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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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% C6 B" {/ E. m 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。 t- S- S% n$ W9 x7 c# B) J0 f
' k3 a. z1 t0 A9 v; [ 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。) j$ [$ L+ N1 N; o8 `5 f, w5 _9 H, n8 ]
# G% ?( r/ ~: \- e _. I, I 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;
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y4 Y( z# _7 G$ r a5 m 以下是java 源码 :
: _/ M) A) |* U! A& y import java.awt.*;1 J% F, x/ S& F' H' z- `0 P
import javax.swing.*;
6 ^! N9 H! N! o1 p1 U( `8 r, o import java.awt.event.*;9 C) R7 r) m) P8 T
import java.util.*;/ i$ ^, s$ a5 m1 L+ X% |
import javax.swing.JOptionPane;
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" m1 h _$ O8 f8 N, R public class TwentyFourPoke_Game extends JFrame: T) x5 b* d$ W. D) H, V
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private JButton jbsolution = new JButton("Find a Solution");9 k1 `' }8 l. f: [
private JButton jbrefresh = new JButton("Refresh");
5 q$ J" ?. `1 @5 b: ^ private JButton jbverify = new JButton("Verify");
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private JLabel jlmessage = new JLabel("Enter an expression:");
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( K+ |' W" V6 L. H2 X private JTextField jtsolution = new JTextField();2 Z4 X6 U9 i; ~# R: k% Q
private JTextField jtexpression = new JTextField();- a2 z6 h7 B3 F: k
# c0 S9 w3 K% W' ? private ImagePanel pp = new ImagePanel();1 I+ y' H" w4 o! m' X$ g+ ~& k: i
. u$ i7 Z; D& H- K0 R1 w/ ^ private int[] card = new int[4];* `% J2 K E0 z* V& t) i! |1 J
private double[] bcard = new double[4];
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! @8 v, L& U$ [5 i# ~. U0 `1 c2 z4 i private double sum;/ q+ G+ Z; }' r7 _4 t4 Y
private double[] temp1 = new double[3];
" f6 q0 ~% Z, F0 p `+ R private double[] temp2 = new double[2];( K& v8 q# s1 r% Q! S2 Q# {* s
private char[] sign = {'+','-','*','/'};
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public TwentyFourPoke_Game()+ \+ q) r/ {2 k" p5 O! l
{
- t0 x$ u; v% Y' ~ JPanel p1 = new JPanel(new GridLayout(1,3));
+ Y6 ?7 t. |2 o( s. M% p p1.add(jbsolution);( n8 J5 \# h+ k+ |
p1.add(jtsolution);+ J3 j' m2 ]2 U2 ]; ]
p1.add(jbrefresh);
' \- {" d" u, f JPanel p3 = new JPanel(new GridLayout(1,3));% l% R+ b4 T& t, n" q6 u0 F
p3.add(jlmessage);
3 j. l, R3 z. L1 A3 E- i6 ?2 f" R$ c p3.add(jtexpression);
3 t( a) j0 J$ S: j& z, v# Y& r p3.add(jbverify);
+ c G. Y$ P3 r! W. T/ d
7 E. `# J* U m5 o' a) \4 P1 L add(p1,BorderLayout.NORTH);
% s) u# e) @& q! E+ V6 r# t. \( N1 U add(pp,BorderLayout.CENTER);
% ?! u5 U4 `: T% i& K: F$ ^+ N add(p3,BorderLayout.SOUTH);& \+ c! F$ F& U3 f6 ~9 T3 o: q
( x9 D/ _- H( L6 E( ] ButtonListener listener = new ButtonListener();4 \3 n! L0 K+ f
jbsolution.addActionListener(listener);
9 x$ Y* d$ I7 E. E4 N jbrefresh.addActionListener(listener);
+ x8 l; l4 a3 ]1 m" k7 v jbverify.addActionListener(listener);
8 k* s! Y. ]/ D& B- E% ?) p, T }$ @' D+ N7 f& q: e5 o2 [0 D# w+ M
& \1 W% r/ T/ B3 D* G% ?! A class ButtonListener implements ActionListener1 q3 k! H, R' T! N" {9 [
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public void actionPerformed(ActionEvent e)" k/ m* r' ]9 F9 A* E/ E: {
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if(e.getSource() == jbsolution)
* s7 E! [4 o: E/ f1 |( x+ B {
2 P8 n6 D7 r7 m' Z4 Q for(int i = 0;i < 4;i++)
& R$ F& }/ C% P {. j7 H5 M j) Q. ]$ D' b5 g: ] }
bcard[i] = (double)card[i] % 13;3 @- i6 \% q9 F
if(card[i] % 13 == 0); ?2 ?8 `: e- K3 D# F
bcard[i] = 13;# B+ O3 m$ y; N8 S$ w) f
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search();
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4 _6 I f, ?6 u7 d2 t! D else if(e.getSource() == jbrefresh)) p# v3 \3 K+ H4 q# d# h
{" b: v' ]3 m$ \2 \4 E% b# d
pp.sshow();/ s- [: Y/ q5 }: L0 j. k
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else if(e.getSource() == jbverify)3 d) l( f: |$ X' p# r( g6 @
{
( `1 @6 x4 V3 N* H; j String expression = jtexpression.getText();
) A7 O& m9 q" j6 U" V c int result = evaluateExpression(expression);8 \3 Z5 j! k0 G" |' l% ~
if(result == 24)# q n- L: G1 m9 D% W& _
{0 i( r# X+ G! x! b" }
JOptionPane.showMessageDialog(null,"恭喜你!你答对了!","消息框",JOptionPane.INFORMATION_MESSAGE);
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else
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JOptionPane.showMessageDialog(null,"抱歉!请再次尝试。","消息框",JOptionPane.INFORMATION_MESSAGE);
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5 Y7 t3 e& O0 V- g: e! z% ~! X public static double calcute(double a,double b,char c)
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if(c == '+')
8 X: J1 V$ m6 G; D/ E& ? return a+b;$ _! e% q9 X: K
else if(c == '-')
0 A/ F C/ A8 c; t% y/ C return a-b;
/ \* |( c; ?( e4 t- ~/ S else if(c == '*')
7 A/ L& x% G5 _8 n return a*b;% A* I4 z. e3 y: g
else if(c == '/' && b != 0)
/ j* l, O9 C A5 X, ~" [/ {9 Z$ ` return a/b;
( P u0 Y% w5 K& n; ]- j. c else
% I- J$ T, ^. ~) L: G3 H return -1;
" a7 t1 t5 S) O7 M/ s. ~ }
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& L2 i$ h1 h% T public void search()
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# {! u" |, s4 ^- X) P. N: Q6 W+ L boolean judge = false;
% P4 u1 h6 ~9 ?$ _, d5 Q# b for(int i=0;i<4;i++)/ W* ?% V) f9 G4 T3 k
//第一次放置的符号
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9 f# f1 t$ ~0 g9 Y9 {* f for(int j=0;j<4;j++). G# p" S! G; J; [
//第二次放置的符号
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for(int k=0;k<4;k++)
5 ~- z) H9 V. Q& q //第三次放置的符号" ?+ h1 c7 t o7 q) {' G' @
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for(int m=0;m<3;m++); ~# W9 n# O5 k8 A
//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
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6 L$ j# d) s+ E/ n' T8 K( R% X if(bcard[m+1]==0 && sign[i]=='/') break;
+ G/ c3 h0 E0 d% ]6 q) Z temp1[m]=calcute(bcard[m],bcard[m+1],sign[i]);
2 z1 { Q, w+ _ temp1[(m+1)%3]=bcard[(m+2)%4];
2 L0 p5 d/ l% X temp1[(m+2)%3]=bcard[(m+3)%4];' B' R; x( P( l
//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& R$ F5 y$ B- `/ @/ P
for(int n=0;n<2;n++)
* I4 `- V- n' E' X) Q: W* ] //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
$ s; p# m( y$ u& {) O; L4 Y2 o {
/ s& m P2 U" e5 d if(temp1[n+1]==0 && sign[j]=='/') break;( \% C3 W- ?6 L& T: _7 l. E# t/ T7 U
temp2[n]=calcute(temp1[n],temp1[n+1],sign[j]);
0 }$ t* P6 a& i. [) j: A7 `8 O temp2[(n+1)%2]=temp1[(n+2)%3];1 d& `; E. R) m! {4 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& k% l' {1 K- A q9 w: U2 S
if(temp2[1]==0 && sign[k]=='/') break;: o7 V, ]; u3 W, C$ t$ b$ _
sum=calcute(temp2[0],temp2[1],sign[k]);
- C* `+ J& L- ~, w+ n. q5 C$ P: ] //计算和
: r- ^2 H# d& W# C7 v& T if(sum==24)5 G' p' _1 B" U4 ]+ T0 q4 z; W
//若和为24
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judge=true;
, x) g1 G9 k& f //判断符为1,表示已求得解- u- U* |/ S' W4 @
if(m==0 && n==0)3 E" w$ L9 I' o5 R7 o* c3 h
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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;, X9 r& F9 M( p
jtsolution.setText(sss);3 \. b* J, N2 d4 T0 Q
return ;
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# }! m" t1 |4 N: O% s, p8 j else if(m==0 && n==1)
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String sss ="("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[j]+(int)bcard[3]+")="+(int)sum;
, G* S" U. Q' w# h! e0 t @ jtsolution.setText(sss);
4 e+ L% w# N- u L+ d1 H" x- ^& U return ;
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else if(m==1 && n==0)
' u! G8 P$ B" e- I# { X {
( d3 b6 ]( U5 d1 }( ~' W String sss ="("+(int)bcard[0]+sign[j]+"("+(int)bcard[1]+sign[i]+(int)bcard[2]+"))"+sign[k]+(int)bcard[3]+"="+(int)sum;
1 Q% P% O p8 o jtsolution.setText(sss);/ }$ Y. x+ B8 c- Z9 r* \0 Y( j
return ;1 f7 E, ?% b' F5 f$ Y
}
; }; _8 O6 N$ K9 Q$ B* _; Z: T else if(m==2 && n==0)
5 u% _( V' Z& w/ p5 E3 | {
. r) A9 h+ U( g0 Z, }2 J String sss ="("+(int)bcard[0]+sign[j]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+")="+(int)sum;
2 G0 z! J2 d1 ]' Q# ~ jtsolution.setText(sss);
' D) g/ |; e3 n8 y; X return ;
( [' h- L4 S4 ` }
5 R% d2 F6 _8 v0 \4 C. U else if(m==2 && n==0)
. z! X! d/ N9 d( U2 _ {
{2 S& k% ?; G) f1 S# G String sss =(int)bcard[0]+sign[k]+"("+(int)bcard[1]+sign[j]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+"))="+(int)sum;7 i1 ]2 r. p: T/ I, C
jtsolution.setText(sss);! x' ^7 @" ]7 P- k1 q$ T& B
return ; c8 k' l4 a- y7 @. W. [* G
}$ _; f! ^" r3 @* y: z- ^# Z4 m6 [. k, R' ^
//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
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}
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9 h! ?8 ^2 R% d9 z# ]) E }
* s6 t$ X% ^* V" h }
+ X6 W1 ^: I2 |' u9 ]4 ]) i' S }
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if(judge==false)7 m- H) h3 g" T* \
jtsolution.setText("No solution!");( `2 o, ^0 d& u4 @* w
//如果没有找到结果,符号位为05 [6 x) o. E2 M" t% U3 b
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public static int evaluateExpression(String expression)
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// Create operandStack to store operands) t: A, C/ S) B% ^! A Z
java.util.Stack operandStack = new java.util.Stack();
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@. \4 v4 O9 k2 n/ f" I' {3 F // Create operatorStack to store operators; i X! K3 _0 H; `2 ]$ l
java.util.Stack operatorStack = new java.util.Stack();: B6 `; @1 r9 m1 k
4 l8 f# K5 r5 s1 h5 z# Q // Extract operands and operators- w9 ?! N. G$ W$ L- d6 {8 y' F+ q
java.util.StringTokenizer tokens = new java.util.StringTokenizer(expression, "()+-/*", true);
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n0 T. O" ~5 v% j K. ~. m2 y5 s // Phase 1: Scan tokens5 H7 H7 I8 |8 @" t) U* E' M- Z% s
while (tokens.hasMoreTokens())
+ U9 D) C$ s: e- e {
7 B$ z+ ^2 f3 Z& D. j, e* o( }& a5 ?0 M& k String token = tokens.nextToken().trim(); // Extract a token U, G9 z* }! W. S1 Y( Z
if (token.length() == 0) // Blank space
+ H9 Z* Q0 `5 l) e) H1 ~/ O1 i continue; // Back to the while loop to extract the next token
* i& m% a7 I( T+ ~ else if (token.charAt(0) == '+' || token.charAt(0) == '-')" O7 v0 |! y' E' Q v
{9 @; ?/ a; R, J" y) `# @5 O# i
// Process all +, -, *, / in the top of the operator stack
, [7 d! s$ A& F$ W" f4 _9 I while (!operatorStack.isEmpty() &&(operatorStack.peek().equals('+') ||operatorStack.peek().equals('-') || operatorStack.peek().equals('*') || A' L! p, [, [6 W$ |
operatorStack.peek().equals('/')))( K# V( h# [6 q! |9 m$ p% t
{
% i+ V# V+ h& v5 @# c6 l processAnOperator(operandStack, operatorStack);
/ q! { O$ ?4 I+ s( P }
( Z: C$ J- v) [: S // Push the + or - operator into the operator stack
" P5 |% p: D8 r$ O& x' t1 d operatorStack.push(new Character(token.charAt(0)));% j$ W7 Q a# U& x8 E0 e/ b
}/ [% j# g2 h% k% U" r
else if (token.charAt(0) == '*' || token.charAt(0) == '/')
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// Process all *, / in the top of the operator stack) x3 h9 m' h' L# i
while (!operatorStack.isEmpty() && (operatorStack.peek().equals('*') || operatorStack.peek().equals('/')))" F. ?; j/ z4 h3 l# ]
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processAnOperator(operandStack, operatorStack);
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9 O. A7 @. h. ]) N- M/ I* f9 n // Push the * or / operator into the operator stack
; V3 ~( @: C; G1 c8 K. M$ b& _6 X operatorStack.push(new Character(token.charAt(0)));
& q" `% v9 C" c% A6 Q- ?6 x }1 [- C, ?4 r) V
else if (token.trim().charAt(0) == '(')+ G2 |: }' [' ] s0 s
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operatorStack.push(new Character('(')); // Push '(' to stack& f; @; s- U2 a+ F$ N$ h* Z8 {
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else if (token.trim().charAt(0) == ')')& s+ m2 a s. ^+ V2 |5 ?' l
{
4 M, a9 Q4 Y. i3 c" d) K // Process all the operators in the stack until seeing '(' l0 ^1 P' I: k( K7 w, m. l! K
while (!operatorStack.peek().equals('('))
1 }2 l$ r! g* k( U7 |! u {
, q- J0 K- c6 Z8 a! C processAnOperator(operandStack, operatorStack);# y$ |! I. i; v. r: E
}
. T* s. g2 Y4 b5 C( k$ }9 q operatorStack.pop(); // Pop the '(' symbol from the stack9 u: o! u9 { U; y* ]
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else9 a; u t6 _& p
{
6 u* ?8 k# Y& g. E: z // An operand scanned
5 y4 S3 T" d T" e5 U // Push an operand to the stack
7 R; d7 e. T/ G" J operandStack.push(new Integer(token));0 C' O* p6 Y D6 c/ T9 f Z' G
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}; d8 @" X$ [& O8 D. E% S# f
! @9 V: g" e3 f5 V4 a9 }# X' n // Phase 2: process all the remaining operators in the stack
1 I+ t% N& b6 j while (!operatorStack.isEmpty())4 U' w* U) U- c
{
R. a0 o( Q" d v processAnOperator(operandStack, operatorStack);
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// Return the result
8 v9 L, g; n. b$ B8 R9 u( w/ Q5 J return ((Integer)(operandStack.pop())).intValue();0 Z2 b2 E( N' R- ~/ e3 d
}/ X: l' o v8 D" e5 R" G/ @( m
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public static void processAnOperator(java.util.Stack operandStack,java.util.Stack operatorStack)
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if (operatorStack.peek().equals('+'))
5 f: s7 A2 G3 Q' I {
8 | ^, V3 s1 q1 `3 Y9 U operatorStack.pop();* T7 z b$ \4 K; V
int op1 = ((Integer)(operandStack.pop())).intValue();
- e* d& n+ h% s- x! K int op2 = ((Integer)(operandStack.pop())).intValue();
( K" T/ F9 v9 e" c9 C- E0 R' k- G operandStack.push(new Integer(op2 + op1));' J3 L: `) v1 C% j3 ^% \& ^
}
6 k% I' s) t* p+ b else if (operatorStack.peek().equals('-'))% ?8 W" n- w! }- T9 {1 x! d
{7 c: {+ D. t0 w* k g6 }. x
operatorStack.pop();
% R' d: S" w- H5 o! g- g int op1 = ((Integer)(operandStack.pop())).intValue();; R) A6 n- J; h. [) y+ {! _
int op2 = ((Integer)(operandStack.pop())).intValue();
: s( q0 {8 K. u( k X operandStack.push(new Integer(op2 - op1));' n) e2 q* i, j; r
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else if (operatorStack.peek().equals('*'))
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operatorStack.pop();
) t& ]0 r" X! U! o int op1 = ((Integer)(operandStack.pop())).intValue();
; Q0 W4 W) u1 z$ x/ ] int op2 = ((Integer)(operandStack.pop())).intValue();, x$ n' w2 |7 D6 V
operandStack.push(new Integer(op2 * op1));: W: A) g+ r5 S3 \: ]
}
, ?4 m7 m% U. R2 S5 v Z8 u else if (operatorStack.peek().equals('/'))
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operatorStack.pop();
1 V3 m/ y7 M! W: S' D int op1 = ((Integer)(operandStack.pop())).intValue();
+ H; [: T/ m, n0 G1 ]: l6 U8 v$ O int op2 = ((Integer)(operandStack.pop())).intValue();
c8 I- s5 o D5 A operandStack.push(new Integer(op2 / op1));
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6 O8 Z, r2 t2 R }7 T- f1 A class ImagePanel extends JPanel$ r# U' O: G! c1 n3 ^6 p, T: V A& k
{6 }7 V7 q6 y& C% B" h* d
public void sshow()
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+ T& w$ ]% O3 p8 [' T int i;
* Y: @* F* b+ W' A8 A for(i = 0;i < 4;i++)* n V0 y) r: w* t% C
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card[i] = (int)(1 + Math.random() * 52);
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repaint();1 j c; T9 _1 I) m0 E
}
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protected void paintComponent(Graphics g)
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super.paintComponent(g);4 y: Q$ ^9 v2 h$ @
int i;
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int h = getHeight();
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int y = 0;
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ImageIcon imageIcon = new ImageIcon("image/card/" + card[i] + ".png");
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if(image != null)
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g.drawImage(image,x,y,w,h,this);
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}
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public static void main(String[] args)
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frame.setTitle("24 Poke Game");' V4 x* h6 S: f' } H
frame.setLocationRelativeTo(null);) Y( F- Y6 h- b
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);. g. V; T+ N; h* P/ }/ W# X
frame.setSize(368,200);
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0 S* z! C$ }. I( } } 复制代码
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