DFS sequence and Euler sequence of the tree

With Euler's formula:

e^jω=cosω+jsinω

Represents the superposition of a cosine signal and a sinusoidal signal, and J indicates that the two signals are orthogonal.

Since e(a+bi)=e a*(cos b+isin b), cos b and sin b cannot be 0 at the same time, so the complex exponent of e cannot be equal to 0, and the negative infinite power of e is equal to 0.

It's Allez-Y, right? It is equal to go go go in English.

Writing velocity in the above form can be said to be Euler's point of view.

Euler's view is the perspective of "waiting for the rabbit", that is, staring at the fixed point in the flow field, and investigating the change law of velocity, temperature, pressure, etc. with time. Therefore, given the coordinates of x,y, that is, the position of a point in a given flow field, and the change of velocity u,v, is examined in the above equation, which is Euler's point of view. The velocity direction at this point is connected with the velocity direction of the adjacent next point, and gradually extends out to form a streamline.

Lagrange's view is the perspective of "catching a thief", that is, staring at a certain particle micro-group, the eyes always follow the marked micro-group, and the trajectory of the micro-mass flow pulls out a line, which is the trace.

When a fixed micromass is taken as the object of analysis and its transport is examined, that is, the governing equation written in the form of the full derivative (with the derivative of the body) of mass, flow, and energy is the equation of the Lagrangian view. With simple variations, the equations of the Lagrangian view can be converted to Euler's equations.

Euler's idea is that since there is no repetition of the unstripped, then the edge that enters the point and the edge that leaves the change point should be equal, that is, the selling edge connected to the change point is an even number, that is, the degree of the point is an even number. The degree of each point in the Seven Bridges problem is odd, so there is no solution to the Seven Bridges problem.

Structural diagram: 37

The main thing is to carry out the torsion operation, that is, when the depth difference between the left and right subtrees is 2, it is judged to be out of balance, and it is necessary to rotate the operation to restore the balance.

A depth-first-search (DFS) algorithm is an algorithm used to traverse or search a tree or graph. Traverse the nodes of the tree along the depth of the tree, searching the branches of the tree as deep as possible.

When the edges of node v have been explored, the search will be traced back to the starting node of the edge where node v was found. This process continues until all nodes that are reachable from the source node have been discovered. If there are still undiscovered nodes, select one of them as the source node and repeat the process until all nodes are accessed.

Depth-first search is a classical algorithm in graph theory, which can generate the corresponding topological sorting table of the target graph, and can easily solve many related graph theory problems, such as the maximum path problem.

A depth-first spanning tree.

The depth-first traversal of a graph is similar to the pre-order traversal of a tree.

So, from this, we can know that the first point of traversal will be the root node of the spanning tree.

The process of traversing a graph is essentially the process of finding its adjacencies for each vertex.

The time it takes depends on the storage results employed.

When representing a graph with an adjacency matrix, the time complexity of finding the adjacency points of each vertex is o(n squared). n is the number of vertices.

However, when the storage structure of the graph is used as an adjacency table, the time complexity of finding the adjacency points is o(e). e is the number of sides in the figure.