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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。4 s0 I7 R9 e2 N! Y
# s& K( i# @* S. R6 \ 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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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。7 W3 j3 Y+ t" r; ]. ]1 V4 X
6 y" B/ c- S& \ 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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以下是java 源码 :
& C% t) N; V4 Z6 `) n8 B# L import java.awt.*;
+ R( ?: t4 U- I7 H! r/ A6 E& q! t import javax.swing.*;
8 @. K7 A# D; E& ^) | X8 M import java.awt.event.*;; K: x8 X' ]9 `6 f1 Y# A5 A s
import java.util.*;
* t. s' p" i- l import javax.swing.JOptionPane;" ~7 T6 u2 i$ \# \( S
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public class TwentyFourPoke_Game extends JFrame+ T: }5 F/ l: c! g* h: @5 i! b
{
3 W2 D6 r) ~3 C* ~8 U private JButton jbsolution = new JButton("Find a Solution");
. D9 s5 _" }* S% C: c% X" f private JButton jbrefresh = new JButton("Refresh");
& ~ g# `' l2 B private JButton jbverify = new JButton("Verify");' q9 n. P) d' s: ?' F
1 w( I# m" B# L& ~3 d) ^3 s; l
private JLabel jlmessage = new JLabel("Enter an expression:");
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+ @: p" L& |8 }6 K* N+ a private JTextField jtsolution = new JTextField();5 K8 t; i2 ^# z, y' U
private JTextField jtexpression = new JTextField();; I: O0 l- @: ~2 s. x! A1 c
7 s, U1 C9 h# s, e$ _ private ImagePanel pp = new ImagePanel();$ E1 e, l: X9 y7 Z1 Z" [8 N1 i
. I% J+ s" s& C8 v8 G
private int[] card = new int[4];0 @( R! I; C& G
private double[] bcard = new double[4];
! |6 [0 }& d% s6 _
/ D1 I7 y, {6 ~# x$ ]8 h private double sum;
1 T) ]1 f0 U* j5 F; T, o private double[] temp1 = new double[3];& Q" y. w# ^! n. p# C. [7 Z
private double[] temp2 = new double[2];' I* R! Y( `: E7 H; N% h5 N. j' Z
private char[] sign = {'+','-','*','/'};' M2 T' f7 }& Y* I f1 D% ^) k
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public TwentyFourPoke_Game()
$ p2 ?# i6 }# M- p {
) M' E6 H* ]- G JPanel p1 = new JPanel(new GridLayout(1,3));
* _" n/ y5 X7 C6 `2 \( ] p1.add(jbsolution);- Q8 s1 R3 p; Z" I
p1.add(jtsolution);* F! Z4 V% t! ^, ` p$ f# F* h8 D
p1.add(jbrefresh);. _3 ^5 P% x f5 M+ P6 n8 x0 C
JPanel p3 = new JPanel(new GridLayout(1,3));3 V2 R# r& Y% z+ g4 H
p3.add(jlmessage);
$ l" R) ^8 }( k2 a p3.add(jtexpression);' Y9 r% `2 j+ ^5 v
p3.add(jbverify);, i0 x% s E# n' M& }& u
# n( n+ G. L8 n- v! N- }5 @
add(p1,BorderLayout.NORTH);7 P" u ]% R7 T7 f
add(pp,BorderLayout.CENTER);
! ~6 _& ^1 ?' K. h& O! o9 W add(p3,BorderLayout.SOUTH);5 C9 t; n3 o( B: U/ B: \, k
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ButtonListener listener = new ButtonListener();
8 ^6 L Z1 S; k0 E jbsolution.addActionListener(listener);
( I0 ]4 k: o. {" o |& V3 K4 H6 U jbrefresh.addActionListener(listener);, h+ z* Q0 k3 p, L# k/ w, y
jbverify.addActionListener(listener);8 x$ J* \. s7 d4 s- H
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3 G8 G3 X O; X* d$ f9 B: M5 s; M
class ButtonListener implements ActionListener
1 f! G w+ M' X {
# _$ h$ G- S5 I6 f& C public void actionPerformed(ActionEvent e)8 Z# w7 G7 ?% y7 g7 j& c5 V
{4 q6 w9 C: b$ N- g# o+ a* n
if(e.getSource() == jbsolution)
6 w. L, _. G" m3 g/ } { }, }8 M6 D2 p7 E4 H) Q+ |3 b% b
for(int i = 0;i < 4;i++)
. m: ]: T$ s4 v, a+ I7 O, q9 |/ N# w {
5 P6 A4 ^7 g# w) L- I bcard[i] = (double)card[i] % 13;
0 B) V' [2 D7 e7 S0 P0 I$ E7 S if(card[i] % 13 == 0)
9 w8 g9 {- W5 q% b3 x8 ` bcard[i] = 13;
( G1 r7 u8 Z* x8 b }
# N3 p) I3 v2 I; Y& J6 B5 T" Y search();1 h2 V0 B5 s4 L" n- i+ m. y
}
7 q; D3 H" k8 s else if(e.getSource() == jbrefresh)1 J ]" N8 z i2 t
{
: |& R6 Y5 v6 X pp.sshow();
2 F0 G0 ?! M8 o2 D # E4 ?: z: y3 [# h
}! ]% f# H. y- X( z [
else if(e.getSource() == jbverify)
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, L( X4 z" R- }$ q* c; B0 S7 ] String expression = jtexpression.getText();; ?* B% n, G2 F: P0 R- M
int result = evaluateExpression(expression);6 }; d4 y* x! V, a# @$ Q
if(result == 24)
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JOptionPane.showMessageDialog(null,"恭喜你!你答对了!","消息框",JOptionPane.INFORMATION_MESSAGE);+ D9 _& h! S- ~+ v# i
}
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JOptionPane.showMessageDialog(null,"抱歉!请再次尝试。","消息框",JOptionPane.INFORMATION_MESSAGE);, N8 f4 t4 C" w! B1 q+ O; S
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}
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public static double calcute(double a,double b,char c)/ J: m7 v$ R+ I
{
' a) n8 o3 ^' K5 n6 x* u) [4 s if(c == '+')$ Z# s0 D# O. d3 l, K5 h b* }
return a+b;6 A: x; A+ s$ ~4 s+ A5 A
else if(c == '-')9 z5 H. L% V& W$ }0 F% T
return a-b;
, f: H4 W& F$ u# j8 Q else if(c == '*')
' d& i8 c, l. P' h! y return a*b;
d Z' `$ T5 A5 b! w else if(c == '/' && b != 0)3 a* T1 k+ z; {* }5 e3 l ^% t
return a/b;6 N- ~: `$ {6 C+ Y% |
else* ]' Q* p- N/ C' ]! y
return -1;+ H! E: F2 s3 l6 G8 ~
}
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0 b. g, K0 y( b2 p a; N1 f public void search()
" W7 F# U7 {0 _3 p6 e3 ]5 K {
0 t: l5 L. p1 e& T boolean judge = false;
" h3 ^! u8 B2 z# ?9 T$ T# J, P for(int i=0;i<4;i++)6 \* n* v `9 m: I. Z5 n
//第一次放置的符号+ b/ u/ M$ L: t" Y: N4 R
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for(int j=0;j<4;j++)8 A9 ], a5 {; l% Y2 m w( D0 `
//第二次放置的符号% \& ?' V2 \$ A+ B
{
/ d' y0 L! ]9 Q' `. }0 c for(int k=0;k<4;k++)
2 B. G* Z# y5 P0 G' n7 @ //第三次放置的符号8 C0 }9 S3 d8 g: \5 E( }; H5 f
{" i8 @) q& @8 u- N0 A1 J1 ^* \8 {: k m
for(int m=0;m<3;m++)
) \' f6 a$ \* k- D1 B X //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' m* u( ?( `: s; X, h
{
0 Y9 |( B' x7 |( Y; Y5 s* T if(bcard[m+1]==0 && sign[i]=='/') break;
8 a+ M& K( C3 Y* Y, t5 E temp1[m]=calcute(bcard[m],bcard[m+1],sign[i]);
" B$ ?) d5 C( ]- H temp1[(m+1)%3]=bcard[(m+2)%4];8 @4 U, u0 ^8 v, ~1 q8 v
temp1[(m+2)%3]=bcard[(m+3)%4];6 [! y) D6 C3 Q' b
//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7 S9 j6 m5 h; ]" {9 e1 H" f
for(int n=0;n<2;n++)8 b' |/ r5 |5 f; B& M9 Z
//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
# R4 T' K& ~5 O8 @7 Y2 ` {
! j& f4 ~/ k0 q- y& l+ C- L if(temp1[n+1]==0 && sign[j]=='/') break;/ M6 U, C9 t& R# K# E1 Q
temp2[n]=calcute(temp1[n],temp1[n+1],sign[j]);
! `% c+ z& Y8 ]7 l temp2[(n+1)%2]=temp1[(n+2)%3];
7 u" y% Z% ?/ c1 [0 n s; G //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
6 h0 v8 q, y. \9 S/ S. b if(temp2[1]==0 && sign[k]=='/') break;% {! S/ l, m. E1 b* o8 l: r1 Z
sum=calcute(temp2[0],temp2[1],sign[k]);
/ {: q/ J. P; m" }& d' [. V' I //计算和* G# v3 h- m0 ?, {7 |
if(sum==24)
7 [- {- A6 q* h$ z. y) F) I. Y) w! ] //若和为24" R* k. ?8 [& g2 a8 V7 { j
{
8 E6 I- V. a0 j& y judge=true;
& d+ `% j U+ b! Y! ` //判断符为1,表示已求得解
# G5 H' d4 d: O$ i. U if(m==0 && n==0)
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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;3 v2 A0 J$ q. h2 U" y6 r: Z
jtsolution.setText(sss);
5 G$ g7 m9 |. a6 F return ;9 R0 _! e$ O0 T- u4 c
}
+ i N# ` |0 `9 m' u else if(m==0 && n==1) ^) [, L1 B4 Q- A O. C
{6 b5 h/ S$ ?' o# L& g' f: K! L
String sss ="("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[j]+(int)bcard[3]+")="+(int)sum;
& l s; |" \1 I/ i% U/ k( t jtsolution.setText(sss);
) c/ k% S* L; u return ;
: {( l" O7 q/ z( r }; g- d3 U' f* Q; |5 r r0 p
else if(m==1 && n==0)1 T. T+ j' U, H! v) D/ N3 g
{8 k5 h, s1 x3 d4 L$ ~4 ]* m
String sss ="("+(int)bcard[0]+sign[j]+"("+(int)bcard[1]+sign[i]+(int)bcard[2]+"))"+sign[k]+(int)bcard[3]+"="+(int)sum;
( G& p5 w) s: O+ ~. k6 M! q. O7 { jtsolution.setText(sss);7 s6 L# M9 `: e( [4 A
return ;
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else if(m==2 && n==0). D6 w1 j8 R, a+ N9 Z
{
: D3 b! B8 r4 j String sss ="("+(int)bcard[0]+sign[j]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+")="+(int)sum;
; F5 t9 P7 ?! Y7 q, O. n/ t jtsolution.setText(sss);2 @1 ^( p$ v6 }- @) L
return ;6 {& w) v0 S M# S4 O
}7 Y+ r8 f1 g1 o& t/ ]$ o+ `- y4 n
else if(m==2 && n==0)
# I3 K; @& J: s {& p! v5 x' _+ f5 o$ @- v1 b7 j4 H
String sss =(int)bcard[0]+sign[k]+"("+(int)bcard[1]+sign[j]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+"))="+(int)sum;. F% R Z' H. P1 n
jtsolution.setText(sss);
; H, u( H7 K* K7 c, X return ;- B. N+ f0 A: V7 W) r
}8 g$ ^% f2 X3 l) f& k
//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7 c7 N' T$ }3 m/ P
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}
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}
i. J* v! h8 H0 w. e% @ }
) q6 t' {- ?& d: D" M- ? if(judge==false)
- E0 \' i1 V! J2 L0 C jtsolution.setText("No solution!");! W O5 @8 [0 t! L& A% {+ N
//如果没有找到结果,符号位为0+ H& _. o5 R7 `$ r& s6 `3 n
}
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, p' O* {/ V8 ?4 d4 {8 ^3 W public static int evaluateExpression(String expression). A0 i3 }% z, R( T# t& P: f
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// Create operandStack to store operands: n6 i" N" @. ~1 R1 r F
java.util.Stack operandStack = new java.util.Stack();
4 i% P/ B7 ^- N! }6 T8 Y) l 3 o$ Y& W5 J& c( Z) z3 B
// Create operatorStack to store operators; Y" y. \/ ]( ^% ?3 H- w# E+ B/ z: B
java.util.Stack operatorStack = new java.util.Stack();
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// Extract operands and operators/ l/ O6 B, W5 i Z+ d- T
java.util.StringTokenizer tokens = new java.util.StringTokenizer(expression, "()+-/*", true);
- ]. a9 _9 U2 F! o1 e2 F+ m
2 \3 Y% i7 i; a // Phase 1: Scan tokens* j2 ?# _' [4 B* k& t- a# Y
while (tokens.hasMoreTokens())# I- d, X" _" h" Z% U3 A0 q
{/ f2 m n: W& G8 z& a8 [. p
String token = tokens.nextToken().trim(); // Extract a token/ D3 L; {+ k2 a+ l" X
if (token.length() == 0) // Blank space
3 F7 Q; w. q4 A! B, n% H9 q continue; // Back to the while loop to extract the next token7 f$ i$ H% J1 I
else if (token.charAt(0) == '+' || token.charAt(0) == '-')$ c3 i5 @# J: v- V
{" x3 L( \+ z, h5 i3 A/ n
// Process all +, -, *, / in the top of the operator stack
5 C" n9 ]6 p+ V: T, p4 l: U0 G while (!operatorStack.isEmpty() &&(operatorStack.peek().equals('+') ||operatorStack.peek().equals('-') || operatorStack.peek().equals('*') ||& ^2 I2 }4 [% b. {4 X9 y
operatorStack.peek().equals('/')))
" B; ]7 i1 u+ A( r; {& U7 A {2 U$ d+ _3 E8 Z& L3 a
processAnOperator(operandStack, operatorStack);
2 j7 u3 g) B. D7 R) w1 @3 ]* b' L }* z2 u5 o2 z2 F/ ~! ~
// Push the + or - operator into the operator stack
# I! e/ O, I9 J9 F: q2 I4 y operatorStack.push(new Character(token.charAt(0)));. A5 F8 ^! U5 _+ {# C1 i
}
5 @6 X$ K$ Z! }6 m else if (token.charAt(0) == '*' || token.charAt(0) == '/')
9 j/ i& @& i7 @5 T9 w7 b {/ N9 Y9 z2 t4 Z6 m5 z5 v& N2 T
// Process all *, / in the top of the operator stack
$ z, k' x. p" V- C1 U while (!operatorStack.isEmpty() && (operatorStack.peek().equals('*') || operatorStack.peek().equals('/')))6 F; i- W2 z+ M. e% {
{* Q) c' @: _; U3 T2 E7 g
processAnOperator(operandStack, operatorStack);, S) e8 r) f$ b
}8 O$ q, D6 ~5 D+ p- t) K
9 g4 H m! R N) R, y$ t+ B' t // Push the * or / operator into the operator stack
" f, s V6 o* U+ N2 j4 [ operatorStack.push(new Character(token.charAt(0)));
& ~2 Q+ o# B6 M$ G9 i: Z }; u; s% B& ~( D' m
else if (token.trim().charAt(0) == '(')
6 F/ g8 ?/ e4 Q$ j7 t8 S! X( r7 j" G {
& @1 Z& X$ N' x operatorStack.push(new Character('(')); // Push '(' to stack
6 o: E$ ?! N0 B+ w" f8 @ }: H3 U( z& ?9 T d4 S
else if (token.trim().charAt(0) == ')')
" ~& p, g; c, H7 W( T1 G- G, @ {
3 t) _* @2 k" @ // Process all the operators in the stack until seeing '('
/ D! b4 `$ V' m4 C7 k while (!operatorStack.peek().equals('('))7 M2 |. D3 p. X! k' n
{/ Z: Z: K" _8 f9 q- S( F; C
processAnOperator(operandStack, operatorStack);0 F6 q5 z) ?" w1 ~! z
}
, Q# F8 y5 m) {' L operatorStack.pop(); // Pop the '(' symbol from the stack* q5 I6 y" [5 c- _# |& L" l6 v( n
}
# O1 [) e+ D/ o$ _1 t4 n else m% K# M( C8 a3 n( h
{! W2 ^1 i) _0 ]6 W, K* ]/ n+ v A
// An operand scanned. k- g4 z& X7 ~6 R
// Push an operand to the stack% [% n( \+ `9 F3 D6 o
operandStack.push(new Integer(token));& Z% e) {0 I3 B0 y! T n. W/ j E
}2 v9 `" `! t* O0 Z1 Q$ y" [; D
}
2 o& d9 q# B$ T7 M5 h
" ]# v# k3 ?5 x* O1 r // Phase 2: process all the remaining operators in the stack
4 j# u: L% \+ u while (!operatorStack.isEmpty())
- Q* h/ @$ [* b! N {
% ]3 X. j5 o; x" l4 v* X5 T processAnOperator(operandStack, operatorStack);( S. f; d1 [* r: q" C6 O$ i
}! L. R% ?3 ?+ q4 W' l t
/ {/ j8 m6 O6 c6 P% Y* N0 D // Return the result3 L! D7 t1 `" e9 r# a3 e h- ?
return ((Integer)(operandStack.pop())).intValue();
f8 h: b m1 P" ^% ]' f8 L8 ] }/ _8 u6 X, @& N0 n1 G k& v
; O7 E" ?" H' H public static void processAnOperator(java.util.Stack operandStack,java.util.Stack operatorStack)+ ~! Q- L$ J$ i8 ?6 e2 {' j
{& e' ~& F [* D
if (operatorStack.peek().equals('+'))
0 ~( `" g# e9 @. _ {3 \% f6 l1 z! v/ ?
operatorStack.pop();' _+ F' v. B5 _
int op1 = ((Integer)(operandStack.pop())).intValue();
$ R3 @8 Q$ }, z0 C7 _ int op2 = ((Integer)(operandStack.pop())).intValue();; b/ l# J/ ?- B: z2 G- o5 D5 L
operandStack.push(new Integer(op2 + op1));/ `! r+ ]6 {$ \
}
}6 O u" M% a else if (operatorStack.peek().equals('-'))
# c e( V% ]" B% M {$ D6 P9 x! E& r( |7 S2 P
operatorStack.pop();
" Z, V- q4 L' C; k' I% { int op1 = ((Integer)(operandStack.pop())).intValue();5 r& g. Q0 ?9 F* z
int op2 = ((Integer)(operandStack.pop())).intValue();( w9 k2 t( H5 _& R: F
operandStack.push(new Integer(op2 - op1));
& n+ P$ @! C8 G% Y8 z. z }& _* o+ T2 Y1 E* a- W3 ~
else if (operatorStack.peek().equals('*'))
# }! [/ l8 l- q7 }5 n- A) Z& A$ l {
1 _5 C# m/ ~7 l `8 w operatorStack.pop(); o8 E. {5 E! n* k+ D% e9 J
int op1 = ((Integer)(operandStack.pop())).intValue();
7 k! t* V" s) X& I( p1 D int op2 = ((Integer)(operandStack.pop())).intValue();
, u+ i% [# f& a$ f3 g# t8 i" y. D operandStack.push(new Integer(op2 * op1));
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else if (operatorStack.peek().equals('/'))
, O3 b1 F1 `: g2 ~ {& ~$ L0 {" e% }
operatorStack.pop();7 H( G, _6 n1 f+ |+ s
int op1 = ((Integer)(operandStack.pop())).intValue();6 W' a; J* W! m+ m2 k2 I1 N6 D( T
int op2 = ((Integer)(operandStack.pop())).intValue();/ R! \" @2 X- Z8 G# i% c4 n
operandStack.push(new Integer(op2 / op1)); R- z. t: C1 V
}
9 t5 r6 [9 ^, h! \ e4 N }8 k5 U$ u4 n9 J- A0 D* L, u' ^3 H
2 I; e: s- w' C. S9 q& L4 g. X9 L0 X. O class ImagePanel extends JPanel/ [. O) J. s3 K! M# m, o& Y9 h6 i
{ J6 _6 H+ f" Z5 Y, Y- e/ F
public void sshow()
4 C2 w& Q8 v- ]$ d& J x {
0 S' w5 ~' m, S3 a int i;; H N2 e# h9 ^' Z# n, F
for(i = 0;i < 4;i++)3 z9 P" a- p7 i
{
! {5 G+ H# ?* H! W( p" Q6 Q card[i] = (int)(1 + Math.random() * 52);* k- L: l6 y1 ^9 E0 R0 t; v
}
/ d7 C2 \9 Y. S% z$ h, G repaint();) @) K( G1 o0 [$ `/ ?+ l3 B
}/ u, L+ D5 ~2 B. m; c& f& e
$ ?3 A8 T1 D) Z' y t5 x
protected void paintComponent(Graphics g)
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super.paintComponent(g);1 T& B) Z+ W6 C6 B" a+ G5 h) w
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int w = getWidth() / 4;8 B; T- L; }+ q v( W% v
int h = getHeight();
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for(i = 0;i < 4;i++)1 E2 K; b% }/ r9 m0 L9 {
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ImageIcon imageIcon = new ImageIcon("image/card/" + card[i] + ".png");
: r: l, G! `4 y K" g Image image = imageIcon.getImage();* E) ^) z" y* {5 N% @8 K: R% {
if(image != null)
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. E M$ b2 z1 q7 Y# Y$ k8 u) c g.drawImage(image,x,y,w,h,this);
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2 k; g; s( G6 u8 @* }" o x += w;
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}
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public static void main(String[] args)
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7 X" Y5 p3 S2 ] TwentyFourPoke_Game frame = new TwentyFourPoke_Game();" k& n2 k# j' v1 U
frame.setTitle("24 Poke Game");
/ c- G. Q2 a1 i6 B4 M( U frame.setLocationRelativeTo(null);) J5 G2 Y+ K+ E/ `$ O( u9 v! n
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);5 T$ q8 X. ~5 ^
frame.setSize(368,200);# ~7 E" p1 H- R) o6 ~9 s* A
frame.setVisible(true);
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3 J( P" m0 N9 B" l _6 k7 l7 Q } 复制代码
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