Recursive Algorithm Learning Series 1 (divide and conquer strategy)

1. Divide and conquer

Instead, we use recursion to solve the problem.AlgorithmThe main technique is to divide a large and complex problem into multiple subproblems. These subproblems can be used as termination conditions or solved in a recursive step, the combination of solutions to all sub-problems constitutes a solution to the original problem.

2. Advantages and Disadvantages of divide and conquer

The divide-and-conquer algorithm usually involves calling one or more recursive methods. When these calls separate data into independent sets to process smaller sets, the divide-and-conquer policy will be very efficient, when data is decomposed, the divide-and-conquer policy may produce a large number of repeated computations, resulting in performance reduction.

3. Draw a rulerProgramAnalysis

A ruler is a simple application of a divide-and-conquer strategy. A ruler is a sequence composed of 1 inch units. Each unit has the longest mark at its end, the mark at 1/2 inch of each inch unit is shorter than the end, the mark at 1/4 is shorter than 1/2, and the mark at 1/8 is shorter than 1/4. Write a program, in an online line, you can use the rule interval to draw a tag, with a specific size mark at a specific position.

Analysis: in a straight line, we can first split this line into two parts, and then split the two parts. Until the accuracy requirements are met. For example, taking the minimum scale as 1/8 inch as an example, drawruler serves as the regression function for the draw scale, and uses the two ends of a line segment (startpos) in the drawruler function ), endpoint (endpos), and variable H are used as parameters. The base height of the tag is baseheight,

The height of the mark should be H * baseheight, and the method of the ruler can be analyzed as follows:

The midpoint of the calculation interval (0.0, 1.0): midpos = (startpost + endpos)/2; draw a mark at the midpoint 1/2, and the height is 3 * baseheight

Separate the midpoint by two straight lines, and then use the nth function drawrule, corresponding start point, end point (0.0, 0.5) and (0.5, 1.0), parameter h-1, in this way, the height can be shorter.

Step 2 (H = 2)

Midpos = (0.0 + 0.5)/2 (1/4), with a height of 2 * baseheight

The height of midpos = (0.5 + 1.0)/2 (3/4) is 2 * baseheight.

Step 1 (H = 1)

Mark at 1/8 and 7/8 respectively. Calculation Method

The height of midpos = (0.0 + 0.25)/2 (1/8) is baseheight.

The height of midpos = (0.75 + 1)/2 (7/8) is baseheight.

As shown in the following figure:

We can regard the mark produced by continuous regression as a node of a binary tree. Root H is the initial value. It is the mark at 1/2, and each parent mark generates two child marks. As shown in

 

4. executable program file

Using system;
Using system. Collections. Generic;
Using system. componentmodel;
Using system. Data;
Using system. drawing;
Using system. text;
Using system. Windows. forms;

Namespace drawr.pdf
{
Public partial class form1: Form
{
Public form1 ()
{
Initializecomponent ();
}

Private void form1_load (Object sender, eventargs E)
{
}

Void drawruler (float startpos, float endpos, int H)
{
Float baseheight = 4;
If (h> 0)
{
Float midpos = (startpos + endpos)/2;
Float Height = H * baseheight;
Drawmark (midpos, height );
Drawruler (startpos, midpos, h-1 );
Drawruler (midpos, endpos, h-1 );
}
}

Void drawmark (float POs, float height)
{
Using (Graphics G = This. creategraphics ())
{
Float xoffset = 100 + Pos;
Float yoffset = 100-height;
Solidbrush brusuh = new solidbrush (color. Black );
Pen P = new pen (brusuh, 1 );
G. drawline (p, xoffset, yoffset, xoffset, 100 );
}
}
Private void form1_paint (Object sender, painteventargs E)
{
# Region draw a straight line first
Using (Graphics G = E. Graphics)
{
Float xoffset = 100;
Float yoffset = 100;
Int Len = 300;
Solidbrush brusuh = new solidbrush (color. Black );
Pen P = new pen (brusuh, 2 );
G. drawline (p, xoffset, yoffset, xoffset + Len, yoffset );
}
# Endregion

Drawruler (0,300, 3 );
}
}
}

/Files/jillzhang/drawruler.rar

5. Learning Summary

This series is a learning series of algorithms. All the content is from textbooks and is not original. Only programs are implemented for individuals. For more details, refer to the data structure C ++ description.

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A person is old and cannot use his head. He occasionally uses algorithms to train his mind to prevent premature aging. Haha
jillzhang jillzhang@126.com