this question in a real interview? Yes
Example
Example 1:
Input: [[1,3], [0,2], [1,3], [0,2]]
Output: true
Explanation:
The graph looks like this:
0----1
| |
| |
3----2
We can divide the vertices into two groups: {0, 2} and {1, 3}.
Example 2:
Input: [[1,2,3], [0,2], [0,1,3], [0,2]]
Output: false
Explanation:
The graph looks like this:
0----1
| \ |
| \ |
3----2
We cannot find a way to divide the set of nodes into two independent subsets.解法1：广度优先
class Solution {
public:
/**
* @param graph: the given undirected graph
* @return: return true if and only if it is bipartite
*/
bool isBipartite(vector> &graph) {
// Write your code here
int n = graph.size();
vector visit(n, 0);
queue qu;
int levelcount = 0;
for (int i = 0; i < n; i++) {
if (visit[i] != 0) {
continue;
}
qu.push(i);
visit[i] = 1;
levelcount = 1;
while (!qu.empty()) {
int nextlevelcount = 0;
while (levelcount > 0) {
int m = qu.front();
qu.pop();
levelcount--;
for (int j = 0; j < graph[m].size(); j++) {
if (visit[graph[m][j]] != 0) {
if (visit[graph[m][j]] == visit[m]) {
return false;
} else {
continue;
}
} else {
visit[graph[m][j]] = 0 - visit[m];
qu.push(graph[m][j]);
nextlevelcount++;
}
}
}
levelcount = nextlevelcount;
}
}
return true;
}
}; 2. 深度优先
特别学习别人的代码，简洁
class Solution {
public:
/**
* @param graph: the given undirected graph
* @return: return true if and only if it is bipartite
*/
bool isBipartite(vector> &graph) {
// Write your code here
int m = graph.size();
if (m == 0) {
return true;
}
vector visit(m, 0);
// not connected tree
for (int i = 0; i < m; i++) {
if (visit[i] == 0) {
visit[i] = 1;
if (DFS(graph, i, 1, visit) == false) {
return false;
}
}
}
return true;
}
bool DFS(vector> &graph, int lastnode, int lastcolor,
vector &visit) {
for (int i = 0; i < graph[lastnode].size(); i++) {
if (visit[graph[lastnode][i]] != 0) {
if (visit[graph[lastnode][i]] != 0 - lastcolor) {
return false;
} else {
continue;
}
} else {
visit[graph[lastnode][i]] = 0 - lastcolor;
if(DFS(graph, graph[lastnode][i], 0 - lastcolor, visit) == false) {
return false;
}
}
}
return true;
}
/*
bool isBipartite(vector>& graph) {
vector colors(graph.size());
for (int i = 0; i < graph.size(); ++i) {
if (colors[i] == 0 && !valid(graph, 1, i, colors)) {
return false;
}
}
return true;
}
bool valid(vector>& graph, int color, int cur, vector& colors) {
if (colors[cur] != 0) return colors[cur] == color;
colors[cur] = color;
for (int i : graph[cur]) {
if (!valid(graph, -1 * color, i, colors)) {
return false;
}
}
return true;
}
*/
};
Topological Sorting
Description
Given an directed graph, a topological order of the graph nodes is defined as follow:
- For each directed edge
A -> Bin graph, A must before B in the order list. - The first node in the order can be any node in the graph with no nodes direct to it.
Find any topological order for the given graph.
You can assume that there is at least one topological order in the graph.
Have you met this question in a real interview?
/**
* Definition for Directed graph.
* struct DirectedGraphNode {
* int label;
* vector neighbors;
* DirectedGraphNode(int x) : label(x) {};
* };
*/
class Solution {
public:
/*
* @param graph: A list of Directed graph node
* @return: Any topological order for the given graph.
*/
vector topSort(vector& graph) {
// write your code here
vector res;
//if (hascycle(graph)) {
// return res;
//}
unordered_set visit;
stack reverseres;
for (int i = 0; i < graph.size(); i++) {
if (visit.find(graph[i]) == visit.end()) {
DFS(graph[i], visit, reverseres);
}
}
while (!reverseres.empty()) {
res.push_back(reverseres.top());
reverseres.pop();
}
return res;
}
vector BFS(vector& graph) {
vector res;
int n = graph.size();
if (n == 0) {
return res;
}
unordered_map status;
for (int i = 0; i < n; i++) {
status[graph[i]] = 0;
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < graph[i]->neighbors.size(); j++) {
status[graph[i]->neighbors[j]]++;
}
}
// find first null input nodes
queue qu;
for (int i = 0; i < n; i++) {
if (status[graph[i]] == 0) {
qu.push(graph[i]);
}
}
while(!qu.empty()) {
DirectedGraphNode* tmp = qu.front();
qu.pop();
res.push_back(tmp);
for (int j = 0; j < tmp->neighbors.size(); j++) {
status[tmp->neighbors[j]]--;
if (status[tmp->neighbors[j]] == 0) {
qu.push(tmp->neighbors[j]);
}
}
}
return res;
}
vector BFS2(vector& graph) {
vector res;
int n = graph.size();
if (n == 0) {
return res;
}
unordered_map status;
for (int i = 0; i < n; i++) {
status[graph[i]] = 0;
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < graph[i]->neighbors.size(); j++) {
status[graph[i]->neighbors[j]]++;
}
}
stack st;
for (int i = 0; i < n; i++) {
if (status[graph[i]] == 0) {
st.push(graph[i]);
}
}
while (!st.empty()) {
DirectedGraphNode* node = st.top();
st.pop();
res.push_back(node);
for (int j = 0; j < node->neighbors.size(); j++) {
status[node->neighbors[j]]--;
if (status[node->neighbors[j]] == 0) {
st.push(node->neighbors[j]);
}
}
}
return res;
}
void DFS(DirectedGraphNode* node, unordered_set& visit,
stack& reverseres) {
visit.insert(node);
for (int j = 0; j < node->neighbors.size(); j++) {
if (visit.find(node->neighbors[j]) == visit.end()) {
DFS(node->neighbors[j], visit, reverseres);
}
}
reverseres.push(node);
}
bool hascycle(vector& graph) {
unordered_set topset;
for (int i = 0; i < graph.size(); i++) {
if (topset.find(graph[i]) != topset.end()) {
continue;
}
unordered_set localset;
stack st;
st.push(graph[i]);
while (!st.empty()) {
DirectedGraphNode* node = st.top();
st.pop();
localset.insert(node);
topset.insert(node);
for (int j = 0; j < node->neighbors.size(); j++) {
if (localset.find(node->neighbors[j]) != localset.end()) {
return true;
}
st.push(node->neighbors[j]);
}
}
}
return false;
}
};
Shortest Path in Undirected Graph
Description
Give an undirected graph, in which each edge's length is 1, and give two nodes from the graph. We need to find the length of the shortest path between the given two nodes.
Have you met this question in a real interview? Yes
Example
Given graph = {1,2,4#2,1,4#3,5#4,1,2#5,3}, and nodeA = 3, nodeB = 5.
1------2 3
\ | |
\ | |
\ | |
\ | |
4 5
return 1.
/**
* Definition for Undirected graph.
* struct UndirectedGraphNode {
* int label;
* vector neighbors;
* UndirectedGraphNode(int x) : label(x) {};
* };
*/
class Solution {
public:
/**
* @param graph: a list of Undirected graph node
* @param A: nodeA
* @param B: nodeB
* @return: the length of the shortest path
*/
int shortestPath(vector graph, UndirectedGraphNode* A, UndirectedGraphNode* B) {
// Write your code here
return specialSolution(graph, A, B);
}
int specialSolution(vector graph, UndirectedGraphNode* A, UndirectedGraphNode* B) {
int n = graph.size();
if (n == 0) {
return 0;
}
unordered_map visit;
queue qu;
// init visit
for (int i = 0; i < n; i++) {
visit[graph[i]] = false;
}
// visit source
qu.push(A);
visit[A] = true;
int level = -1;
int levelcount = 1;
// visit other nodes
while (!qu.empty()) {
level++;
int newlevelcount = 0;
while (levelcount > 0) {
UndirectedGraphNode* node = qu.front();
qu.pop();
if (node == B) {
return level;
}
int m = node->neighbors.size();
for (int i = 0; i < m; i++) {
if (visit[node->neighbors[i]] == true) {
continue;
}
qu.push(node->neighbors[i]);
newlevelcount++;
}
levelcount--;
}
levelcount = newlevelcount;
}
return 0;
}
int generalSolution(vector graph, UndirectedGraphNode* A, UndirectedGraphNode* B) {
int n = graph.size();
if (n == 0) {
return 0;
}
unordered_map dist;
unordered_map visit;
int visitcount = 0;
// init dist, visit
for (int i = 0; i < n; i++) {
dist[graph[i]] = INT_MAX;
visit[graph[i]] = false;
}
// visit source node
dist[A] = 0;
visit[A] = true;
visitcount = 1;
int m = A->neighbors.size();
for (int i = 0; i < m; i++) {
if (visit[A->neighbors[i]] == true) {
continue;
}
dist[A->neighbors[i]] = 1;
}
// visit other nodes
while (visitcount <= n) {
// find min path
UndirectedGraphNode * minnode = NULL;
int minpath = INT_MAX;
for (int i = 0; i < n; i++) {
if (visit[graph[i]] == true) {
continue;
}
if (dist[graph[i]] < minpath) {
minpath = dist[graph[i]];
minnode = graph[i];
}
}
if (minnode == NULL) {
break;
} else {
int s = minnode->neighbors.size();
for (int i = 0; i < s; i++) {
if (visit[minnode->neighbors[i]] == true) {
continue;
}
if (dist[minnode] + 1 < dist[minnode->neighbors[i]]) {
dist[minnode->neighbors[i]] = dist[minnode] + 1;
}
}
visit[minnode] = true;
visitcount++;
}
}
return (dist[B] == INT_MAX ? 0 : dist[B]);
}
};
Clone Graph
Description
Clone an undirected graph. Each node in the graph contains a label and a list of its neighbors.
How we serialize an undirected graph:
Nodes are labeled uniquely.
We use # as a separator for each node, and , as a separator for node label and each neighbor of the node.
As an example, consider the serialized graph {0,1,2#1,2#2,2}.
The graph has a total of three nodes, and therefore contains three parts as separated by #.
- First node is labeled as
0. Connect node0to both nodes1and2. - Second node is labeled as
1. Connect node1to node2. - Third node is labeled as
2. Connect node2to node2(itself), thus forming a self-cycle.
Visually, the graph looks like the following:
1
/ \
/ \
0 --- 2
/ \
\_/Have you met this question in a real interview? Yes
Example
return a deep copied graph.
/**
* Definition for undirected graph.
* struct UndirectedGraphNode {
* int label;
* vector neighbors;
* UndirectedGraphNode(int x) : label(x) {};
* };
*/
class Solution {
public:
/*
* @param node: A undirected graph node
* @return: A undirected graph node
*/
UndirectedGraphNode* cloneGraph(UndirectedGraphNode* node) {
// write your code here
if (node == NULL) {
return NULL;
}
unordered_map status;
queue qu;
// create new nodes pairs
qu.push(node);
while (!qu.empty()) {
UndirectedGraphNode* tmp = qu.front();
qu.pop();
UndirectedGraphNode* newnode = new UndirectedGraphNode(tmp->label);
status[tmp] = newnode;
for (int i = 0; i < tmp->neighbors.size(); i++) {
if (status.find(tmp->neighbors[i]) == status.end()) {
qu.push(tmp->neighbors[i]);
}
}
}
// build graph
unordered_map::iterator it;
for (it = status.begin(); it != status.end(); it++) {
UndirectedGraphNode* tmp = it->first;
for (int i = 0; i < tmp->neighbors.size(); i++) {
status[tmp]->neighbors.push_back(status[tmp->neighbors[i]]);
}
}
return status[node];
}
};