用Objective-C的foundation框架解决表达式求值问题

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。

//
//  ExpressionString.h
//  exp1_2
//
//  Created by junz on 12/27/14.
//  Copyright (c) 2014 Caspar. All rights reserved.
//

#import <Foundation/Foundation.h>

@interface ExpressionString : NSObject
@property NSString *expString;
- (NSString*)caculateExpression;  
@end

//
//  ExpressionString.m
//  exp1_2
//
//  Created by junz on 12/27/14.
//  Copyright (c) 2014 Caspar. All rights reserved.
//

#import "ExpressionString.h"
#import "ExpressionEvaluation.h"
@implementation ExpressionString
@synthesize expString;
- (NSString*)caculateExpression
{
    NSMutableArray *array = [[NSMutableArray alloc] init];
    for (int i = 0; i < [self.expString length]; i++)//初始化构造数组array存放所有字符
    {
        NSMutableString *s = [[NSMutableString alloc] init];
        s = [NSMutableString stringWithString: [self.expString substringWithRange:NSMakeRange(i, 1)]];
        if ([s isEqualToString:@"÷"]) s = [NSMutableString stringWithString: @"/"];
        else if ([s isEqualToString:@"×"]) s = [NSMutableString stringWithString: @"*"];
        else ;
        array[i] = s;
    }
    array[[array count]] = @"#";//在array数组的末尾加上#作判断符用
    //初始化2个栈，OPTR存放操作符，OPND存放操作数
    NSMutableArray *OPTR = [[NSMutableArray alloc] init];
    NSMutableArray *OPND = [[NSMutableArray alloc] init];
    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
    ExpressionEvaluation *next = [ExpressionEvaluation alloc];
    double sum = 0;   //表达式中操作数的值
    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
    int breakflag = 1;
    current.str = array[i];
    while (![current.str isEqualToString: @"#"])//表达式未遍历完，则不断循环遍历
    {
        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
        {
            sum = 10 * sum + ([[current str] intValue]);
            if (i >= ([array count] -  1))
            {
                break;
            }
            [current setStr: array[++i]];
            if (![current isDigital]) {
                OPND[++k] = [NSString stringWithFormat:@"%f", sum];
                sum = 0;
            }
        }
        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
        double temp = 0;
        if (i < ([array count] -  1)) {//判断表达式的正确性
            [next setStr: array[i+1]];
            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

                breakflag = 0;
                break;
            }
        }        
        //如果OPTR栈为空，则将当前current所指的操作符进栈
        if ((j == -1) && ![current.str isEqualToString:@"#"])
        {
            OPTR[++j] = [current str];
            [current setStr: array[++i]];
            flag = 0;
        }
        //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
        while (flag && (j >= 0)) {
            ExpressionEvaluation *aa = [ExpressionEvaluation alloc];
            ExpressionEvaluation *bb = [ExpressionEvaluation alloc];
            if ([current.str isEqualToString:@"#"] && (j == -1)) {
                break;
            }
            switch ([[current precede:OPTR[j]] isEqualToString:@"<"])
            {
                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
                    OPTR[++j] = [current str];
                    [current setStr: array[++i]];
                    flag = 0;
                    break;
                case false:
                    switch ([[current precede:OPTR[j]] isEqualToString:@"="])
                {
                    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
                        j = j - 1;
                        [current setStr: array[++i]];
                        break;
                    case false:
                        switch ([[current precede:OPTR[j]] isEqualToString:@">"])
                    {   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
                            aa.str = OPND[k--];
                            bb.str = OPND[k--];
                            temp = [bb compute: OPTR[j--] anOtherStr:aa.str];
                            OPND[++k] = [NSString stringWithFormat:@"%f", temp];
                            break;
                        case false: breakflag = 0;break; //判断优先权为0时候的情况
                    }
                }
                default: break;
            }
            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
            {
                OPTR[++j] = [current str];
                [current setStr: array[++i]];
                flag = 0;
            }
        }
    }
    if (breakflag) {
        //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。
        NSMutableString *ss = [NSMutableString stringWithString:OPND[0]];
        while ([[ss substringWithRange:NSMakeRange(ss.length-1, 1)] isEqualToString:@"0"]) {
            [ss deleteCharactersInRange:NSMakeRange(ss.length-1, 1)];
        }
        if ([[ss substringWithRange:NSMakeRange(ss.length-1, 1)] isEqualToString:@"."]) [ss deleteCharactersInRange:NSMakeRange(ss.length-1, 1)];
        return ss;
    }
    else return @"This is not a correct expression, can not evaluate";
}
@end

//
//  ExpressionEvaluation.h
//  exp1_2
//
//  Created by junz on 12/27/14.
//  Copyright (c) 2014 Caspar. All rights reserved.
//

#import <Foundation/Foundation.h>

@interface ExpressionEvaluation : NSObject
@property NSMutableString* str;

-(id) init;
-(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
@end

//
//  ExpressionEvaluation.m
//  exp1_2
//
//  Created by junz on 12/27/14.
//  Copyright (c) 2014 Caspar. All rights reserved.
//

#import "ExpressionEvaluation.h"

@implementation ExpressionEvaluation
@synthesize str;

-(id) init
{
    self.str = [[NSMutableString alloc] init];
    return self;
}
-(BOOL) isDigital
{
    if (([self.str isGreaterThanOrEqualTo:@"0"]) && ([self.str isLessThanOrEqualTo:@"9"])) {
        return YES;
    }
    else return NO;
}
-(NSString*) precede:(NSString*) a
{
    NSInteger i = 0, j = 0;
    NSArray *priori = [[NSArray alloc] initWithObjects:
                       [NSArray arrayWithObjects:@">",@">",@"<",@"<",@"<",@">",@">", nil],
                       [NSArray arrayWithObjects:@">",@">",@"<",@"<",@"<",@">",@">", nil],
                       [NSArray arrayWithObjects:@">",@">",@">",@">",@"<",@">",@">", nil],
                       [NSArray arrayWithObjects:@">",@">",@">",@">",@"<",@">",@">", nil],
                       [NSArray arrayWithObjects:@"<",@"<",@"<",@"<",@"<",@"=",@"0", nil],
                       [NSArray arrayWithObjects:@">",@">",@">",@">",@"=",@"0",@">", nil],
                       [NSArray arrayWithObjects:@"<",@"<",@"<",@"<",@"<",@"0",@"=", nil],
                       nil];
    if ([a isEqualToString:@"+"])  i = 0;
    else if ([a isEqualToString:@"-"])  i = 1;
    else if ([a isEqualToString:@"*"])  i = 2;
    else if ([a isEqualToString:@"/"])  i = 3;
    else if ([a isEqualToString:@"("])  i = 4;
    else if ([a isEqualToString:@")"])  i = 5;
    else if ([a isEqualToString:@"#"])  i = 6;
    else ;
    
    if ([self.str isEqualToString:@"+"])  j = 0;
    else if ([self.str isEqualToString:@"-"])  j = 1;
    else if ([self.str isEqualToString:@"*"])  j = 2;
    else if ([self.str isEqualToString:@"/"])  j = 3;
    else if ([self.str isEqualToString:@"("])  j = 4;
    else if ([self.str isEqualToString:@")"])  j = 5;
    else if ([self.str isEqualToString:@"#"])  j = 6;
    else ;

    return  priori[i][j];
}
-(double) compute: (NSString*)opnt anOtherStr: (NSString*)a
{
    double sum = 0;
    if ([opnt isEqualToString:@"+"])  sum = [self.str doubleValue] + [a doubleValue];
    else if ([opnt isEqualToString:@"-"])  sum = [self.str doubleValue] - [a doubleValue];
    else if ([opnt isEqualToString:@"*"])  sum = [self.str doubleValue] * [a doubleValue];
    else if ([opnt isEqualToString:@"/"])  sum = [self.str doubleValue] / [a doubleValue];
    else ;
    return sum;
}
@end

//
//  main.m
//  exp1_2
//
//  Created by junz on 12/27/14.
//  Copyright (c) 2014 Caspar. All rights reserved.
//

#import "ExpressionString.h"
#import "ExpressionEvaluation.h"

int main(int argc, const char * argv[]) {
    @autoreleasepool {
        ExpressionString *es = [ExpressionString alloc];
//        [es setExpString:@"1000÷2"];
//        [es setExpString:@"10÷6×7+15-8"];
//        [es setExpString:@"10÷÷6×7+15-8"];  //属于错误情况2
        [es setExpString:@"10÷(6+2)(7)+15-8"]; //属于错误情况1
        NSLog(@"%@",[es caculateExpression]);
    }
    return 0;
}

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。