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Phn I. GII THIU TNG QUANI. M T BI TON, MC TIU CN T C

1.1.1. M t bi ton Tng quan v bi ton:

t 8 qun hu trn bn c vua 8

8 sao cho khng c qun hu no c thtn cng c qun hu khc (theo lut chi c vua), ngha l phi t cc qun husao cho khng c hng, ct hoc ng cho no trn bn c c hn 1 qun hu. (Ccqun hu ny khng phn bit mu sc, ta ch quan tm n quyn ca qun hukhi t chng trn bn c). Chng hn, mt cch t qun hu ng nh sau :

0 1 2 3 4 5 6 7

0 Q

1 Q

2 Q

3 Q

4 Q

5 Q

6 Q

7 Q

Hnh 1.1.1 Hng xy dng chng trnh trong ti:

Ta xy dng chng trnh cho php ngi dng chn v tr cho qun hu hng u tin ca bn c, cc qun hu cn li s do chng trnh tnh ton v tm rav tr thch hp cho chng ri in ra mn hnh.

1.1.2. Mc tiu cn t cPhi hin th giao din bn c vua 8 x 8 trn mn hnh cng vi cc mc la

chn km theo.Phi cho php ngi dng chn v tr cho qun hu hng u tin.Phi t by qun hu cn li ln bn c sao cho khng c qun hu no c th

tn cng cc qun hu khc (theo lut chi c vua).Phi m bo thi gian thc thi chng trnh nhanh.Phi c giao din d s dng.

II. HNG GII QUYT V K HOCH THC HIN1.2.1. Hng gii quyt

Trc tin ta qui c rng: bn c 8 x 8 s c ch s hng v ct c nh st 0 n 7. Hnh minh ha:

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0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

Hnh 1.2.1Ta cn t cc qun hu ln lt ln bn c vua 8 x 8 theo ng yu cu bi

ton. V vy, trc khi thc hin iu ny, ta cn xy dng mt hong cung cho ccqun hu ny trc khi cho chng xut trn. Hong cung ny chnh l mng mt

chiu c 8 phn t, ta gi tn mng mt chiu ny l arr[8]. Mng arr[8] c ch s t 0n 7. ngha ca mng arr[8] trong bi ton: ch s ca mng chnh l hng trn

bn c, gi tr ca mng chnh l ct trn bn c. V d: arr[i]=j th i l hng th i, j lct th j.

cc qun hu c th xut trn an ton, ngha l khng b qun hu khctn cng ta cn xy dng chin thut cho chng. Chin thut ny c hiu n ginnh sau: tm v tr m ti ct v hai ng cho u khng c qun hu no chiuti th s nhanh chn nhy vo v tr . Ln lt nh th cho n qun hu cui cng.Ring qun hu hng u tin ta khng cn xc nh v tr cho n v y, ta s xy

dng chng trnh cho php ngi dng chn v tr cho qun hu hng u tin.Vic xy dng hong cung v cc chin thut c thc hin bng ngnng Microsoft Visual C# 2005 (bn Express).

1.2.2. K hach thc hinK hoch thc hin qua cc bc sau:

- Bc 1: Tm hiu bi ton v xc nh cc yu cu.- Bc 2: Phn tch cc yu cu ca bi ton tht k v xc nh hng gii

quyt bi ton.- Bc 3: Quyt nh c xy dng cc cu trc d liu cn thit cho bi ton

hay khng? Nu cn ta cn xy dng sn dng sau ny.

- Bc 4: Xy dng lu (ngn ng gi) cho bi ton.- Bc 5:Phc tho giao din ha ca chng trnh, xy dng giao din

ha th hin hnh nh ca bn c v cc chc nng ca chng trnh.- Bc 5: Bt tay vo vit chng trnh tht s v debug cc li pht sinh.- Bc 6: Tng hp li v vit bo co.

Phn II. C S L THUYTI. CC KHI NIM S DNG TRONG TI

Khi nim s dng cho lut chi c vua ca qun hu:- Chiu (chiu n, ang chiu, chiu ti): qun hu chiu (hay qun

hu ang chiu hay qun hu chiu n hay qun hu chiu ti) tc l qun hu angc kh nng tn cng mt qun c khc ang nm trn ct, hng hay mt trong hai

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0 0 1 2 3 4 5 6 7

1 1 2 3 4 5 6 7 8

2 2 3 4 5 6 7 8 9

3 3 4 5 6 7 8 91

0

4 4 5 6 7 8 91

0

1

1

5 5 6 7 8 91

0

1

1

1

2

6 6 7 8 91

0

1

1

1

2

1

3

7 7 8 91

0

1

1

1

2

1

3

1

4

Hnh 2.2.3- duongcheohieu (tc l ng cho hiu): hiu ca ch s hng v

ct ca cc nm trn ng cho ny bng nhau. Hnh sau minh ha ng chohiu:

0 1 2 3 4 5 6 7

0 0 -1 -2 -3 -4 -5 -6 -7

1 1 0 -1 -2 -3 -4 -5 -6

2 2 1 0 -1 -2 -3 -4 -5

3 3 2 1 0 -1 -2 -3 -4

4 4 3 2 1 0 -1 -2 -3

5 5 4 3 2 1 0 -1 -2

6 6 5 4 3 2 1 0 -1

7 7 6 5 4 3 2 1 0

Hnh 2.2.4II. KT QU VN DNG L THUYT VO TI

Ta vn dng c tnh chiu ca qun hu cng vi cc bin mng c tn cot,duongcheotong, duongcheohieu kim tra xem v tr no l ph hp t qun hu.

Ta s dng k thut quay lui tm ng i thch hp cho qun hu.

Phn III. NG DNG

I. PHN TCH YU CU BI TON, XY DNG CC CU TRC DLIU CN THITYu cu ca bi ton: t 8 qun hu ln bn c vua 8 x 8 sao cho chng

khng th chiu ln nhau (theo lut chi c vua). Trong ti ny ta cho ngi dngchn v tr ca qun hu hng u tin, sau t 7 qun hu cn li vo bn c saocho c 8 qun hu khng th chiu ln nhau.

Xy dng cc cu trc d liu cn thit: sau khi phn tch bi ton v xc nhhng gii quyt, ta khng cn xy dng cu trc d liu phc tp no c, ch cn xydng vi bin mng (phc v cho thut tan v ha) kt hp vi k thut quay lui tm li gii cho bi ton.

II. GII THUT (LU - NGN NG GI) Lu gn gi tr true cho cc bin mng cot[] kiu boolean (gi trl true ch ra rng cc ct cn trng, cha c qun hu no chiu ti)

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Lu gn gi tr true cho cc ng cho (nhng ng cho cgi tr true l nhng ng cho cn trng, cha c qun hu no chiu ti)

Lu thc hin vic tm v tr thch hp cho cc qun hu trn bnc (tc l tm gi tr ca cc arr[i] vi i>0 v i=0 l hng s 0, m hng s

0 th v tr ca qun hu l do ngi dng chn)

5

begin

l = 0

l =1

i = length-1

i - -j = arr[i]

cot[j] = trueduongcheohieu[j-i+7]=trueduongcheotong[j+i]=true

i ++

j ++

S

S

S

S

j ++

Ch thch: length l kch thc ca mng

arr[] y length=8

S

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Lu thc hin vic in ra mn hnh cc qun hu:

III. GII THIU CHNG TRNHChng trnh c giao din ha d nhn, s dng d dng bng cch click

chut, khng cn thit phi tm hiu cch thc s dng.Khi m chng trnh ln, xut hin hnh nh sau:

Hnh 3.3.1

7

begin

i =0

i

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Trong trng hp ngi dng cn tr gip: nhn vo nt tr gip, phn trgip s ngay lp tc hin ln trn form, lc by gi form c hnh nh sau:

Hnh 3.3.2

Hnh nh sau minh ha mt trng hp s dng ca ngi dng:

Hnh 3.3.3

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Khi mun tr v trng thi ban u nh lc mi m chng trnh, ta click vont hy. Sau khi click nt hy, giao din nh ban u:

Khi ngi dng mun ng chng trnh, ch cn nhn vo nt Thot, chngtrnh s ng li.

Phn IV. KT LUNI. NHN XT KT QU T C

- i vi chng trnh:Xy dng c giao din bn c 8 x 8 cng cc chc nng km theo s

dng chng trnh.Xy dng c cc hm tm li gii cho bi ton v cho ra kt qu ng.Thi gian thc thi nhanh.- i vi bn thn:Bit lut chi c vua.Hiu hn v ngn ng Microsoft Visual C# 2005.

II. HN CHCh p dng k thut quay lui tm ng i ng cho cc qun hu nn kt

qu bi ton ch cho ra mt nghim.III. HNG PHT TRIN

Xy dng thm cc chc nng tin ch cho ngi dng nh: chn v tr bt kca qun hu (c hng v ct), cho php chn mu cho bn c theo mun, cho phpm rng hay thu hp kch thc bn c (4 x 4, 8 x 8,).

Xy dng thm tin ch chn m thanh vo gy cm gic thch th khi dngchng trnh cho ngi dng.

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p dng thm k thut ton khc tm ra nhiu nghim hn cho bi ton.

PHN PH LC Hng dn s dng: nm trong phn III mc III.Gii thiu chng

trnh. Demo chi tit (trnh by trn lp) Cc biu mu, chng t, cng thc c s dng thc hin

ti: c ly ch yu t ti liu tham kho. Chng trnh ngun: Chng trnh c vit bng ngn ng

Microsoft Visual C# 2005 (bn Express):using System;using System.Collections.Generic;using System.ComponentModel;using System.Data;using System.Drawing;using System.Text;

using System.Windows.Forms;namespace NienLuan1{ publicpartialclassForm1 : DevComponents.DotNetBar.Office2007Form

{ privateint[] arr; privatebool[] duongcheotong; privatebool[] duongcheohieu; privatebool[] cot;

public Form1(){

InitializeComponent();

}

privatevoid Form1_Load(object sender, EventArgs e){

comboBox1.SelectedIndex = 0;}

privatevoid Form1_Paint(object sender, PaintEventArgs e){

Graphics g = e.Graphics; Pen p = newPen(Color.SteelBlue, 2);

g.DrawRectangle(p, 50, 50, 320, 320);p.Dispose();

SolidBrush sb1 = newSolidBrush(Color.MintCream); SolidBrush sb2 = newSolidBrush(Color.Tomato);

g.FillRectangle(sb1, 50, 50, 40, 40);g.FillRectangle(sb1, 130, 50, 40, 40);g.FillRectangle(sb1, 210, 50, 40, 40);g.FillRectangle(sb1, 290, 50, 40, 40);g.FillRectangle(sb1, 90, 90, 40, 40);g.FillRectangle(sb1, 170, 90, 40, 40);g.FillRectangle(sb1, 250, 90, 40, 40);g.FillRectangle(sb1, 330, 90, 40, 40);g.FillRectangle(sb1, 50, 130, 40, 40);g.FillRectangle(sb1, 130, 130, 40, 40);g.FillRectangle(sb1, 210, 130, 40, 40);

g.FillRectangle(sb1, 290, 130, 40, 40);g.FillRectangle(sb1, 90, 170, 40, 40);g.FillRectangle(sb1, 170, 170, 40, 40);g.FillRectangle(sb1, 250, 170, 40, 40);

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g.FillRectangle(sb1, 330, 170, 40, 40);g.FillRectangle(sb1, 50, 210, 40, 40);g.FillRectangle(sb1, 130, 210, 40, 40);g.FillRectangle(sb1, 210, 210, 40, 40);g.FillRectangle(sb1, 290, 210, 40, 40);g.FillRectangle(sb1, 90, 250, 40, 40);

g.FillRectangle(sb1, 170, 250, 40, 40);g.FillRectangle(sb1, 250, 250, 40, 40);g.FillRectangle(sb1, 330, 250, 40, 40);g.FillRectangle(sb1, 50, 290, 40, 40);g.FillRectangle(sb1, 130, 290, 40, 40);g.FillRectangle(sb1, 210, 290, 40, 40);g.FillRectangle(sb1, 290, 290, 40, 40);g.FillRectangle(sb1, 90, 330, 40, 40);g.FillRectangle(sb1, 170, 330, 40, 40);g.FillRectangle(sb1, 250, 330, 40, 40);g.FillRectangle(sb1, 330, 330, 40, 40);g.FillRectangle(sb2, 90, 50, 40, 40);g.FillRectangle(sb2, 170, 50, 40, 40);

g.FillRectangle(sb2, 250, 50, 40, 40);g.FillRectangle(sb2, 330, 50, 40, 40);g.FillRectangle(sb2, 50, 90, 40, 40);g.FillRectangle(sb2, 130, 90, 40, 40);g.FillRectangle(sb2, 210, 90, 40, 40);g.FillRectangle(sb2, 290, 90, 40, 40);g.FillRectangle(sb2, 90, 130, 40, 40);g.FillRectangle(sb2, 170, 130, 40, 40);g.FillRectangle(sb2, 250, 130, 40, 40);g.FillRectangle(sb2, 330, 130, 40, 40);g.FillRectangle(sb2, 50, 170, 40, 40);g.FillRectangle(sb2, 130, 170, 40, 40);g.FillRectangle(sb2, 210, 170, 40, 40);

g.FillRectangle(sb2, 290, 170, 40, 40);g.FillRectangle(sb2, 90, 210, 40, 40);g.FillRectangle(sb2, 170, 210, 40, 40);g.FillRectangle(sb2, 250, 210, 40, 40);g.FillRectangle(sb2, 330, 210, 40, 40);g.FillRectangle(sb2, 50, 250, 40, 40);g.FillRectangle(sb2, 130, 250, 40, 40);g.FillRectangle(sb2, 210, 250, 40, 40);g.FillRectangle(sb2, 290, 250, 40, 40);g.FillRectangle(sb2, 90, 290, 40, 40);g.FillRectangle(sb2, 170, 290, 40, 40);g.FillRectangle(sb2, 250, 290, 40, 40);g.FillRectangle(sb2, 330, 290, 40, 40);g.FillRectangle(sb2, 50, 330, 40, 40);g.FillRectangle(sb2, 130, 330, 40, 40);g.FillRectangle(sb2, 210, 330, 40, 40);g.FillRectangle(sb2, 290, 330, 40, 40);

} privatevoid comboBox1_KeyPress(object sender, KeyPressEventArgse)

{e.Handled = true;

} privatevoid button3_Click(object sender, EventArgs e)

{ this.Close();


{ int i, j;

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Graphics g3 = this.CreateGraphics(); Pen p3 = newPen(Color.SteelBlue, 2);

g3.DrawRectangle(p3, 50, 50, 320, 320);p3.Dispose();

SolidBrush sb111 = newSolidBrush(Color.MintCream); SolidBrush sb222 = newSolidBrush(Color.Tomato);

g3.FillRectangle(sb111, 50, 50, 40, 40);g3.FillRectangle(sb111, 130, 50, 40, 40);g3.FillRectangle(sb111, 210, 50, 40, 40);g3.FillRectangle(sb111, 290, 50, 40, 40);g3.FillRectangle(sb111, 90, 90, 40, 40);g3.FillRectangle(sb111, 170, 90, 40, 40);g3.FillRectangle(sb111, 250, 90, 40, 40);g3.FillRectangle(sb111, 330, 90, 40, 40);g3.FillRectangle(sb111, 50, 130, 40, 40);g3.FillRectangle(sb111, 130, 130, 40, 40);g3.FillRectangle(sb111, 210, 130, 40, 40);g3.FillRectangle(sb111, 290, 130, 40, 40);g3.FillRectangle(sb111, 90, 170, 40, 40);


g3.FillRectangle(sb111, 210, 290, 40, 40);g3.FillRectangle(sb111, 290, 290, 40, 40);g3.FillRectangle(sb111, 90, 330, 40, 40);g3.FillRectangle(sb111, 170, 330, 40, 40);g3.FillRectangle(sb111, 250, 330, 40, 40);g3.FillRectangle(sb111, 330, 330, 40, 40);g3.FillRectangle(sb222, 90, 50, 40, 40);g3.FillRectangle(sb222, 170, 50, 40, 40);g3.FillRectangle(sb222, 250, 50, 40, 40);g3.FillRectangle(sb222, 330, 50, 40, 40);g3.FillRectangle(sb222, 50, 90, 40, 40);g3.FillRectangle(sb222, 130, 90, 40, 40);g3.FillRectangle(sb222, 210, 90, 40, 40);g3.FillRectangle(sb222, 290, 90, 40, 40);g3.FillRectangle(sb222, 90, 130, 40, 40);g3.FillRectangle(sb222, 170, 130, 40, 40);g3.FillRectangle(sb222, 250, 130, 40, 40);g3.FillRectangle(sb222, 330, 130, 40, 40);g3.FillRectangle(sb222, 50, 170, 40, 40);g3.FillRectangle(sb222, 130, 170, 40, 40);g3.FillRectangle(sb222, 210, 170, 40, 40);g3.FillRectangle(sb222, 290, 170, 40, 40);g3.FillRectangle(sb222, 90, 210, 40, 40);g3.FillRectangle(sb222, 170, 210, 40, 40);g3.FillRectangle(sb222, 250, 210, 40, 40);g3.FillRectangle(sb222, 330, 210, 40, 40);g3.FillRectangle(sb222, 50, 250, 40, 40);g3.FillRectangle(sb222, 130, 250, 40, 40);g3.FillRectangle(sb222, 210, 250, 40, 40);g3.FillRectangle(sb222, 290, 250, 40, 40);

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g3.FillRectangle(sb222, 90, 290, 40, 40);g3.FillRectangle(sb222, 170, 290, 40, 40);g3.FillRectangle(sb222, 250, 290, 40, 40);g3.FillRectangle(sb222, 330, 290, 40, 40);g3.FillRectangle(sb222, 50, 330, 40, 40);g3.FillRectangle(sb222, 130, 330, 40, 40);

g3.FillRectangle(sb222, 210, 330, 40, 40);g3.FillRectangle(sb222, 290, 330, 40, 40);g3.Dispose();//Khai bao cac bien mangarr = newint[8];

Icon[] iconArr = newIcon[8]; Graphics[] gArr = newGraphics[8];

duongcheotong = newbool[15];duongcheohieu = newbool[15];cot = newbool[8];//gan gia tri true cho cot

for (int l = 0; l < 8; l++){

cot[l] = true;} //gan gia tri true cho dong for (int l = 0; l < 15; l++)

{duongcheohieu[l] = true;duongcheotong[l] = true;

} //vi tri cua quan hau o hang thu 0 do nguoi dung chon

arr[0] = Convert.ToInt32(comboBox1.Text) - 1;cot[arr[0]] = false;duongcheotong[arr[0] - 0] = false;duongcheohieu[arr[0] - 0 + 7] = false;

//Bat dau tim vi tri cho 7 quan hau con lai tren ban co for (i = 0; i < arr.Length; i++)

{ if (i >= 1)

{ for (j = 0; j < arr.Length; j++)

{ if (cot[j] == true && duongcheohieu[j - i +7] == true && duongcheotong[j + i] == true)

{arr[i] = j;cot[j] = false;duongcheohieu[j - i + 7] = false;duongcheotong[j + i] = false;

break;}

elseif (j >= arr.Length - 1){

while (j >= arr.Length - 1){

i--;j = arr[i];cot[j] = true;duongcheohieu[j - i + 7] = true;duongcheotong[j + i] = true;j++;

}

}

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}}

} //in ra man hinh for (i = 0; i < arr.Length; i++)

{

iconArr[i] = newIcon("favicon1.ico");gArr[i] = this.CreateGraphics();gArr[i].DrawIcon(iconArr[i], (this.Width / 11) + (40

* (arr[i])), (this.Height / 8) + (40 * i));gArr[i].Dispose();

}}

privatevoid button2_Click(object sender, EventArgs e){

comboBox1.SelectedIndex = 0; Graphics g2 = this.CreateGraphics(); Pen p2 = newPen(Color.SteelBlue, 2);

g2.DrawRectangle(p2, 50, 50, 320, 320);

p2.Dispose(); SolidBrush sb11 = newSolidBrush(Color.MintCream); SolidBrush sb22 = newSolidBrush(Color.Tomato);

g2.FillRectangle(sb11, 50, 50, 40, 40);g2.FillRectangle(sb11, 130, 50, 40, 40);g2.FillRectangle(sb11, 210, 50, 40, 40);g2.FillRectangle(sb11, 290, 50, 40, 40);g2.FillRectangle(sb11, 90, 90, 40, 40);g2.FillRectangle(sb11, 170, 90, 40, 40);g2.FillRectangle(sb11, 250, 90, 40, 40);g2.FillRectangle(sb11, 330, 90, 40, 40);g2.FillRectangle(sb11, 50, 130, 40, 40);g2.FillRectangle(sb11, 130, 130, 40, 40);

g2.FillRectangle(sb11, 210, 130, 40, 40);g2.FillRectangle(sb11, 290, 130, 40, 40);g2.FillRectangle(sb11, 90, 170, 40, 40);g2.FillRectangle(sb11, 170, 170, 40, 40);g2.FillRectangle(sb11, 250, 170, 40, 40);g2.FillRectangle(sb11, 330, 170, 40, 40);g2.FillRectangle(sb11, 50, 210, 40, 40);g2.FillRectangle(sb11, 130, 210, 40, 40);g2.FillRectangle(sb11, 210, 210, 40, 40);g2.FillRectangle(sb11, 290, 210, 40, 40);g2.FillRectangle(sb11, 90, 250, 40, 40);g2.FillRectangle(sb11, 170, 250, 40, 40);g2.FillRectangle(sb11, 250, 250, 40, 40);g2.FillRectangle(sb11, 330, 250, 40, 40);g2.FillRectangle(sb11, 50, 290, 40, 40);g2.FillRectangle(sb11, 130, 290, 40, 40);g2.FillRectangle(sb11, 210, 290, 40, 40);g2.FillRectangle(sb11, 290, 290, 40, 40);g2.FillRectangle(sb11, 90, 330, 40, 40);g2.FillRectangle(sb11, 170, 330, 40, 40);g2.FillRectangle(sb11, 250, 330, 40, 40);g2.FillRectangle(sb11, 330, 330, 40, 40);g2.FillRectangle(sb22, 90, 50, 40, 40);g2.FillRectangle(sb22, 170, 50, 40, 40);g2.FillRectangle(sb22, 250, 50, 40, 40);g2.FillRectangle(sb22, 330, 50, 40, 40);g2.FillRectangle(sb22, 50, 90, 40, 40);g2.FillRectangle(sb22, 130, 90, 40, 40);g2.FillRectangle(sb22, 210, 90, 40, 40);g2.FillRectangle(sb22, 290, 90, 40, 40);

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g2.FillRectangle(sb22, 90, 130, 40, 40);g2.FillRectangle(sb22, 170, 130, 40, 40);g2.FillRectangle(sb22, 250, 130, 40, 40);g2.FillRectangle(sb22, 330, 130, 40, 40);g2.FillRectangle(sb22, 50, 170, 40, 40);g2.FillRectangle(sb22, 130, 170, 40, 40);


g2.FillRectangle(sb22, 330, 290, 40, 40);g2.FillRectangle(sb22, 50, 330, 40, 40);g2.FillRectangle(sb22, 130, 330, 40, 40);g2.FillRectangle(sb22, 210, 330, 40, 40);g2.FillRectangle(sb22, 290, 330, 40, 40);g2.Dispose();


{label19.Visible = true;

}

}

}

TI LIU THAM KHO Ti liu sch:

[1] Nguyn c Ngha Nguyn T Thnh.Ton Ri Rc. Chng 4 phn 4.4. Nhxut bn gio dc. H ni, 1999.[2]Th.S. Nguyn Vn Linh.Gii Thut. Chng 3 phn 3.5. i Hc Cn Th. CnTh, 12/2003.

Ti liu web:Trang google.com v thc hin tm kim vi kha bi ton 8 qun hu

Trang www.congdongcviet.com phn lp trnh C#Trang http://vi.wikipedia.org/wiki/B%C3%A0i_to%C3%A1n_t%C3%A1m_qu%C3%A2n_h%E1%BA%ADuTrang http://www.ddth.com/showthread.php?t=8076Trang http://www.it-hui.com/index.php?topic=3117.0Trang http://www.animatedrecursion.com/advanced/the_eight_queens_problem.htmlTrang http://www.math.utah.edu/~alfeld/queens/queens.htmlDin nhttp:// forums.congdongcviet.comTrang http://tailieuit.com/forum/toan-roi-rac-203/bai-toan-8-quan-hau-va-cac-van-de-lien-quan-8842/

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