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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。, L% {, J5 d( q
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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。+ W3 O2 L" ?& p3 ~* U
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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;* V" I$ G7 e( X4 w+ l& @
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以下是java 源码 :9 `+ [ }6 i( U% \: ]
import java.awt.*;- F" x) I0 J0 ?: f( t. P& D3 Y
import javax.swing.*;
: U3 a }" @% s import java.awt.event.*;
! @* E2 N! T/ N import java.util.*;% O+ ]' k( E9 @" M, a; X
import javax.swing.JOptionPane;
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public class TwentyFourPoke_Game extends JFrame
1 E. Q2 q6 j1 p9 O {
% x. v( r' B; I# b private JButton jbsolution = new JButton("Find a Solution");1 D8 \3 \) W( b! L8 I; O8 k
private JButton jbrefresh = new JButton("Refresh");
4 S6 y) J& ?' u* y: h private JButton jbverify = new JButton("Verify");
, d4 p* n' H' O
# P+ `* x; ^8 D4 m" G1 M private JLabel jlmessage = new JLabel("Enter an expression:");
6 S( X* Y7 [8 P& g! d
, h0 z' b& i" I5 F. H private JTextField jtsolution = new JTextField();1 C+ Q# i( N; n; F
private JTextField jtexpression = new JTextField();8 z( D( w; S. _! W! C1 N a
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private ImagePanel pp = new ImagePanel();2 h7 u; h# s: r& {/ \7 T+ W" P
" I4 l- @" w/ v7 p$ w
private int[] card = new int[4];
" I. N7 X2 \& ^% | private double[] bcard = new double[4];( N9 ~0 P& I! n
5 X W$ ?2 d4 J private double sum;
* `6 s+ \3 Q, T. |3 `- _ private double[] temp1 = new double[3];
* a. B' R2 n7 Z4 F9 j) v; I& ]# V private double[] temp2 = new double[2];
$ b# @ _1 }' W9 i% f8 ^+ Z/ n private char[] sign = {'+','-','*','/'};" p" a8 c3 h4 j5 k8 A
3 |4 R! J/ L% B4 Y8 x) K( I; N
i" C% i, g4 H2 M# h public TwentyFourPoke_Game()( _4 v! H; ^8 A& a3 i* \. n
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JPanel p1 = new JPanel(new GridLayout(1,3));) L: Z3 D3 u G/ }( O# s% H: m( Q
p1.add(jbsolution);0 ^! t8 z Q4 j3 E! F$ z
p1.add(jtsolution);7 ]4 }! x& J, z/ H
p1.add(jbrefresh);8 l P4 j9 e2 ^+ q' k( k
JPanel p3 = new JPanel(new GridLayout(1,3));) b \. ?2 O/ Q$ Q/ ]2 X
p3.add(jlmessage);
# D- d- m0 Q7 |2 c0 k, R5 m) O p3.add(jtexpression);
% d! B( |) Y" e& X5 r4 Q2 a. S p3.add(jbverify);
9 j3 k4 f3 t+ E5 x# r
6 a/ o7 k. q/ O4 e5 V2 M- ~ add(p1,BorderLayout.NORTH);
4 Z! B- Z) U& |: e) T+ h* F add(pp,BorderLayout.CENTER);& V5 ]$ [9 h! q8 e1 x) l D4 f" e
add(p3,BorderLayout.SOUTH);
) e+ A* e1 D/ D/ x9 R
% b0 @% V+ i% V {/ v ButtonListener listener = new ButtonListener();. N+ b/ W# {4 j
jbsolution.addActionListener(listener);! j3 C; J M+ j9 t4 ]3 B
jbrefresh.addActionListener(listener);
" I) l$ T: Y! U5 ~ jbverify.addActionListener(listener);( ?& Q' n+ o4 Y" \1 r- {
}" L) n- z1 { A" U# F8 ?
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class ButtonListener implements ActionListener4 i; {# o2 l- I. o' \1 i( ^- H
{4 F2 x6 q4 t0 n* B2 u5 p
public void actionPerformed(ActionEvent e)
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if(e.getSource() == jbsolution); f- J' s' ~- x8 L b% Y e
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for(int i = 0;i < 4;i++)
0 x9 |5 \* k5 p( @" } {
0 I+ x. G* M2 x, h U+ x bcard[i] = (double)card[i] % 13;4 {2 g4 v# S5 R% A& g- I
if(card[i] % 13 == 0)
& x' b) e8 u4 u9 \( I3 d% @ bcard[i] = 13;
; V3 ?% O& Q2 O/ L3 T& G" o2 P }) }& {6 Z( k4 E+ `+ P& E, Y
search();
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else if(e.getSource() == jbrefresh); C1 a) P, E' R# I) k
{+ d% I4 N1 S8 I- e$ l. j
pp.sshow();
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$ h% p% I. m+ [5 i' N0 W }
2 }0 F7 a; e' M/ Q' z) h- d% b else if(e.getSource() == jbverify)% o. n, ^4 w k- H' d& E
{
8 t& \6 l5 E! A$ G6 _ x/ ^4 j String expression = jtexpression.getText();
5 T; C' z3 y' q8 u/ C int result = evaluateExpression(expression);
* T& w3 ~/ e8 U if(result == 24)3 }9 b1 d0 v4 C h( }0 f
{
" Z% R& R2 ~# C0 @ JOptionPane.showMessageDialog(null,"恭喜你!你答对了!","消息框",JOptionPane.INFORMATION_MESSAGE);
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else, b4 {5 I7 \! T0 x
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JOptionPane.showMessageDialog(null,"抱歉!请再次尝试。","消息框",JOptionPane.INFORMATION_MESSAGE);- _ n6 k4 _% j
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}
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( v6 P' Q. X- |1 d# @+ U public static double calcute(double a,double b,char c)! c+ \* v' G7 D5 i
{
# y6 H9 z- y9 A' a% n if(c == '+')) w9 n* Y) O4 b! m5 \
return a+b;
3 r2 x' r$ q3 y: i4 t else if(c == '-')
" ^; o. G( L8 B! s' q- R return a-b;
: t3 I* ?0 R" B9 [ else if(c == '*')
* n+ l' ]( b& F8 ?' I& ? return a*b;
8 N8 |# J c7 [* f else if(c == '/' && b != 0)
# v; G0 ?6 C1 n2 F B5 ] return a/b;" c8 J. c9 t7 ~8 {) T
else
6 _6 L; i5 x" m+ {2 p$ O1 s; m9 M4 o$ j return -1;
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. f1 F* a) D$ S( T6 r public void search()
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+ }( ~* I2 [/ C5 a) _ boolean judge = false;5 X$ z7 x8 ?4 Z- b/ c
for(int i=0;i<4;i++)5 u2 W/ |: p! r2 M% [
//第一次放置的符号
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$ x3 y9 B4 K7 k% t for(int j=0;j<4;j++)& I1 X9 ]3 W9 b8 j' A
//第二次放置的符号; B; F2 a9 X7 x5 f \) x; y+ ~$ Z+ c9 @
{
% H% }1 G# s. X* ]7 Q# s- Y for(int k=0;k<4;k++)
2 f% r2 d1 g% s //第三次放置的符号 p+ v! h5 g& k4 f' }/ B
{
) S0 E# ?$ F, X6 A' A for(int m=0;m<3;m++)
. C0 |! E8 h' n5 _1 h //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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if(bcard[m+1]==0 && sign[i]=='/') break;
9 h+ \; x& E4 B8 A* P temp1[m]=calcute(bcard[m],bcard[m+1],sign[i]);
: @9 \+ j0 p3 w temp1[(m+1)%3]=bcard[(m+2)%4];
% t7 I# i0 S9 G+ b- t# c* m temp1[(m+2)%3]=bcard[(m+3)%4];
) x. Y2 t8 ] ]% |+ w z: t2 I //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
4 F5 D4 W7 m2 }1 [! N- Q1 N for(int n=0;n<2;n++)9 S2 H1 W8 T3 d% y
//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 e( s: |. ?4 C5 E
{
+ R- P+ U- R0 |3 `9 |3 y* b( w7 x if(temp1[n+1]==0 && sign[j]=='/') break;2 N( h8 h- K7 {% B6 R4 M
temp2[n]=calcute(temp1[n],temp1[n+1],sign[j]);+ n4 C7 _2 m; I7 \2 |0 r# Q
temp2[(n+1)%2]=temp1[(n+2)%3];) x# \( {0 y4 b, f0 x
//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
. w3 [0 ~. o T# z/ | if(temp2[1]==0 && sign[k]=='/') break;
. w$ z9 \ s p. z% ` sum=calcute(temp2[0],temp2[1],sign[k]);/ {7 E/ Y+ Z2 `$ ?
//计算和
8 q, ^6 ^+ d2 Z, h( [ if(sum==24)
0 p8 i X6 U2 _ K' p5 b7 { //若和为24( \! z1 a2 X0 p! b0 V% Y
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judge=true;
3 B1 K* R; I- `( z6 A //判断符为1,表示已求得解
: n( R% z$ [- n) H+ b, Y& J1 {8 p- { if(m==0 && n==0)1 o5 X; x" L. X$ v! Y! X
{
9 d' L( ]9 D0 A- i5 o1 F String sss ="(("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[j]+(int)bcard[2]+")"+sign[k]+(int)bcard[3]+"="+(int)sum;
0 Z8 `: D- Y8 l! J jtsolution.setText(sss);
$ J; @+ K. u& y* l& a return ;
% F' g; t# P" T+ p ? }% F' G3 o( }" j {
else if(m==0 && n==1)" P$ k1 L9 {1 B% H
{
$ j. O' ]# L0 ~+ | String sss ="("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[j]+(int)bcard[3]+")="+(int)sum;' n" ], D. I' y. @9 T; |/ d7 b
jtsolution.setText(sss);
& H3 i5 k1 V2 w4 [* b( K$ n return ;- ]& C1 a! z: X& M' `6 P
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else if(m==1 && n==0)2 z I6 }' q5 [5 r/ W
{
2 M0 Y2 Q% Z$ Y: o* } String sss ="("+(int)bcard[0]+sign[j]+"("+(int)bcard[1]+sign[i]+(int)bcard[2]+"))"+sign[k]+(int)bcard[3]+"="+(int)sum;
: _/ u/ N$ z9 s; M, w; [ jtsolution.setText(sss);
u8 M; g/ o8 M0 F% F return ;
7 c2 P* `, L3 [3 Q7 c2 a }
, P' k% c3 k9 T6 H; z6 w else if(m==2 && n==0)' J, G8 s j; h; J
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String sss ="("+(int)bcard[0]+sign[j]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+")="+(int)sum;5 _5 u( Y" r" N5 Y' L
jtsolution.setText(sss); b6 r/ m8 W7 e7 r' Z! s5 {% P
return ;) M1 |& g5 ]( E, K3 s: T
}/ z, ~- `/ ]) K1 \
else if(m==2 && n==0)
$ L. M/ _) u9 t {% ?$ H& j u7 d$ m# J) H2 j
String sss =(int)bcard[0]+sign[k]+"("+(int)bcard[1]+sign[j]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+"))="+(int)sum;) L1 p! T( Q8 P2 J$ `
jtsolution.setText(sss);! z4 M0 A3 r' g N2 W4 _4 T1 z
return ;7 F$ f* m8 w! `6 c# { K
}
+ \, {, W' _* i; I0 X7 a6 d0 X //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+ w1 E$ U: D( z* k) S' s
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}
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}
7 ^2 f; j3 C) q) u, ` }
- V9 R( @5 `5 d3 I3 q; y }
8 D4 i. v/ N7 n6 X if(judge==false)- I+ |, l; }5 |! z1 ^ H" x$ L
jtsolution.setText("No solution!");' i4 @/ t: O$ f6 W- h8 `8 z
//如果没有找到结果,符号位为0$ [* f2 q7 ~- J
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public static int evaluateExpression(String expression)
5 |9 T' \: B0 B* R/ i {
( U# i8 Y- h# h/ n: X- v c4 h // Create operandStack to store operands
* S. C2 l# d b0 J2 ^+ { java.util.Stack operandStack = new java.util.Stack();9 m6 n8 Q% a. D
6 g; c }- b2 J$ I8 K0 Y // Create operatorStack to store operators% n# e" u @4 ~+ w8 \' G
java.util.Stack operatorStack = new java.util.Stack(); p, ] b5 p6 u. z2 {
4 v+ U! s) |& n) k
// Extract operands and operators
& B& t+ Y2 H# i5 J java.util.StringTokenizer tokens = new java.util.StringTokenizer(expression, "()+-/*", true);0 r6 h: y8 Z: q- N3 q* Y
; T* Y8 W+ t/ q/ N8 \0 \2 a // Phase 1: Scan tokens& |3 f8 X2 W( m. }# K% f
while (tokens.hasMoreTokens()); w7 e( W/ Z6 w" D
{' }* |0 ~" z& [$ P+ ~9 e
String token = tokens.nextToken().trim(); // Extract a token m' L/ C2 u7 `- d! ^( A
if (token.length() == 0) // Blank space
, s# g+ P; f, W1 A continue; // Back to the while loop to extract the next token
6 Q9 K9 F c. a* q" `) @' I else if (token.charAt(0) == '+' || token.charAt(0) == '-')
( f, J4 V1 h* `+ L {
, k; |* `+ [1 C; [ // Process all +, -, *, / in the top of the operator stack
9 I1 ?9 ]1 _: P while (!operatorStack.isEmpty() &&(operatorStack.peek().equals('+') ||operatorStack.peek().equals('-') || operatorStack.peek().equals('*') ||
; p' l4 u2 R, N, P' k, }$ s. S operatorStack.peek().equals('/')))
9 a: o7 _$ F% Q6 G: m4 k" { {+ j& m! w, Q* o6 m# a: @4 ~4 D- r
processAnOperator(operandStack, operatorStack);3 T4 e: r% w# N8 i7 N% t
}
) {# ~( I& o% }+ b; H: i/ c3 Z // Push the + or - operator into the operator stack P4 S! ?. Q! ~8 X4 h
operatorStack.push(new Character(token.charAt(0)));; @; t$ g9 c ]1 N) o% v Q0 q |$ ^
}
% I/ o1 g* V) Z, t1 ~* f+ k6 ~* i5 W else if (token.charAt(0) == '*' || token.charAt(0) == '/')
7 O1 L2 a# [% S4 ~2 h0 D/ T/ r {( N8 A+ ~8 h( g, H0 _
// Process all *, / in the top of the operator stack6 V1 G9 d; ?% u3 `8 o' k* Q
while (!operatorStack.isEmpty() && (operatorStack.peek().equals('*') || operatorStack.peek().equals('/')))
5 ?# C* P! ]# x z {
' c5 p, |3 |" n9 o processAnOperator(operandStack, operatorStack);
% d% i( F% F: m$ v4 M4 \ }
2 b6 q( P& q6 s4 E' n
5 s0 z; e! K9 P9 \- Q0 h // Push the * or / operator into the operator stack
8 z) q. H% W& \0 K0 H0 d( D operatorStack.push(new Character(token.charAt(0)));/ E4 K6 V8 ]+ o- k0 d
}; C+ d7 g, v& m
else if (token.trim().charAt(0) == '(')" j& g, v: }8 i. M" d4 D0 w% v
{
$ z# q T7 ~& K' w& I7 s% G operatorStack.push(new Character('(')); // Push '(' to stack
! p2 Z$ D _ L6 C6 T9 ]- t% p }
' r. T# x4 e8 S5 R& T else if (token.trim().charAt(0) == ')')- w* ^, V2 s; d
{
, H' I6 W6 j5 w% D! i // Process all the operators in the stack until seeing '('
7 _0 ^/ G Q. z& q, C7 O* _* Z while (!operatorStack.peek().equals('('))7 V7 ~$ }+ H" w+ Z) J
{6 q$ ?6 }3 P, \6 f2 V% N! G' z
processAnOperator(operandStack, operatorStack);
4 B- d3 p5 y6 o' |5 d' j }
+ ?$ D. V# K1 J+ W, N# y7 @ operatorStack.pop(); // Pop the '(' symbol from the stack
; b1 ~3 j' T& B9 A/ R }
# `+ g4 D( Y! l+ | else
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// An operand scanned
. G4 R4 B5 s+ {+ W' `6 j- u7 F // Push an operand to the stack$ S. w8 b9 H+ a0 w7 s
operandStack.push(new Integer(token));' o% V; I! y& d# @& {. ?
}
+ \) n* D O; @4 |3 n3 m }
2 V* N! A& b" a r
5 p1 s/ x# I: [/ I; O // Phase 2: process all the remaining operators in the stack
9 v1 @" a2 G; B1 m- O: i* |3 k3 w while (!operatorStack.isEmpty())
: X. Y# u/ Q9 q# d3 V {% u/ k2 Y2 P3 K( l. M
processAnOperator(operandStack, operatorStack);6 p6 H* _* q. R) F/ t2 z
}
, g% W k( v9 x' l
) j8 F& u2 A, J# _, a // Return the result+ V7 U5 @1 @2 H+ e3 O3 k( X0 p
return ((Integer)(operandStack.pop())).intValue();. ]$ v: N7 {2 }. {7 d7 T. N3 D+ w
}/ C7 i; S4 u) H$ ?
0 d& h" U6 G0 b( g, G
public static void processAnOperator(java.util.Stack operandStack,java.util.Stack operatorStack)
( ]2 W, B# p* o$ b# W9 P; \- j4 E {
; Q" F2 A- K$ L8 c. d0 a if (operatorStack.peek().equals('+'))
; @5 B$ R j7 x0 c- n. d {3 g" h, e& ]4 C2 R' ?4 ~! T
operatorStack.pop();- h: w( @5 x( G1 H
int op1 = ((Integer)(operandStack.pop())).intValue();
* w& d o4 H C9 ]( u, f int op2 = ((Integer)(operandStack.pop())).intValue();
3 x4 G- ?$ l; ~# N% ? operandStack.push(new Integer(op2 + op1));' ~: X$ S) ?7 w- B
}9 Z' \- \7 S% k/ N
else if (operatorStack.peek().equals('-'))' y, O4 K7 M) f9 u9 Y. p. d% _% O- t" J
{
: c( C: Y* E2 m3 r. h7 i$ L8 A operatorStack.pop();
" [/ |) I; s; J6 ~ int op1 = ((Integer)(operandStack.pop())).intValue();/ Z, E' W4 E# d
int op2 = ((Integer)(operandStack.pop())).intValue();; M: f' s% g7 M2 q6 k" ?
operandStack.push(new Integer(op2 - op1));
' _7 t2 C) v Y7 a' V6 a; D }9 {: {4 S" r: D- l
else if (operatorStack.peek().equals('*'))
( A4 z3 f4 E F2 A! T- ^8 r( M {% N4 r7 A% \8 e' I. n' P# S
operatorStack.pop();; F$ A+ _9 o$ ~& Z/ N# j/ J
int op1 = ((Integer)(operandStack.pop())).intValue();
& L8 W! G- E) i/ `2 I1 | int op2 = ((Integer)(operandStack.pop())).intValue();
+ y' H0 {; d) ?1 W$ k( z operandStack.push(new Integer(op2 * op1));
3 F. y1 v$ u+ S- y, g }
@ n7 I/ ]/ ^+ k/ m: W4 W else if (operatorStack.peek().equals('/'))
6 Z2 k K- }" Z1 k( Z v {
% N( y* v5 w- ^ operatorStack.pop();/ u Z0 b; `; a5 d8 R
int op1 = ((Integer)(operandStack.pop())).intValue();2 ]; l1 F0 K' E, I
int op2 = ((Integer)(operandStack.pop())).intValue();
9 W! J- m5 M. }0 {/ ] operandStack.push(new Integer(op2 / op1));
9 P; r% ]! m0 J9 h! W }
0 Y# p9 v( T. i" \) Z$ P7 F ` }
% x5 O+ r( p$ h- C$ p& h 4 ^" q2 {% g9 n0 C! t
class ImagePanel extends JPanel- j) d+ C1 n& |/ f8 Z4 F& S
{
- I& Y5 M$ u3 {4 F5 }4 M public void sshow()
3 s$ {3 ~0 r4 P' @7 o& W2 Q {
! D3 f# @$ q) f# I int i;
/ N( Z# c" _% u: _4 w1 t4 x& V for(i = 0;i < 4;i++)& d7 U& f3 V0 n, U) ~; e
{
0 X0 t! K. }9 N9 w- ? card[i] = (int)(1 + Math.random() * 52);
; h; i+ {! A! x }
0 L0 \2 a& _9 U$ U repaint();( V% N1 `% ^ j$ ?+ h' V, h
}9 y3 \& [6 Y' u' n4 `
+ ]- x* S; k% A1 f1 p9 f/ z& { protected void paintComponent(Graphics g)
' @9 r$ x% ^* z7 r) }. l {
# q4 M+ L" ]" F) Q! Q' |% d; `# i super.paintComponent(g);
+ Q% u; n* I3 B2 y( b& I2 o! h& S+ O int i;+ Q! ^0 K& n0 h
int w = getWidth() / 4;
2 n `' @5 D- `, E% g3 }, B int h = getHeight();/ R, k' R9 x% t' O8 W
int x = 0;( Y4 f9 x) Z' I' z6 |4 S* p. ]+ `
int y = 0;8 x/ J4 [* v1 N% h$ z- V
for(i = 0;i < 4;i++)' {, S) e1 Z: ]* O3 c
{
8 n5 I0 d2 V/ }! @6 f# T ImageIcon imageIcon = new ImageIcon("image/card/" + card[i] + ".png");
2 y: t% ]9 h* L- S Image image = imageIcon.getImage();. [" a5 y# o1 f) O8 F- s3 n, F
if(image != null): h9 _% n" i r* n
{
( M4 z9 P! V" y: } J4 t% A6 L g.drawImage(image,x,y,w,h,this);
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x += w;, t* d* d" B/ T6 v+ B( Q7 | j
}
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public static void main(String[] args)
5 \( M* X" e( A9 `( v, p {
1 F+ i! P, ]! r9 f TwentyFourPoke_Game frame = new TwentyFourPoke_Game();
7 O- N- P* e9 X9 m# F! W: ~: }1 j* k frame.setTitle("24 Poke Game");2 c1 A: @7 k9 @8 m7 P' f: o& J
frame.setLocationRelativeTo(null);
2 Y* V8 k: l2 s, `% z" r frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
7 {" A0 F% A* H6 f" q' ~ frame.setSize(368,200);
" }$ @- ^6 n& J$ w8 [* E frame.setVisible(true);1 C2 D2 B. \) z6 y1 R+ e
}. z, P w+ q/ L6 c2 f
} 复制代码 9 ] z- U6 A- i9 x
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