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给出四个数字,要求,在其间添加运算符和括号,使得计算结果等于24。
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括号的放置即为决定哪几个数先进行计算。所以,我们先确定首先进行计算的两个相邻的数,计算完成后,就相当于剩下三个数字,仍需要在它们之间添加符号;然后再决定在这三个数中哪两个相邻的数先计算。由此,我们就成功解决了数字的运算次序问题,此时不需要再考虑不同运算符号的优先级问题,因为括号的优先级高于加减乘除。
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4 X2 ?, v* T' u$ ?; t 通过循环,我们可以得到第一第二第三次计算的运算符,再通过计算,就可以得出和,若和等于24,即为所求解。1 _/ Y7 U$ t$ t' F X! D, P! O
7 F5 p8 {8 _. ~9 _9 \ 在输出格式中,由于括号的放置共六种情况,故根据计算先后顺序的不同,输出时在不同地方放置括号;: b0 Y7 h% f: n! p8 r
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以下是java 源码 :
7 g/ r0 H$ k% |( ~4 f import java.awt.*;: V7 N, o) `( l! @4 ^5 X0 F6 K/ v
import javax.swing.*;
; T: u% B. Z) N* h import java.awt.event.*;
* b0 S; G0 B" r3 l import java.util.*;; }9 t1 _% u$ W! O4 s9 P' P
import javax.swing.JOptionPane;
* [( V: w6 L. D 1 B9 s' ?+ D5 l8 |; Q
public class TwentyFourPoke_Game extends JFrame
5 J5 Y3 J+ T. \" ~/ t9 u& y* e {
& @5 Y4 U# N; M" ^" b private JButton jbsolution = new JButton("Find a Solution");$ L% \4 M& O5 x3 C1 C ~; p
private JButton jbrefresh = new JButton("Refresh");6 }/ l p( W6 v# o9 M* n
private JButton jbverify = new JButton("Verify");3 j: ^! j- u$ a0 `+ `' u0 }. V
; a% d* h/ M7 P# P9 u
private JLabel jlmessage = new JLabel("Enter an expression:");# I# ~- o. K+ T0 [
0 Z0 X; d5 F0 o" h, H0 s8 S6 v( [
private JTextField jtsolution = new JTextField();
- A7 X9 E& t0 R# M private JTextField jtexpression = new JTextField();
3 K* ^4 c1 X, k
" W+ S i! S7 J; h8 H! p. O private ImagePanel pp = new ImagePanel();
+ F# I1 D+ G: r0 i/ f/ H; s! ~
?4 [0 i; [: X2 ~ private int[] card = new int[4];
/ R/ ]# ?0 F6 e! i! S7 s1 S# E3 L private double[] bcard = new double[4];; B4 _% w% h+ P- Z/ \8 c
; f1 j# v- B1 [. a6 G) \ private double sum;
6 O* w3 ?( G: t0 j private double[] temp1 = new double[3];* P7 x- \: ~. |
private double[] temp2 = new double[2];4 A+ y& j' i% W: B( w
private char[] sign = {'+','-','*','/'};
( }1 @3 u( Q6 m# b9 ^" x @ 9 a! o% u2 r, W/ i3 m( o) C
# U0 }% Q; P5 Y6 k+ u public TwentyFourPoke_Game()$ |. u# x6 C: U1 r: F ~, x9 W
{
# Z, t+ T8 x2 A# w7 y( t) B# w, v. C JPanel p1 = new JPanel(new GridLayout(1,3));
8 i3 K Y# t1 D* p( B5 g p1.add(jbsolution);
4 w9 F2 L+ B) \8 L p1.add(jtsolution);
A) G# D( K- W5 [* y0 r! ` p1.add(jbrefresh);
; H2 I6 f, c5 L! p4 u" L JPanel p3 = new JPanel(new GridLayout(1,3));
( M3 Q) R9 o- V6 [1 o p3.add(jlmessage);. U$ {! G+ _6 V: D: N
p3.add(jtexpression);( [# i% {, E+ i, O
p3.add(jbverify);
! [( v* y/ P3 J! y' } W & d' E) P( l Y
add(p1,BorderLayout.NORTH);# Y0 b$ G1 O) }2 Q. y! W0 Z3 @3 \
add(pp,BorderLayout.CENTER);
1 \9 i- M5 v6 ~ add(p3,BorderLayout.SOUTH);
- q! ^, w6 V" G' f: F
! K% T1 N$ { N3 k ButtonListener listener = new ButtonListener();
# I" O% r S5 O4 H+ K" b jbsolution.addActionListener(listener);
$ J3 U5 w1 B9 K jbrefresh.addActionListener(listener);2 K! [2 k0 @# o
jbverify.addActionListener(listener);
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3 ~, m9 W2 {& P0 p* |& q
3 Z8 T0 U8 k6 j class ButtonListener implements ActionListener
) @7 x! \* ? v* Q2 p6 F* M$ v {. i, z Y. |' ^
public void actionPerformed(ActionEvent e)5 i) b$ i: w8 f5 {: t- o
{
7 g( t8 P6 Q; f2 j/ w& [4 w0 ^ if(e.getSource() == jbsolution)
4 Y6 R! Z; }- x+ S' f {
: z" X8 _' J% T, w+ E: t6 b8 c for(int i = 0;i < 4;i++)
/ j& w( f `; e1 c+ K. E {; k) d9 y; b" u" l- s
bcard[i] = (double)card[i] % 13;
9 D0 L: O' |8 q# Q- }( \ if(card[i] % 13 == 0)- }3 x2 N* b0 [8 N" A9 k9 F2 z
bcard[i] = 13;) Q, v' I! @1 h5 C' ]
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search();
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else if(e.getSource() == jbrefresh)/ @8 q& n6 I5 t# Z* R$ p
{
* Y- ` g, |5 M( Q! b" d0 ^ pp.sshow();- B- I3 {+ \! c5 A
j Q4 Q5 U8 d: E
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else if(e.getSource() == jbverify)* E" R# d( [. V( c1 h
{
. s# r5 J7 k. a- p, @/ `; n2 a) j% h String expression = jtexpression.getText();( w+ U0 e$ y7 o# i! a
int result = evaluateExpression(expression);4 h6 a% A8 W& \: a2 v
if(result == 24)/ e" y. P& v1 f/ X$ L( C" ~
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JOptionPane.showMessageDialog(null,"恭喜你!你答对了!","消息框",JOptionPane.INFORMATION_MESSAGE);/ l, U& r& J: A3 i; C9 I3 S
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else
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. ^: q( F5 C( x' P' j! q+ } JOptionPane.showMessageDialog(null,"抱歉!请再次尝试。","消息框",JOptionPane.INFORMATION_MESSAGE); }) }4 L7 n7 R
}
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}" s3 ^/ @& Y0 J" @
}
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9 H9 k6 C' s0 W! m3 h. k! T public static double calcute(double a,double b,char c)7 P9 [! C- s9 w$ t
{9 K5 X! u) O8 O6 @2 U0 `" `) C" n
if(c == '+')& E M5 Y9 G* H7 D4 _
return a+b;. l* o9 O5 L1 _ R" a) L* y
else if(c == '-')# t. u' a8 F7 m( f
return a-b;! u: X* u- {' G1 {1 \6 k
else if(c == '*')4 l. G0 G9 E- C3 [3 K" U; E
return a*b;
, I. P W, K& R else if(c == '/' && b != 0)
4 Z1 m; _- i* d# x return a/b;
o3 A* D4 c5 ~$ K& j3 b; } else
' n1 U: X' _0 M) Q/ \ return -1;
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& o( p' w6 a$ O9 ~, v public void search()8 m( |. V) q9 Y: L2 [' |
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boolean judge = false;
9 w5 E' G) w9 O$ e+ z for(int i=0;i<4;i++)
' x& [# I* u9 ?! ?2 B" o! N //第一次放置的符号
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for(int j=0;j<4;j++): f5 p6 H" R# i+ k7 Z( b; T; Z! }
//第二次放置的符号
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1 k( r7 d2 Z2 Q5 n7 V, h for(int k=0;k<4;k++)7 d7 H' W/ y; J; M0 S) E! j
//第三次放置的符号4 N- A W- Y0 t) o6 v* P- C
{
2 e* Q& R. f" e9 v. e for(int m=0;m<3;m++)
6 i. l1 f% a. T0 Q2 c //首先计算的两个相邻数字,共有3种情况,相当于括号的作用
# Q$ w- L, l c1 c {4 z( u% Q1 ~8 B7 s
if(bcard[m+1]==0 && sign[i]=='/') break;. l6 X$ ^- D& l" i+ i6 k
temp1[m]=calcute(bcard[m],bcard[m+1],sign[i]);
$ m% f- h5 I! z: L temp1[(m+1)%3]=bcard[(m+2)%4];
9 ?0 V g- {+ ~6 D1 h0 ]* z- F temp1[(m+2)%3]=bcard[(m+3)%4];
: X# _0 J9 b2 o- ]- o7 \ //先确定首先计算的两个数字,计算完成相当于剩下三个数,按顺序储存在temp数组中
1 W& s4 {/ X* F. }' Z$ J4 K for(int n=0;n<2;n++)& j# i* L* Y! G, \' x
//三个数字选出先计算的两个相邻数字,两种情况,相当于第二个括号
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if(temp1[n+1]==0 && sign[j]=='/') break;# u+ u) q7 @/ [6 `& t! w
temp2[n]=calcute(temp1[n],temp1[n+1],sign[j]);. v1 t% |4 h: u% Z# [
temp2[(n+1)%2]=temp1[(n+2)%3];
7 I4 \( Y2 c- J( o, U( X2 L //先确定首先计算的两个数字,计算完成相当于剩下两个数,按顺序储存在temp数组中
- `1 n3 E, h4 i' s if(temp2[1]==0 && sign[k]=='/') break;/ Y0 k4 K& U( c0 z! z! ]: c
sum=calcute(temp2[0],temp2[1],sign[k]);5 w% S4 i/ _3 L T& K
//计算和
6 `& L. t5 `9 p& b9 W2 Q+ U if(sum==24)
9 z1 |) p8 ~+ X //若和为24) X+ D1 G. t7 s: j: s& ?
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judge=true;
% E7 Y# O6 m) A //判断符为1,表示已求得解
c# ~ w: i& A# I if(m==0 && n==0)3 Z9 S$ j$ F: T1 @& z
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String sss ="(("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[j]+(int)bcard[2]+")"+sign[k]+(int)bcard[3]+"="+(int)sum;
: S4 i: i# N8 k) ?- Z! e jtsolution.setText(sss);
2 b. o+ o2 `. {% y8 s. Q- o return ;
7 k" m; z. b! n# r( g: P% p4 m }
8 _/ T. M% `) I/ d9 z& h. ~+ A; g) ^* C else if(m==0 && n==1)
- M0 b4 L$ D. A( \3 v7 }- ]' S' p {
! A" Q9 z8 l; X+ Y# d String sss ="("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[j]+(int)bcard[3]+")="+(int)sum;3 I" }7 E0 N6 l' R2 I3 A- t3 N* R
jtsolution.setText(sss);- O2 X t0 }3 x, T I5 X
return ;4 z3 ^' s0 D' }0 J+ C/ D9 V; H
}
7 c6 b8 e6 m$ J: Y! g( I# Y1 e0 @. t else if(m==1 && n==0)' Z; c: a* _, t6 O
{
: [+ Y$ ^; y: z [5 A5 F& X' f String sss ="("+(int)bcard[0]+sign[j]+"("+(int)bcard[1]+sign[i]+(int)bcard[2]+"))"+sign[k]+(int)bcard[3]+"="+(int)sum;
8 |# q Q# T5 y7 q3 m8 \ jtsolution.setText(sss);7 n0 S0 U; ?6 s& p
return ;
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else if(m==2 && n==0)5 r% k( Y8 s( {4 [; h! t4 m
{
7 D1 E5 m2 O( ?( @/ ? String sss ="("+(int)bcard[0]+sign[j]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+")="+(int)sum;6 e5 F$ z& M& D
jtsolution.setText(sss);
% M: R, N9 \. q, _1 ~0 x5 _, Z* S return ;) ]" u$ q( A. j& T! r6 x& V' d- h
}
# b! m4 |. r4 F( I& L else if(m==2 && n==0)
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String sss =(int)bcard[0]+sign[k]+"("+(int)bcard[1]+sign[j]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+"))="+(int)sum;" Z& |5 q- ~% x4 ]- \, B
jtsolution.setText(sss);
^0 _- p* \! g8 N4 g# e4 ~ return ;
. t( J* w4 [7 V; d }
8 ~( P1 ^/ r8 [2 {' V //m=0,1,2 n=0,1表示六种括号放置可能,并按照这六种可能输出相应的格式的计算式( E. N4 s ^! N% w4 D3 s
+ d; ]& ?6 I; m6 e
}
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}& _1 v* u2 q7 R4 X$ ^4 `% X& }1 ~
}4 Z3 {" ]2 E1 Q9 ]
}
# V! t' m( ^) m! @2 D( c# @ if(judge==false)3 G! L$ P1 S2 v$ Z; y1 Y
jtsolution.setText("No solution!");; H) M) O# n- p
//如果没有找到结果,符号位为0, M7 b* \% a4 T q- ^9 l8 Z% ~
}
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/ L. g Y; u& }' p( [) u! A public static int evaluateExpression(String expression); L, n4 i' b* _% W
{3 M. n4 s% `* n4 Z. s
// Create operandStack to store operands+ J4 L' t/ N1 _- V
java.util.Stack operandStack = new java.util.Stack();
( k) k/ Z6 Q% X" N. `8 M1 C9 M/ J- d
. S# g3 ` d4 |9 I // Create operatorStack to store operators1 [" @ b0 A0 A& K. }* ^( x
java.util.Stack operatorStack = new java.util.Stack();
{$ H' B5 Q+ S' A2 f9 D# q6 [
3 |. Q6 y: M7 g. a0 r3 b& a) k | // Extract operands and operators
g# V6 N' {' w4 Z3 }8 w3 B java.util.StringTokenizer tokens = new java.util.StringTokenizer(expression, "()+-/*", true);; {& m7 P1 S3 x
: T4 o- H0 {+ c6 c$ ]9 U+ z // Phase 1: Scan tokens
0 G3 p0 `7 f# c9 J5 C4 Q7 s, _# I while (tokens.hasMoreTokens())
% f0 I4 o7 o# m3 V {0 Z6 J4 Z3 l7 N0 j8 R' l- R
String token = tokens.nextToken().trim(); // Extract a token
$ o, k$ }. Z E0 A5 u( {+ r if (token.length() == 0) // Blank space# D- j! F3 E* V1 Y# M, h
continue; // Back to the while loop to extract the next token
7 G: e& {+ O7 G: |1 x* @8 u' x else if (token.charAt(0) == '+' || token.charAt(0) == '-')
& j# g# H- d; k( k( L3 X/ e5 T- H2 t {
9 s. k7 e; ^) B4 m3 k! R% j // Process all +, -, *, / in the top of the operator stack
# j, i( b1 M/ U0 [2 x5 `- { while (!operatorStack.isEmpty() &&(operatorStack.peek().equals('+') ||operatorStack.peek().equals('-') || operatorStack.peek().equals('*') ||
; ]$ I, i2 [! V; X7 V operatorStack.peek().equals('/')))
4 v7 d3 @2 J* Q/ e3 a {
6 u3 S. e1 N# ^' a: A processAnOperator(operandStack, operatorStack); m& h0 X' {: Y: [% c( k7 n
}2 ?6 |/ }- e2 u) E$ T0 |
// Push the + or - operator into the operator stack
! U0 T; L- }; s9 T operatorStack.push(new Character(token.charAt(0)));1 ]7 ^. n" Z1 K3 J: X3 t
}2 T2 v$ d5 Z5 r7 p7 j: z! `/ l
else if (token.charAt(0) == '*' || token.charAt(0) == '/')$ H" ~) y* ~. K( N' Y
{
/ H1 E8 M% J* m# C3 N- @ // Process all *, / in the top of the operator stack: D/ _' X, y1 p$ `+ V
while (!operatorStack.isEmpty() && (operatorStack.peek().equals('*') || operatorStack.peek().equals('/')))
! q$ T- W1 s5 t: m {
( F( A @2 M% b2 }4 m3 ^. K processAnOperator(operandStack, operatorStack);
0 L7 G+ g, r1 [. q2 k& k+ O1 z" C }
( X% o- ]9 S" \3 L
8 b" |0 E) [" r) g3 d n5 L // Push the * or / operator into the operator stack
& y0 K/ C# P9 }' m2 \# u8 U operatorStack.push(new Character(token.charAt(0)));; Z) x7 E3 q$ n' e
}1 p& R1 k" r0 N8 O8 N8 @
else if (token.trim().charAt(0) == '(')
$ ?# F* Z$ u8 A' X) G {
+ A" {3 f' P ^! K' B" [ operatorStack.push(new Character('(')); // Push '(' to stack4 ~4 E: |; ]4 ~3 P# b9 u; G Q1 R/ t
}! E' N* h1 h6 j( n+ V* D
else if (token.trim().charAt(0) == ')')
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// Process all the operators in the stack until seeing '('9 M' x4 D/ t+ [% \
while (!operatorStack.peek().equals('('))
% U# D; J* ^! c% x& l {
8 ?2 A8 j* c" ?1 F: \ processAnOperator(operandStack, operatorStack);
' j; G) K$ k1 ~7 R8 @- m; C }
% J2 A+ d) ~4 X$ G' A' T operatorStack.pop(); // Pop the '(' symbol from the stack4 Q- O; l- F% x9 r( X
}
& }+ u6 l7 ~0 r6 n$ d1 Y+ M else5 z: |% p0 Q) J" x% T4 J
{ [$ q5 ~* z& Y1 w: M% C
// An operand scanned& ?) N4 G0 w1 t; p
// Push an operand to the stack+ ~3 C6 G: K, x( q* I
operandStack.push(new Integer(token));9 x+ F& _6 @; X* {: n% s
}
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; B1 c. V3 ~! e/ ]) s# v' j' \0 i- E
1 r8 ^( e7 r2 q- g# C* u( j // Phase 2: process all the remaining operators in the stack
+ b8 S$ I6 r6 j! y$ f while (!operatorStack.isEmpty())
$ H& l% l0 J4 ~$ w# I+ `: ?; K {9 g i! W; i% d; S U
processAnOperator(operandStack, operatorStack);% Z6 U( K$ `5 b) t4 ]
}5 U0 Y- n% b2 I
) m- I+ H/ w9 g% X) B) U+ E
// Return the result& S/ w3 U, I0 A; w, X$ V4 i
return ((Integer)(operandStack.pop())).intValue();% Y7 b) S+ n/ L
}
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public static void processAnOperator(java.util.Stack operandStack,java.util.Stack operatorStack)9 I; @( L* K$ ~2 p. z
{
: x2 a/ o( c: _5 I if (operatorStack.peek().equals('+')) F* b$ q6 z, w
{" {" O& I, y1 `
operatorStack.pop();3 O m Q1 j6 s8 F1 @
int op1 = ((Integer)(operandStack.pop())).intValue();3 K7 g6 F, t7 M" f
int op2 = ((Integer)(operandStack.pop())).intValue();
- B( s7 j# t6 }1 H7 T% m operandStack.push(new Integer(op2 + op1));
& [ T# V9 r7 K* O, v: w+ K4 T8 y }
5 g4 ? Q! i" B6 } else if (operatorStack.peek().equals('-')). p" k% \2 J- o0 b
{' O: i+ l- P4 n9 J" W
operatorStack.pop();% A0 c1 }: Z/ \" l; x+ s) |
int op1 = ((Integer)(operandStack.pop())).intValue();. W4 e7 m" l+ A9 N7 r
int op2 = ((Integer)(operandStack.pop())).intValue();& e. ?) N' |/ |( ]* q
operandStack.push(new Integer(op2 - op1));5 R3 ~) z1 d' c! k9 T% g8 o
}5 ~/ A6 M' u3 }( D2 g2 b V
else if (operatorStack.peek().equals('*'))% ?/ a l$ w$ ?! _9 m/ C$ M
{" j4 v$ b: K0 R6 {) R
operatorStack.pop();
% g- z- t1 |7 N8 @; b int op1 = ((Integer)(operandStack.pop())).intValue();- k0 K \/ `# d& D$ J6 o7 o
int op2 = ((Integer)(operandStack.pop())).intValue();# s0 @- _+ T* {3 j) H d5 [
operandStack.push(new Integer(op2 * op1));
9 N* [# K' o Y/ [' L2 v0 x }
+ X) O: Z5 S; w, p else if (operatorStack.peek().equals('/'))
4 Y5 d7 L3 a6 S( r% E8 q/ v$ e( f5 V {% E, b8 I. T: h1 E2 j* d
operatorStack.pop();
2 L% f/ ?8 Y% h3 W' G- {1 e" F, k" J int op1 = ((Integer)(operandStack.pop())).intValue();
" m/ Q: V8 Q; h2 p3 Q( l- Z3 y int op2 = ((Integer)(operandStack.pop())).intValue();
( {" p( G* f$ k+ p p @- w$ R operandStack.push(new Integer(op2 / op1));
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$ X. T r* i6 |: }9 l( @: S' @ }5 p' b4 j- s2 \; X' x$ `) m: ^
# V. N n. h. O, m/ e
class ImagePanel extends JPanel( A9 K+ q- X( E4 D3 o) ^
{
5 P/ ? @5 }" D5 `% {2 ~ public void sshow(): _, y. q% U$ M) h$ Z2 X
{
% ]; V8 K5 {( n5 n& X int i;
7 x: a" e5 r: }: _ for(i = 0;i < 4;i++)
; N' g+ A4 s: w% ? {+ k* u: V' y2 U) r
card[i] = (int)(1 + Math.random() * 52);2 Y5 m8 A( k- L
}# ?0 u2 K! v. ^
repaint();
/ x. c5 W! C$ ]. w% X }* Y* O# G' t+ f- K% U0 ]
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protected void paintComponent(Graphics g)
6 Y ^2 @. y/ ^' x* j {, U* t% V. Q& L4 N( S! x$ t
super.paintComponent(g);, O6 k3 u9 ?4 `2 h
int i;
: ~( ^: V% t3 e6 e/ N+ c int w = getWidth() / 4;- i$ E3 A1 F3 f4 Q- d; g
int h = getHeight();
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int y = 0;
; J/ h9 P, u5 G1 X3 T for(i = 0;i < 4;i++)
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ImageIcon imageIcon = new ImageIcon("image/card/" + card[i] + ".png");
9 S# \- j0 e8 O1 x" Z4 h Image image = imageIcon.getImage();
# F7 c$ u! J2 o5 \4 y if(image != null)9 ?, D+ z$ O ^
{
" ~9 s5 Z) ?8 U' i) | g.drawImage(image,x,y,w,h,this);
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% V1 X X5 n6 U" y# n x += w;
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}
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public static void main(String[] args) w9 p# l( v& @: v: e9 x
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TwentyFourPoke_Game frame = new TwentyFourPoke_Game();
% ^+ c$ S {* O2 ~ frame.setTitle("24 Poke Game");" G) c$ D+ z3 p
frame.setLocationRelativeTo(null);
, c" o: W4 p1 p5 \! j+ M. ? frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
9 D* A! W4 {, P: l1 S frame.setSize(368,200);
( E# Q' R+ b1 `" i8 A frame.setVisible(true);
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$ L+ f$ y$ P# K) q9 X$ W( Q } 复制代码 3 u9 ~- U u- l2 b/ i% f6 X
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