主要思想：
本程序分2个类
一个是ExpressionString类，主要用于存储表达式以及对它进行求值。以下是该类中的内容：
(NSString *)expString//用于存储要计算的表达式；
-(NSString*)caculateExpression//就用于计算该表达式的值。
另外一个类是ExpressionEvaluation，此类用于辅助ExpressionString类来对表达式进行求值。以下是该类中的内容：
-(id) init; //初始化函数
-(BOOL) isDigital; //判断是否是数字
-(NSString*) precede:(NSString*) a; //判断当前操作符和栈顶操作符的优先级
-(double) compute: (NSString*) opnt anOtherStr: (NSString*) a; //出栈计算
在main函数中，只需要3步就行了。定义、发送赋值消息、输出结果。3个步骤如下：
ExpressionString *es = [ExpressionString alloc];
[es setExpString:@"10÷6×7+15-8"];
//[es setExpString:@"10÷÷6×7+15-8"]; 此步骤是用于检查错误的测试用例，当使用这步时，系统会输出错误提示信息。
//[es setExpString:@"1000÷2"]; 此步骤用于检测整除之后输出整型，而不是浮点型的值。
NSLog(@"%@",[es caculateExpression]);
具体代码如下：共5个文件。
1 // 2 // ExpressionString.h 3 // exp1_2 4 // 5 // Created by junz on 12/27/14. 6 // Copyright (c) 2014 Caspar. All rights reserved. 7 // 8 9 #import <Foundation/Foundation.h> 10 11 @interface ExpressionString : NSObject 12 @property NSString *expString; 13 - (NSString*)caculateExpression; 14 @end
1 //
2 // ExpressionString.m
3 // exp1_2
4 //
5 // Created by junz on 12/27/14.
6 // Copyright (c) 2014 Caspar. All rights reserved.
7 //
8
9 #import "ExpressionString.h"
10 #import "ExpressionEvaluation.h"
11 @implementation ExpressionString
12 @synthesize expString;
13 - (NSString*)caculateExpression
14 {
15 NSMutableArray *array = [[NSMutableArray alloc] init];
16 for (int i = 0; i < [self.expString length]; i++)//初始化构造数组array存放所有字符
17 {
18 NSMutableString *s = [[NSMutableString alloc] init];
19 s = [NSMutableString stringWithString: [self.expString substringWithRange:NSMakeRange(i, 1)]];
20 if ([s isEqualToString:@"÷"]) s = [NSMutableString stringWithString: @"/"];
21 else if ([s isEqualToString:@"×"]) s = [NSMutableString stringWithString: @"*"];
22 else ;
23 array[i] = s;
24 }
25 array[[array count]] = @"#";//在array数组的末尾加上#作判断符用
26 //初始化2个栈，OPTR存放操作符，OPND存放操作数
27 NSMutableArray *OPTR = [[NSMutableArray alloc] init];
28 NSMutableArray *OPND = [[NSMutableArray alloc] init];
29 ExpressionEvaluation *current = [ExpressionEvaluation alloc]; //设置一个遍历指针current，从0开始对表达式进行遍历
30 ExpressionEvaluation *next = [ExpressionEvaluation alloc];
31 double sum = 0; //表达式中操作数的值
32 int i = 0, k = -1, j = -1;//i用来遍历表达式，k用来记录OPND的大小，j用来记录OPTR的大小
33 int breakflag = 1;
34 current.str = array[i];
35 while (![current.str isEqualToString: @"#"])//表达式未遍历完，则不断循环遍历
36 {
37 while ([current isDigital]) //判断当前指针所指的字符是不是数字，如果是，则将数字存入OPND
38 {
39 sum = 10 * sum + ([[current str] intValue]);
40 if (i >= ([array count] - 1))
41 {
42 break;
43 }
44 [current setStr: array[++i]];
45 if (![current isDigital]) {
46 OPND[++k] = [NSString stringWithFormat:@"%f", sum];
47 sum = 0;
48 }
49 }
50 NSInteger flag = 1; //当current指针指向操作符时，则需要与OPTR栈顶元素进行比较
51 double temp = 0;
52 if (i < ([array count] - 1)) {//判断表达式的正确性
53 [next setStr: array[i+1]];
54 if (![next isDigital] && ((![current.str isEqualToString:@")"] && ![next.str isEqualToString:@"("]) || [current.str isEqualToString:@")"] && [next.str isEqualToString:@"("]) { //情况1：")(";情况2："**"或者"//"等等
55
56 breakflag = 0;
57 break;
58 }
59 }
60 //如果OPTR栈为空，则将当前current所指的操作符进栈
61 if ((j == -1) && ![current.str isEqualToString:@"#"])
62 {
63 OPTR[++j] = [current str];
64 [current setStr: array[++i]];
65 flag = 0;
66 }
67 //如果当前OPTR不为空，则将current所指的操作符与OPTR栈顶元素进行比较
68 while (flag && (j >= 0)) {
69 ExpressionEvaluation *aa = [ExpressionEvaluation alloc];
70 ExpressionEvaluation *bb = [ExpressionEvaluation alloc];
71 if ([current.str isEqualToString:@"#"] && (j == -1)) {
72 break;
73 }
74 switch ([[current precede:OPTR[j]] isEqualToString:@"<"])
75 {
76 case true: //如果OPTR栈顶元素小于current所指的操作符，则current所指的操作符进栈
77 OPTR[++j] = [current str];
78 [current setStr: array[++i]];
79 flag = 0;
80 break;
81 case false:
82 switch ([[current precede:OPTR[j]] isEqualToString:@"="])
83 {
84 case true: //如果OPTR栈顶元素等于current所指的操作符，则消去括号，并使current指向下一个字符
85 j = j - 1;
86 [current setStr: array[++i]];
87 break;
88 case false:
89 switch ([[current precede:OPTR[j]] isEqualToString:@">"])
90 { case true://如果OPTR栈顶元素大于current所指的操作符，出栈计算，将结果入OPND栈
91 aa.str = OPND[k--];
92 bb.str = OPND[k--];
93 temp = [bb compute: OPTR[j--] anOtherStr:aa.str];
94 OPND[++k] = [NSString stringWithFormat:@"%f", temp];
95 break;
96 case false: breakflag = 0;break; //判断优先权为0时候的情况
97 }
98 }
99 default: break;
100 }
101 if ((j == -1) && ![current.str isEqualTo:@"#"])//判断OPTR栈是否为空，为空则将current所指的操作符入栈
102 {
103 OPTR[++j] = [current str];
104 [current setStr: array[++i]];
105 flag = 0;
106 }
107 }
108 }
109 if (breakflag) {
110 //以下代码主要是为了防止类似10/2=5.000000的问题，程序从后往前逐个删除0，使最终得到10/2=5。
111 NSMutableString *ss = [NSMutableString stringWithString:OPND[0]];
112 while ([[ss substringWithRange:NSMakeRange(ss.length-1, 1)] isEqualToString:@"0"]) {
113 [ss deleteCharactersInRange:NSMakeRange(ss.length-1, 1)];
114 }
115 if ([[ss substringWithRange:NSMakeRange(ss.length-1, 1)] isEqualToString:@"."]) [ss deleteCharactersInRange:NSMakeRange(ss.length-1, 1)];
116 return ss;
117 }
118 else return @"This is not a correct expression, can not evaluate";
119 }
120 @end
1 // 2 // ExpressionEvaluation.h 3 // exp1_2 4 // 5 // Created by junz on 12/27/14. 6 // Copyright (c) 2014 Caspar. All rights reserved. 7 // 8 9 #import <Foundation/Foundation.h> 10 11 @interface ExpressionEvaluation : NSObject 12 @property NSMutableString* str; 13 14 -(id) init; 15 -(BOOL) isDigital; //判断是否是数字 16 -(NSString*) precede:(NSString*) a; //判断当前操作符和栈顶操作符的优先级 17 -(double) compute: (NSString*) opnt anOtherStr: (NSString*) a; //出栈计算 18 @end
1 //
2 // ExpressionEvaluation.m
3 // exp1_2
4 //
5 // Created by junz on 12/27/14.
6 // Copyright (c) 2014 Caspar. All rights reserved.
7 //
8
9 #import "ExpressionEvaluation.h"
10
11 @implementation ExpressionEvaluation
12 @synthesize str;
13
14 -(id) init
15 {
16 self.str = [[NSMutableString alloc] init];
17 return self;
18 }
19 -(BOOL) isDigital
20 {
21 if (([self.str isGreaterThanOrEqualTo:@"0"]) && ([self.str isLessThanOrEqualTo:@"9"])) {
22 return YES;
23 }
24 else return NO;
25 }
26 -(NSString*) precede:(NSString*) a
27 {
28 NSInteger i = 0, j = 0;
29 NSArray *priori = [[NSArray alloc] initWithObjects:
30 [NSArray arrayWithObjects:@">",@">",@"<",@"<",@"<",@">",@">", nil],
31 [NSArray arrayWithObjects:@">",@">",@"<",@"<",@"<",@">",@">", nil],
32 [NSArray arrayWithObjects:@">",@">",@">",@">",@"<",@">",@">", nil],
33 [NSArray arrayWithObjects:@">",@">",@">",@">",@"<",@">",@">", nil],
34 [NSArray arrayWithObjects:@"<",@"<",@"<",@"<",@"<",@"=",@"0", nil],
35 [NSArray arrayWithObjects:@">",@">",@">",@">",@"=",@"0",@">", nil],
36 [NSArray arrayWithObjects:@"<",@"<",@"<",@"<",@"<",@"0",@"=", nil],
37 nil];
38 if ([a isEqualToString:@"+"]) i = 0;
39 else if ([a isEqualToString:@"-"]) i = 1;
40 else if ([a isEqualToString:@"*"]) i = 2;
41 else if ([a isEqualToString:@"/"]) i = 3;
42 else if ([a isEqualToString:@"("]) i = 4;
43 else if ([a isEqualToString:@")"]) i = 5;
44 else if ([a isEqualToString:@"#"]) i = 6;
45 else ;
46
47 if ([self.str isEqualToString:@"+"]) j = 0;
48 else if ([self.str isEqualToString:@"-"]) j = 1;
49 else if ([self.str isEqualToString:@"*"]) j = 2;
50 else if ([self.str isEqualToString:@"/"]) j = 3;
51 else if ([self.str isEqualToString:@"("]) j = 4;
52 else if ([self.str isEqualToString:@")"]) j = 5;
53 else if ([self.str isEqualToString:@"#"]) j = 6;
54 else ;
55
56 return priori[i][j];
57 }
58 -(double) compute: (NSString*)opnt anOtherStr: (NSString*)a
59 {
60 double sum = 0;
61 if ([opnt isEqualToString:@"+"]) sum = [self.str doubleValue] + [a doubleValue];
62 else if ([opnt isEqualToString:@"-"]) sum = [self.str doubleValue] - [a doubleValue];
63 else if ([opnt isEqualToString:@"*"]) sum = [self.str doubleValue] * [a doubleValue];
64 else if ([opnt isEqualToString:@"/"]) sum = [self.str doubleValue] / [a doubleValue];
65 else ;
66 return sum;
67 }
68 @end
1 //
2 // main.m
3 // exp1_2
4 //
5 // Created by junz on 12/27/14.
6 // Copyright (c) 2014 Caspar. All rights reserved.
7 //
8
9 #import "ExpressionString.h"
10 #import "ExpressionEvaluation.h"
11
12 int main(int argc, const char * argv[]) {
13 @autoreleasepool {
14 ExpressionString *es = [ExpressionString alloc];
15 // [es setExpString:@"1000÷2"];
16 // [es setExpString:@"10÷6×7+15-8"];
17 // [es setExpString:@"10÷÷6×7+15-8"]; //属于错误情况2
18 [es setExpString:@"10÷(6+2)(7)+15-8"]; //属于错误情况1
19 NSLog(@"%@",[es caculateExpression]);
20 }
21 return 0;
22 }
总结：此程序能求解正确表达式的值，但是容错性稍微差了些，比如在main函数中，发这样一条消息：[es setExpString:@"10÷(6+2)(+15-8"];程序直接奔溃，没有实现很好的容错。
解决方法：
需要针对ExpressionString类中的compute方法进行改进。
1、对OPND和OPTR数组取数据时，把取出来的数据在OPND和OPTR中删除；
2、在返回值时，通过判断OPND和OPTR的大小来进行，而不是直接返回OPND[0]。
由于时间问题，此改进的操作等有时间的时候再搞。现在先暂且放一放。
时间： 2024-08-04 01:21:20