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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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' h- G: [6 C; Z- I* E" c 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。9 C- ]! b5 Q& S
, w+ F7 z8 s: T T& ^- m 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。) `% B5 Y/ _# c8 m8 ]
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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;, t: k9 t' V6 e! ^
: t9 K: n) [0 a9 @2 } 以下是java 源码 :
+ O7 Y" j" ^2 Z2 g- O4 T import java.awt.*;
0 \6 s9 X# p7 k, T4 Q; Z import javax.swing.*;
9 I8 D9 k# M9 A; W, _8 b import java.awt.event.*;% L6 I$ K, ?' e; e
import java.util.*;4 l. f% L) y0 S+ ]. `6 ~; x9 V
import javax.swing.JOptionPane;* k" m9 ?( q, R% m
; J0 ?1 V) a- [3 ]: e& j6 f public class TwentyFourPoke_Game extends JFrame! f! L- Y" e# ?2 z, ]" M* y# s
{
' X' l7 I9 l( ^: s private JButton jbsolution = new JButton("Find a Solution");% s W' f, w6 b
private JButton jbrefresh = new JButton("Refresh");
3 Q% e/ [+ J- M& n, c- N E private JButton jbverify = new JButton("Verify");5 F) u% v! _6 R! s) [4 Y
2 @& ~1 O" D* ^& z; z: ~8 L
private JLabel jlmessage = new JLabel("Enter an expression:");
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private JTextField jtsolution = new JTextField();+ k! B! {5 h6 L( P( j3 U4 A1 E
private JTextField jtexpression = new JTextField();
& F+ c- ?- Z, }5 C+ ]. X
6 M5 p* G* J, d) s2 E. R& W private ImagePanel pp = new ImagePanel();# S# X. E; C* o7 L# `. R/ Z
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private int[] card = new int[4];
9 t. k/ g5 ~/ w1 b private double[] bcard = new double[4];8 Z" K1 [, y1 q T
/ Y0 a+ ]/ S& X private double sum; X; @1 {# V, [; p- W, Q" N
private double[] temp1 = new double[3];
/ @4 a# h3 g$ J, V9 o, B& [. _/ | private double[] temp2 = new double[2]; j' O% Y+ G2 P( n! A- \
private char[] sign = {'+','-','*','/'};2 D* x0 C p6 p' n9 C4 q' x
+ Y5 o( c) ^0 M
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public TwentyFourPoke_Game()( ?4 J. J9 s" I+ ?! j
{
3 L R" c% w! W0 c1 c JPanel p1 = new JPanel(new GridLayout(1,3));
d8 u% G' d/ x p1.add(jbsolution);
Z( H, s" d$ s( A p1.add(jtsolution);
( Z ^: y# X& T! N- O p1.add(jbrefresh);
; W5 C% T7 c' j! m' k JPanel p3 = new JPanel(new GridLayout(1,3));
" I5 @7 [4 g, f) g+ c! n8 q+ q p3.add(jlmessage);# I1 W+ T+ t9 i" C% [5 I
p3.add(jtexpression);
- K+ r* f" X5 f$ S5 t5 {2 Z# \ p3.add(jbverify);% ?3 j1 L l! g( N" J1 a; g- C' U
5 T" L6 l* F& K1 t" `8 Z8 V- S
add(p1,BorderLayout.NORTH);
' f. s. f$ q( j+ j9 O' k7 g add(pp,BorderLayout.CENTER);' C* P, b! S. y* [6 P. U, x
add(p3,BorderLayout.SOUTH);% R6 i( s! i3 d3 v2 ]) B9 ?) \2 S# F
% B b8 B. _8 R4 N, b8 _& p7 A ButtonListener listener = new ButtonListener(); s0 |6 Y4 H* z: l, f
jbsolution.addActionListener(listener);, C8 ?. u6 D0 d0 u! W. T
jbrefresh.addActionListener(listener);
4 X" X8 z9 U5 ] jbverify.addActionListener(listener); |- \8 K. ^# k' n7 M5 r: c) @0 z
}
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class ButtonListener implements ActionListener, O) C, s }. Q4 @# S% P
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public void actionPerformed(ActionEvent e): S4 ]5 U% a# b; B
{
" ?8 x( k9 v! X9 L0 g if(e.getSource() == jbsolution)9 ^- I7 J9 S) o; V2 ~- K
{
. N* O# N! O( W* b" ` for(int i = 0;i < 4;i++)- x) [6 s5 E7 U0 T5 h
{
G9 A% ~) z& B- M/ v bcard[i] = (double)card[i] % 13;
K; V. ?; Q2 M6 e" T5 b if(card[i] % 13 == 0)1 ^+ {! j) W9 y/ H- E5 Q1 g; C
bcard[i] = 13;
! E0 `. _# F# |+ Q! M: }' N8 v& L }
4 S7 R. g, Z4 H$ l/ M search();
+ f8 t& v1 a0 [8 x }5 w! u( D$ V$ A0 Z
else if(e.getSource() == jbrefresh)
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pp.sshow();5 |; [4 r. s$ ?; D% ]
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else if(e.getSource() == jbverify)3 s! T" ?* \8 B4 p6 M9 m1 U* `
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String expression = jtexpression.getText();5 O ^$ @# v& @: l `1 B0 Z4 ~- e
int result = evaluateExpression(expression);
% O+ H& l' e5 C& v7 G2 A9 N1 z if(result == 24)2 ]0 u# L1 w7 n; r
{% X+ t, W6 H0 {2 D* a* G6 e; H
JOptionPane.showMessageDialog(null,"恭喜你!你答对了!","消息框",JOptionPane.INFORMATION_MESSAGE);0 K2 q; u3 l" N8 ]+ f; e
}
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{4 c4 X5 q: x% L) ]; p
JOptionPane.showMessageDialog(null,"抱歉!请再次尝试。","消息框",JOptionPane.INFORMATION_MESSAGE);2 O7 F1 p2 P3 C1 c# i6 [4 u6 ]
}
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}
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public static double calcute(double a,double b,char c)
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if(c == '+')
8 v" ~5 m/ k3 i- @& { return a+b;$ E! w/ ^1 ^. s0 n$ U) Q
else if(c == '-')5 ~' E% w6 [9 v
return a-b;4 v5 @. j: z! T* l7 M
else if(c == '*') A" V8 z( z7 O0 h, j K' Y6 S
return a*b;
# ?) w2 h/ S2 v; B- C& g# m else if(c == '/' && b != 0)+ _9 f( Z! s/ h" }, L: \( m
return a/b;. t' W( O, c D7 Z9 W
else
3 l6 I3 n0 n% Q9 N# B3 i return -1;/ w0 |5 x/ g% O7 {2 Z
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public void search()6 T$ _) Y2 X, `4 M. S% k
{
D) M7 |7 b7 v% G boolean judge = false;
( q+ A1 Z$ _; b n" ~% P for(int i=0;i<4;i++)) M4 ^- n9 t4 ^; Q. W
//第一次放置的符号) P6 C$ J& k7 Q% z. H5 q
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for(int j=0;j<4;j++); s& [2 s1 D5 c- t( [: Y
//第二次放置的符号9 Z8 V% i) b9 k. Z8 X3 H
{
' B# Q3 \, I7 R; a9 q! O for(int k=0;k<4;k++)5 h8 |. Z5 X+ O9 I9 ^
//第三次放置的符号
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7 e: x# ]$ m* q for(int m=0;m<3;m++)8 m( j* L3 P+ ]6 H3 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
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if(bcard[m+1]==0 && sign[i]=='/') break;
, k, c, L( z! |' F0 i temp1[m]=calcute(bcard[m],bcard[m+1],sign[i]);
4 c" r: ^+ v: c- q2 H1 { temp1[(m+1)%3]=bcard[(m+2)%4];
) T& a5 Y/ w1 F1 o7 f6 w) c2 } temp1[(m+2)%3]=bcard[(m+3)%4];
: A+ U' A5 y# x9 n" L5 J) 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+ ]" d* b/ M$ n, \' S% k
for(int n=0;n<2;n++)4 c8 h) l \+ H* q+ b$ t
//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;
) h' ]& w$ Q- @) e, O" l temp2[n]=calcute(temp1[n],temp1[n+1],sign[j]);( L& n) ]5 ~9 G* j4 E
temp2[(n+1)%2]=temp1[(n+2)%3];4 p* S9 D+ M2 M f% B
//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
3 Y- D' E! k- F. z0 ] if(temp2[1]==0 && sign[k]=='/') break;0 I( x* }+ `: x3 H8 a% u- a( [
sum=calcute(temp2[0],temp2[1],sign[k]);
" {" R+ ?2 {" R, G4 r& { //计算和7 g/ R. n4 n- x! t4 O" v4 n
if(sum==24)
3 R& \9 r* ]) d. T u8 Q# t0 D) J //若和为24
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judge=true;$ H" X9 o& _. n5 q$ h, r/ ^
//判断符为1,表示已求得解
# w2 X/ C4 e- k. | if(m==0 && n==0)
7 g& c( F5 o. {+ O7 u ] {
6 q2 q* [+ p# Q$ @& E6 v A String sss ="(("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[j]+(int)bcard[2]+")"+sign[k]+(int)bcard[3]+"="+(int)sum;! N1 O" V. D2 L
jtsolution.setText(sss);
6 }( ~( R1 o" F, x return ;
7 f# m7 x* w2 F3 T9 c/ a$ O' C }6 A& V7 K1 \3 q l/ v2 ?9 ]0 ^
else if(m==0 && n==1)
! N; {3 ?8 h" l {
; i: W. |( j ? S- l; L4 ~ String sss ="("+(int)bcard[0]+sign[i]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[j]+(int)bcard[3]+")="+(int)sum;
4 y7 b7 b' r" w5 {; l jtsolution.setText(sss);
0 R) N( `7 F8 C- H/ c return ;
+ Y7 B3 B0 A; ]5 J7 i) } }% f' t* @% j9 p' J5 h5 v
else if(m==1 && n==0)
9 {$ n1 I" J, ?7 W' K {
7 P& T; L7 L3 G- Y& c2 k& C8 _+ N& h String sss ="("+(int)bcard[0]+sign[j]+"("+(int)bcard[1]+sign[i]+(int)bcard[2]+"))"+sign[k]+(int)bcard[3]+"="+(int)sum;; p$ [, ?. [; N8 \/ K
jtsolution.setText(sss);( a! h9 V5 M6 [8 S; H- d# b# i- F
return ;9 E, u2 O" U! t" c; k- X z7 m0 h
}
* C+ U, I+ b$ U- A7 `+ w! H* V else if(m==2 && n==0)
7 h2 y7 h( q! T {
* O5 e: b- \+ h# e& v7 r String sss ="("+(int)bcard[0]+sign[j]+(int)bcard[1]+")"+sign[k]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+")="+(int)sum;$ U0 k0 T+ f7 G4 M( f0 y
jtsolution.setText(sss);
% k/ q8 v6 p$ ]4 r7 z" h3 l8 N return ;
# c( q) g/ Z8 H9 @1 P. I! V& P }
! \9 p) Y4 h2 B! |$ W: Q else if(m==2 && n==0)7 I- h3 K' w) ?4 n% X
{" M* N% @: e U0 Z
String sss =(int)bcard[0]+sign[k]+"("+(int)bcard[1]+sign[j]+"("+(int)bcard[2]+sign[i]+(int)bcard[3]+"))="+(int)sum;* ? l6 I1 T( J+ P- S9 u) Z
jtsolution.setText(sss);# V# L! ^ w3 l; {9 Y- g1 ^# `
return ;
& a! L: y0 Z9 S v' \ }
% x2 u6 @9 q! b! a0 j //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' H* k) ~ V$ ~. V& p- @
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1 F1 o( K+ n7 F7 n+ M }
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}
% J4 m7 Y7 f1 {, v9 V" h* [1 t2 H }& B% I1 j" T( p& `6 {9 _. @+ s
}
. s" A9 D# o6 \0 S- y! I2 y' z# T if(judge==false)! n" r1 R( L: S* @1 K2 Y# k
jtsolution.setText("No solution!");
" j ^7 M; ?) P9 y; D1 H //如果没有找到结果,符号位为0
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) L% u$ G$ a* ?5 c/ A$ }2 c: v public static int evaluateExpression(String expression)
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// Create operandStack to store operands* V% R; _, d, `) R+ U
java.util.Stack operandStack = new java.util.Stack();# A) X% s' f [
; X. K7 y( [. A+ g // Create operatorStack to store operators
9 m2 `( g9 [( J java.util.Stack operatorStack = new java.util.Stack();
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// Extract operands and operators4 K$ ^( T# l" B. K- l1 i+ e3 i6 m `
java.util.StringTokenizer tokens = new java.util.StringTokenizer(expression, "()+-/*", true);" S( q" u8 X' m( J4 W
8 t, G, }! B( @' K4 t/ O
// Phase 1: Scan tokens' R" w9 ~8 d }5 m" D/ `4 h; S
while (tokens.hasMoreTokens())
" d8 C* P/ j6 y' y; T6 T {
- ~) E' \- T1 g7 B5 t& H String token = tokens.nextToken().trim(); // Extract a token5 H2 ]% I1 `2 ~4 H6 C: }: j
if (token.length() == 0) // Blank space
$ r5 |; d7 @3 F# \! i, d' F* b continue; // Back to the while loop to extract the next token5 ` n9 w- l7 d, W e4 i
else if (token.charAt(0) == '+' || token.charAt(0) == '-')
# e7 L# R% L$ d- ?$ @8 @ {8 l: R8 _+ t6 F; y5 H, X
// Process all +, -, *, / in the top of the operator stack
& p" r! ~9 Q6 B. f n. h while (!operatorStack.isEmpty() &&(operatorStack.peek().equals('+') ||operatorStack.peek().equals('-') || operatorStack.peek().equals('*') ||
& i1 d ?8 H# t. i1 ~8 X operatorStack.peek().equals('/')))
0 B0 l8 N0 v/ V2 U7 c0 n {
$ {- t7 r8 T7 B1 L- W" a9 N processAnOperator(operandStack, operatorStack);# h. T* g2 o& d. `0 N
}" a- y6 Q+ x# ~0 [
// Push the + or - operator into the operator stack+ I4 }. k) f# c. V1 X3 k( `% d* j- }
operatorStack.push(new Character(token.charAt(0)));' Z; r8 g- i6 h8 ^4 l5 @4 g$ a8 T
}
2 a6 X5 ?$ y3 B else if (token.charAt(0) == '*' || token.charAt(0) == '/')9 o6 K; X6 n7 p9 x5 L
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// Process all *, / in the top of the operator stack
7 i5 P. ?( k! C+ e; v! a$ K; z while (!operatorStack.isEmpty() && (operatorStack.peek().equals('*') || operatorStack.peek().equals('/')))
" E7 n+ \6 z0 ? {& }( y$ k" V6 B* N, l; @
processAnOperator(operandStack, operatorStack);# v: i+ ~! W7 Q" y( p& K
}
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// Push the * or / operator into the operator stack
! q: k6 r( i9 Y* g operatorStack.push(new Character(token.charAt(0)));# i6 G9 O. \ B# Z
}
5 W$ E' C% S$ Y% V3 x else if (token.trim().charAt(0) == '(')
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operatorStack.push(new Character('(')); // Push '(' to stack
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+ ^( h0 U5 D! v6 Q else if (token.trim().charAt(0) == ')')
$ X6 t+ ]7 x. d# p9 g7 Y/ J {
7 Y2 r" H$ ], A$ T# J9 H/ u // Process all the operators in the stack until seeing '('
6 N6 \& @9 w+ N, k6 Y& F* u while (!operatorStack.peek().equals('('))+ ~. E- k; x0 F+ L. O$ q
{
3 w( g0 j \3 C- { processAnOperator(operandStack, operatorStack);$ \+ l% ?! w. o) ?8 W
}. m4 T1 N( P1 }8 ]) Z! \( h3 l9 c
operatorStack.pop(); // Pop the '(' symbol from the stack. K; a( c; F7 E$ ^/ _
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else, G z% l+ B4 C6 q M8 n
{
% m% H+ }+ s& k. X // An operand scanned1 Q# Y7 n* W, E
// Push an operand to the stack
! l6 J: \6 R! M3 ? operandStack.push(new Integer(token));
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% \8 ]6 M, P& z1 x$ a" e 0 x1 z& ^! r4 m" ]3 r
// Phase 2: process all the remaining operators in the stack/ D1 f# d" y# V6 ]& |1 d
while (!operatorStack.isEmpty())
" P8 @+ z, Z- K5 Z$ B) K+ u {
! Q. Y# U$ x. O( C processAnOperator(operandStack, operatorStack);
6 z4 u6 s5 ?3 a4 u }
1 j4 h; X' J( Q* }8 {1 g! n% { ( \" i$ _6 S7 {
// Return the result
1 v0 z H# H1 D$ Z( t5 A return ((Integer)(operandStack.pop())).intValue();
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* S, Y# \5 }! S) A$ c5 {
public static void processAnOperator(java.util.Stack operandStack,java.util.Stack operatorStack)# T) l$ W* ~; r7 _$ t8 u5 x" ]
{
& P# \3 z0 f; e0 ~ if (operatorStack.peek().equals('+'))
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operatorStack.pop();, }$ H- X `0 y7 C
int op1 = ((Integer)(operandStack.pop())).intValue();* U& |6 @/ R6 b& o
int op2 = ((Integer)(operandStack.pop())).intValue();+ I; h3 w r1 a
operandStack.push(new Integer(op2 + op1));) [/ h! |, ]. P; N" l0 I/ V7 H1 g
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else if (operatorStack.peek().equals('-'))1 A. t6 c. y% i8 `, l7 }( @- \8 {3 x! }
{
( R: f" i9 x _$ r/ e0 i operatorStack.pop();4 T; F/ S6 T. J
int op1 = ((Integer)(operandStack.pop())).intValue();
- a) b8 r1 h% b% S0 o( ^$ u int op2 = ((Integer)(operandStack.pop())).intValue();
% `" I- J- r4 Q1 p7 N% ^! {/ P, M" ^ operandStack.push(new Integer(op2 - op1));- h2 d: J" ^8 B% e c2 R; C
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else if (operatorStack.peek().equals('*')), o5 {6 D8 k7 |+ N: C7 m
{) u ~- {( F( ~4 f5 ^( e! x% [5 b
operatorStack.pop();
3 _5 L! a! I0 u int op1 = ((Integer)(operandStack.pop())).intValue();
k o' {" _. j4 h1 { int op2 = ((Integer)(operandStack.pop())).intValue();% r, O" o( j ?# j A- t, p+ v' m
operandStack.push(new Integer(op2 * op1));& A6 ^. @4 j" J) s
}# v. a# y! J* F6 n0 A D0 t* O
else if (operatorStack.peek().equals('/'))( _$ s1 ~! m9 b0 C3 t4 P
{
+ c& N* s; v: i9 A, Q& y) G: |) p operatorStack.pop();$ N1 d* W0 w; i8 N4 T" ^: t" d
int op1 = ((Integer)(operandStack.pop())).intValue();
- p& n, [. v' I: V$ h$ \/ Z( D int op2 = ((Integer)(operandStack.pop())).intValue(); N: R$ D; i/ ?) k& {9 K
operandStack.push(new Integer(op2 / op1));
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}
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class ImagePanel extends JPanel1 T+ I7 k9 J: ?" a: l4 K, q
{3 |6 O2 k% b! S# l. {1 P
public void sshow()
0 S2 G5 k% f+ n {
" ~/ {: q; F8 w4 N int i;
& B X* Y. Y+ s% z for(i = 0;i < 4;i++)9 ?: l& K) B' w: k o( `
{
: s: P. j# n; f2 a card[i] = (int)(1 + Math.random() * 52);
: S% B! b! X) X; z0 Z }( Y* b: F' D! T: u# f
repaint();3 X/ w% G# x4 r( i" v1 b* [
}
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protected void paintComponent(Graphics g)
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super.paintComponent(g);
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int w = getWidth() / 4;
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int x = 0;8 t: O" f' ?$ U7 d$ Z
int y = 0;# L$ N/ k2 `6 N1 d
for(i = 0;i < 4;i++)
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ImageIcon imageIcon = new ImageIcon("image/card/" + card[i] + ".png");
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if(image != null)
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' F/ U; E9 Y+ l8 a g.drawImage(image,x,y,w,h,this);
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6 ?5 y+ A/ F; f- Z' V' L public static void main(String[] args)
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/ v% o% j0 l2 O$ h+ o X TwentyFourPoke_Game frame = new TwentyFourPoke_Game();5 N8 f) c. U4 X( N/ C; g$ }
frame.setTitle("24 Poke Game");
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frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
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} 复制代码
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