图算法
1.关于拓扑序( 207. Course Schedule)
a.题意
There are a total of n courses you have to take, labeled from 0 to n - 1.
Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]
Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?
For example:
2, [[1,0]]
There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.2, [[1,0],[0,1]]
There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.
大概的题意就是,有0到n-1的课程然后要判断是否存在一个拓扑序,存在返回true,不存在返回false
b.思路分析
这是道拓扑序的题目,我们可以用这样一个算法,每次从图中去掉入度为0的点然后重复这一过程,直到移除所有点,如果中途发现不存在入度为0的点则说明存在回边那么没有拓扑序。
c.代码实现
我们用一个二维数组来存这个图,然后用inDegree数组表示图中每个点的入度,把入度为0的点依次放入队列,每次去掉队列头的点直至队列为空,判断最后一共删除多少点,和原先的点数作比较就可以知道是否有拓扑序了
class Solution {
public:
bool canFinish(int numCourses, vector< pair<int, int> >& prerequisites) {
bool myGraph[numCourses][numCourses];
int inDegree[numCourses];
memset(inDegree,0,sizeof(inDegree));
memset(myGraph,0,(numCourses) * numCourses);
for (int i = 0;i < prerequisites.size();i++)
{
myGraph[prerequisites[i].second][prerequisites[i].first] = true;
inDegree[prerequisites[i].first]++;
}
std::queue<int> toDelete;
for (int i = 0;i < numCourses;i++)
{
if (inDegree[i] == 0)
{
toDelete.push(i);
}
}
if (toDelete.empty())
{
return false;
}
int count = toDelete.size();
while (!toDelete.empty())
{
int top = toDelete.front();
toDelete.pop();
for (int i = 0;i < numCourses;i++)
{
if (myGraph[top][i])
{
inDegree[i]--;
if (inDegree[i] == 0)
{
toDelete.push(i);
count++;
}
}
}
}
return (count == numCourses);
}
};
2.关于点与点之间的距离( 399. Evaluate Division)
a.题意
Equations are given in the format A / B = k, where A and B are variables represented as strings, and k is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return -1.0.
Example:
Given a / b = 2.0, b / c = 3.0.
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .
return [6.0, 0.5, -1.0, 1.0, -1.0 ].The input is: vector
b.思路分析
可以把这个问题看成图的距离问题,把字符当成点,把字符间的倍数关系当成一个点到另一个点之间的距离,例如a/b=2,就是a到b距离为2,b到a距离为0.5,这样就是求两个点之间距离问题了,我们用一个map来存图,然后使用深度优先算法来求距离即可
c.代码实现
首先我用map来存这个图,map的键是一个点a,值是一个map,这个map的键值分别是a能到达的点以及对应边的长度
unordered_map
class Solution {
public:
vector<double> calcEquation(vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries) {
unordered_map<string,unordered_map<string,double>> myMap;
for (int i = 0;i < values.size();i++)
{
myMap[equations[i].first].insert(make_pair(equations[i].second,values[i]));
if(values[i] != 0)
myMap[equations[i].second].insert(make_pair(equations[i].first,1 / values[i]));
}
std::vector<double> ans;
for (auto i : queries)
{
std::set<string> visited;
double temp = DFS(i.first,i.second,myMap,visited);
ans.push_back(temp);
}
return ans;
}
double DFS(string start,string end,unordered_map<string,unordered_map<string,double>> &myMap,set<string> &visited)
{
if (myMap[start].find(end) != myMap[start].end())
{
return myMap[start][end];
}
visited.insert(start);
for (auto i : myMap[start])
{
if (visited.find(i.first) == visited.end())
{
visited.insert(i.first);
double temp = DFS(i.first,end,myMap,visited);
if (temp != (-1.0))
{
return i.second * temp;
}
}
}
return -1.0;
}
};