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栈的作用——波兰表达式的运用，计算字符表达式

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栈的作用——波兰表达式的运用，计算字符表达式

目录
  • 栈的作用——波兰表达式的运用，计算字符表达式
  • 1 创建一个链栈
    • （1）链栈的存储结构
    • （2）打印
    • （3）进栈
    • （4）出栈
  • 2 中缀表达式转换为后缀表达式
  • 3 计算后缀表达式

1 创建一个链栈

​ 需完成进栈，出栈，打印的操作。

（1）链栈的存储结构

#define SUCCESS			1
#define ERROR			0
#define MAXSIZE			5

typedef int ElemType;
typedef int LIST_STATUS;
typedef char ElemCharType;

typedef struct _Node {
	ElemType Data;
	struct _Node *Next;
}Node;

typedef struct _LINK_STACK {
	Node * Top;
	int Count;
}LINK_STACK;

（2）打印

LIST_STATUS PrintLinkStack(LINK_STACK * const LinkStack) {
	Node *TraStackNode;

	printf("PrintLinkStack start\n");

	if (NULL == LinkStack) {
		return ERROR;
	}

	printf("LinkStack->Top = 0x%x\n", LinkStack->Top);
	printf("LinkStack->Count = %d\n", LinkStack->Count);

	TraStackNode = LinkStack->Top;

	while (TraStackNode != NULL) {
		printf("TraStackNode = 0x%x, TraStackNode->Data = %d\n", TraStackNode, TraStackNode->Data);
		TraStackNode = TraStackNode->Next;
	}

	printf("PrintLinkStack end\n\n");
	return SUCCESS;
}

（3）进栈

LIST_STATUS PushLinkStack(LINK_STACK *LinkStack, int PushData) {
	LINK_STACK *TraLinkStack = LinkStack;
	Node *PushNode;

	printf("PushLinkStack start\n");

	if (NULL == LinkStack) {
		return ERROR;
	}

	PushNode = (Node *)malloc(sizeof(Node));
	PushNode->Data = PushData;
	PushNode->Next = TraLinkStack->Top;

	TraLinkStack->Top = PushNode;
	TraLinkStack->Count++;

	printf("PushLinkStack end\n");
	return SUCCESS;
}

（4）出栈

LIST_STATUS PopLinkStack(LINK_STACK *LinkStack, int *PopData) {
	LINK_STACK *TraLinkStack = LinkStack;
	LINK_STACK *DeleteNode;

	printf("PopLinkStack start\n");

	if (NULL == LinkStack || NULL == LinkStack->Top) {
		return ERROR;
	}

	*PopData = TraLinkStack->Top->Data;

	DeleteNode = TraLinkStack->Top;
	TraLinkStack->Top = TraLinkStack->Top->Next;
	TraLinkStack->Count--;
	free(DeleteNode);

	printf("PopLinkStack end\n");
	return SUCCESS;
}

2 中缀表达式转换为后缀表达式

（1）需求与算法

中缀表达式为：9+(3-1)*3+10/2

要转换成后缀表达式为：9 3 1 - 3 * + 10 2 / +

算法：

符号优先级："* /" > " + -"，“(”与“)”做特殊情况处理

（2）进栈

① 进栈原则：新元素优先级 > 栈顶元素优先级

② 当新元素为“("，进栈

③ 只进新元素

（3)出栈

① 出栈的原则：新元素优先级 <= 栈顶元素优先级

②当新元素为“)”时，将到栈里面“(”（包括）之前的符号全部出栈

① 当符号不为"()"时，满足出栈原则时，新元素不断与栈顶元素比，不断出栈，直到不满足出栈条件，或者遇到“(”时，将新元素入栈

② 最后栈里面的元素也要按顺序出栈

（3）其它注意的问题

①注意多位数的处理

②注意每个数之间要有空格隔开

代码：

bool IfPopValid(LINK_STACK * const LinkStack, char NewChar) {
	LINK_STACK *TraStackNode = LinkStack;

	printf("IfNewCharPriorityNotHigh start\n");

	/*Empty LinkStack*/
	if (TraStackNode->Top == NULL && TraStackNode->Count == 0) {
		return false;
	}

	if (NewChar == '(') {
		return false;
	} else if (NewChar == ')') {
		return true;
	} else if (NewChar == '+' || NewChar == '-') {
		return true;	
	} else if (NewChar == '*' || NewChar == '/') {
		if (TraStackNode->Top->Data == '+' || TraStackNode->Top->Data == '-') {
			return false;
		} else if (TraStackNode->Top->Data == '*' || TraStackNode->Top->Data == '/') {
			return true;
		}
	}

	printf("IfNewCharPriorityNotHigh end\n\n");
}

LIST_STATUS PushInfixExpression(LINK_STACK *LinkStack, char NewChar) {
	LINK_STACK *TraStackNode = LinkStack;
	Node *AddNode = (Node *)malloc(sizeof(Node));

	LIST_STATUS Status;

	printf("PushInfixExpression start\n");
	printf("In PushInfixExpression, NewChar = %c\n", NewChar);

	Status = PushLinkStack(LinkStack, NewChar);

	printf("PushInfixExpression end\n\n");

	return Status;
}

LIST_STATUS PopInfixExpression(LINK_STACK *LinkStack, char NewChar, char *PostfixExpression, int *PostEIndex) {
	LINK_STACK *TraStackNode = LinkStack;
	int *PopData = (int)malloc(sizeof(int));
	
	printf("PopInfixExpression start\n");

	printf("PopData = 0x%x\n", PopData);
	printf("In PopInfixExpression, NewChar = %c\n", NewChar);
	printf("In PopInfixExpression, PostfixExpression = %s\n", PostfixExpression);

	PrintCharLinkStack(LinkStack);

	if (NewChar == ')') {
		while (TraStackNode->Top != NULL) {
			if (TraStackNode->Top->Data != '(') {
				PopLinkStack(TraStackNode, PopData);
				PostfixExpression[(*PostEIndex)++] = *PopData;
				PostfixExpression[(*PostEIndex)++] = ' ';
			}else if (TraStackNode->Top->Data == '(') {
				PopLinkStack(TraStackNode, PopData);
				break;
			}
			//TraStackNode->Top = TraStackNode->Top->Next;
		}
	} else if (NewChar == '+' || NewChar == '-') {
		while ((TraStackNode->Top != NULL) && (TraStackNode->Top->Data != '(')) {
			PopLinkStack(TraStackNode, PopData);
			PostfixExpression[(*PostEIndex)++] = *PopData;
			PostfixExpression[(*PostEIndex)++] = ' ';

			//TraStackNode->Top = TraStackNode->Top->Next;
		}
		PushLinkStack(LinkStack, NewChar);
	} else if (NewChar == '*' || NewChar == '/') {
		while ( (TraStackNode->Top != NULL) && (TraStackNode->Top->Data != '(') && 
			((TraStackNode->Top->Data == '*') || (TraStackNode->Top->Data == '/')) ) {
			PopLinkStack(TraStackNode, PopData);
			printf("*PopData = %c\n", *PopData);
			PostfixExpression[(*PostEIndex)++] = *PopData;
			PostfixExpression[(*PostEIndex)++] = ' ';

			//TraStackNode->Top = TraStackNode->Top->Next;
		}
		PushLinkStack(LinkStack, NewChar);
	}

	printf("In PopInfixExpression, PostfixExpression = %s\n", PostfixExpression);

	printf("PopData = 0x%x\n", PopData);
	free(PopData);

	PrintCharLinkStack(LinkStack);

	printf("PopInfixExpression end\n\n");
}


/*RPN*/
void RPNString(void) {
	char InfixExpression[] = "9+(3-1)*3+10/2";//9 3 1 - 3 * + 10 2 / +
	//char InfixExpression[] = "9313102";//9313102
	//char InfixExpression[] = "2+1*3+2/1";//2 1 3 * + 2 1 / +
	//char InfixExpression[] = "14*23/32";//14 23 * 32 /
	//char InfixExpression[] = "(2+1)";//2 1 +
	//char InfixExpression[] = "3+(2-1)";//3 2 1 - +
	//char InfixExpression[] = "3+(2-1)*4";//3 2 1 - 4 * +

	char *PostfixExpression = (char *)malloc(sizeof(char) * sizeof(InfixExpression) * 2);
	int PostEIndex = 0;
	int TraIndex = 0;
	int ResData;
	
	LINK_STACK *LinkStack = (LINK_STACK *)malloc(sizeof(LINK_STACK));
	LinkStack->Top = NULL;
	LinkStack->Count = 0;

	LINK_STACK *TraStackNode = LinkStack;

	char *PopData = (char *)malloc(sizeof(char));

	printf("InfixExpression = %s\n", InfixExpression);
	
	for (TraIndex = 0; TraIndex < strlen(InfixExpression); ++TraIndex) {
		printf("In RPNString, InfixExpression[%d] = %c\n", TraIndex, InfixExpression[TraIndex]);
		if (InfixExpression[TraIndex] >= '0' && InfixExpression[TraIndex] <= '9') {
			PostfixExpression[PostEIndex++] = InfixExpression[TraIndex];
			/*long number*/
			while ( (TraIndex + 1 < strlen(InfixExpression)) && ((InfixExpression[TraIndex + 1] >= '0' && InfixExpression[TraIndex + 1] <= '9')) ) {
				PostfixExpression[PostEIndex++] = InfixExpression[++TraIndex];				
			}
			PostfixExpression[PostEIndex++] = ' ';
		} else if (IfPopValid(LinkStack, InfixExpression[TraIndex]) == true) {
			PopInfixExpression(LinkStack, InfixExpression[TraIndex], PostfixExpression, &PostEIndex);
		} else if (IfPopValid(LinkStack, InfixExpression[TraIndex]) == false) {
			PushInfixExpression(LinkStack, InfixExpression[TraIndex]);
		}
	}

	printf("In RPNString, PostfixExpression = %s\n", PostfixExpression);

	/*Pop remain operator*/
	printf("Pop remain operator\n");
	while ((TraStackNode->Top != NULL) && (TraStackNode->Count != 0)) {
		if (TraStackNode->Top->Next == NULL) {
			PopLinkStack(LinkStack, PopData);
			PostfixExpression[PostEIndex++] = *PopData;
		} else {
			PopLinkStack(LinkStack, PopData);
			PostfixExpression[PostEIndex++] = *PopData;
			PostfixExpression[PostEIndex++] = ' ';
		}
	}

	PrintCharLinkStack(LinkStack);

	PostfixExpression[PostEIndex++] = '\0';
	
	printf("In RPNString, PostfixExpression = %s\n\n", PostfixExpression);
	
	/*Operate PostfixExpression*/
	ResData = OpPostfixFunc(PostfixExpression, strlen(PostfixExpression));

	printf("In RPNString, ResData = %d\n", ResData);

	free(PostfixExpression);
	free(LinkStack);

3 计算后缀表达式

（1）需求与算法

后缀表达式：9 3 1 - 3 * + 10 2 / +

计算出结果：20

算法：

（2）遇到数字

​ 将数进栈

(3)遇到符号

​ 将栈的最上面两个元素出栈，第一个出栈的元素作为被操作数，第二个出栈的元素作为操作数，符号操作的结果进栈

(4)其它注意的问题

①注意多位数的处理

②注意每个数之间有空格隔开

代码：

int OpPopDataFunc(char Op, int Data1, int Data2) {
	int ResData;

	if (Op == '+') {
		ResData = Data2 + Data1;
		return ResData;
	} else if (Op == '-') {
		ResData = Data2 - Data1;
		return ResData;
	} else if (Op == '*') {
		ResData = Data2 * Data1;
		return ResData;
	} else if (Op == '/') {
		ResData = Data2 / Data1;
		return ResData;
	}
}

int OpPostfixFunc(char *PostfixExpressionInput, int PostfixExpressionInputSize) {
	//char PostfixExpression[] = "1 10 + 234 - 10 *";
	//char PostfixExpression[] = "2 1 +";
	//char PostfixExpression[] = "9 3 1 - 3 * + 10 2 / +";
	char *PostfixExpression = PostfixExpressionInput;

	int Ret;
	int TraIndex = 0;

	LINK_STACK *LinkStack = (LINK_STACK *)malloc(sizeof(LINK_STACK));
	LinkStack->Top = NULL;
	LinkStack->Count = 0;
	
	int PushData = 0;
	int *PopData1 = (int *)malloc(sizeof(int));
	int *PopData2 = (int *)malloc(sizeof(int));	
	int *ResData1 = (int *)malloc(sizeof(int));
	int ResData2 = 0;
	int OpData;	

	printf("\nOpPostfixFunc start\n");
	printf("In OpPostfixFunc, PostfixExpression = %s\n", PostfixExpression);
	printf("PostfixExpressionInputSize = %d\n", PostfixExpressionInputSize);

	for (TraIndex = 0; TraIndex < PostfixExpressionInputSize; ++TraIndex) {
		printf("PostfixExpression[%d] = %c\n", TraIndex, PostfixExpression[TraIndex]);
		if (PostfixExpression[TraIndex] == ' ') {
			continue;
		} else if (PostfixExpression[TraIndex] >= '0' && PostfixExpression[TraIndex] <= '9') {
			PushData = PostfixExpression[TraIndex] - 48;
			printf("PushData 01 = %d\n", PushData);

			/*Judge wheather PostfixExpression[TraIndex] is long number*/
			while ((TraIndex + 1 < PostfixExpressionInputSize) && (PostfixExpression[TraIndex + 1] != ' ')) {
				printf("In while, PostfixExpression[%d] = %c\n", TraIndex + 1, PostfixExpression[TraIndex + 1]);
				PushData = PushData * 10 + (PostfixExpression[TraIndex + 1] - 48);
				++TraIndex;				
				printf("PushData 02 = %d\n", PushData);
			}

			/*Push should make PostfixExpression[TraIndex] int type */
			PushLinkStack(LinkStack, PushData);
			PrintLinkStack(LinkStack);
		} else if (PostfixExpression[TraIndex] == '+' || PostfixExpression[TraIndex] == '-' || PostfixExpression[TraIndex] == '*' || PostfixExpression[TraIndex] == '/') {
			PopLinkStack(LinkStack, PopData1);
			PopLinkStack(LinkStack, PopData2);

			/*
			printf("*PopData1 = %d\n", *PopData1);
			printf("*PopData2 = %d\n", *PopData2);			
			*/
			OpData = OpPopDataFunc(PostfixExpression[TraIndex], *PopData1, *PopData2);
			printf("OpData = %d\n", OpData);

			PushLinkStack(LinkStack, OpData);
		}	
	}

	PrintLinkStack(LinkStack);

	if (LinkStack->Count == 1) {
		PopLinkStack(LinkStack, ResData1);

		printf("*ResData1 = %d\n", *ResData1);

		ResData2 = *ResData1;
	}

	free(LinkStack);
	free(ResData1);
	free(PopData1);
	free(PopData2);

	printf("In OpPostfixFunc, ResData2 = %d\n", ResData2);

	return ResData2;
}

打印结果：

InfixExpression = 9+(3-1)*3+10/2

In RPNString, InfixExpression[0] = 9

In RPNString, InfixExpression[1] = +

IfNewCharPriorityNotHigh start

IfNewCharPriorityNotHigh start

PushInfixExpression start

In PushInfixExpression, NewChar = +

PushLinkStack start

PushLinkStack end

PushInfixExpression end

In RPNString, InfixExpression[2] = (

IfNewCharPriorityNotHigh start

IfNewCharPriorityNotHigh start

PushInfixExpression start

In PushInfixExpression, NewChar = (

PushLinkStack start

PushLinkStack end

PushInfixExpression end

In RPNString, InfixExpression[3] = 3

In RPNString, InfixExpression[4] = -

IfNewCharPriorityNotHigh start

PopInfixExpression start

PopData = 0xf15f00

In PopInfixExpression, NewChar = -

In PopInfixExpression, PostfixExpression = 9 3 屯屯屯屯屯屯屯屯屯屯屯屯屯?

PrintCharLinkStack start

LinkStack->Top = 0xf20338

LinkStack->Count = 2

TraStackNode = 0xf20338, TraStackNode->Data = (

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PushLinkStack start

PushLinkStack end

In PopInfixExpression, PostfixExpression = 9 3 屯屯屯屯屯屯屯屯屯屯屯屯屯?

PopData = 0xf15f00

PrintCharLinkStack start

LinkStack->Top = 0xf20370

LinkStack->Count = 3

TraStackNode = 0xf20370, TraStackNode->Data = -

TraStackNode = 0xf20338, TraStackNode->Data = (

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PopInfixExpression end

In RPNString, InfixExpression[5] = 1

In RPNString, InfixExpression[6] = )

IfNewCharPriorityNotHigh start

PopInfixExpression start

PopData = 0xf15f00

In PopInfixExpression, NewChar = )

In PopInfixExpression, PostfixExpression = 9 3 1 屯屯屯屯屯屯屯屯屯屯屯屯?

PrintCharLinkStack start

LinkStack->Top = 0xf20370

LinkStack->Count = 3

TraStackNode = 0xf20370, TraStackNode->Data = -

TraStackNode = 0xf20338, TraStackNode->Data = (

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

In PopInfixExpression, PostfixExpression = 9 3 1 - 屯屯屯屯屯屯屯屯屯屯屯?

PopData = 0xf15f00

PrintCharLinkStack start

LinkStack->Top = 0xf15ec8

LinkStack->Count = 1

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PopInfixExpression end

In RPNString, InfixExpression[7] = *

IfNewCharPriorityNotHigh start

IfNewCharPriorityNotHigh start

PushInfixExpression start

In PushInfixExpression, NewChar = *

PushLinkStack start

PushLinkStack end

PushInfixExpression end

In RPNString, InfixExpression[8] = 3

In RPNString, InfixExpression[9] = +

IfNewCharPriorityNotHigh start

PopInfixExpression start

PopData = 0xf15f00

In PopInfixExpression, NewChar = +

In PopInfixExpression, PostfixExpression = 9 3 1 - 3 屯屯屯屯屯屯屯屯屯屯?

PrintCharLinkStack start

LinkStack->Top = 0xf20370

LinkStack->Count = 2

TraStackNode = 0xf20370, TraStackNode->Data = *

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

PushLinkStack start

PushLinkStack end

In PopInfixExpression, PostfixExpression = 9 3 1 - 3 * + 屯屯屯屯屯屯屯屯?

PopData = 0xf15f00

PrintCharLinkStack start

LinkStack->Top = 0xf15ec8

LinkStack->Count = 1

TraStackNode = 0xf15ec8, TraStackNode->Data = +

PrintCharLinkStack end

PopInfixExpression end

In RPNString, InfixExpression[10] = 1

In RPNString, InfixExpression[12] = /

IfNewCharPriorityNotHigh start

IfNewCharPriorityNotHigh start

PushInfixExpression start

In PushInfixExpression, NewChar = /

PushLinkStack start

PushLinkStack end

PushInfixExpression end

In RPNString, InfixExpression[13] = 2

In RPNString, PostfixExpression = 9 3 1 - 3 * + 10 2 屯屯屯屯屯妄

Pop remain operator

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

PrintCharLinkStack start

In RPNString, PostfixExpression = 9 3 1 - 3 * + 10 2 / +

OpPostfixFunc start

In OpPostfixFunc, PostfixExpression = 9 3 1 - 3 * + 10 2 / +

PostfixExpressionInputSize = 22

PostfixExpression[0] = 9

PushData 01 = 9

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf20408

LinkStack->Count = 1

TraStackNode = 0xf20408, TraStackNode->Data = 9

PrintLinkStack end

PostfixExpression[1] =

PostfixExpression[2] = 3

PushData 01 = 3

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf20440

LinkStack->Count = 2

TraStackNode = 0xf20440, TraStackNode->Data = 3

TraStackNode = 0xf20408, TraStackNode->Data = 9

PrintLinkStack end

PostfixExpression[3] =

PostfixExpression[4] = 1

PushData 01 = 1

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf20478

LinkStack->Count = 3

TraStackNode = 0xf20478, TraStackNode->Data = 1

TraStackNode = 0xf20440, TraStackNode->Data = 3

TraStackNode = 0xf20408, TraStackNode->Data = 9

PrintLinkStack end

PostfixExpression[5] =

PostfixExpression[6] = -

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

OpData = 2

PushLinkStack start

PushLinkStack end

PostfixExpression[7] =

PostfixExpression[8] = 3

PushData 01 = 3

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf20698

LinkStack->Count = 3

TraStackNode = 0xf20698, TraStackNode->Data = 3

TraStackNode = 0xf204d8, TraStackNode->Data = 2

TraStackNode = 0xf20408, TraStackNode->Data = 9

PrintLinkStack end

PostfixExpression[9] =

PostfixExpression[10] = *

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

OpData = 6

PushLinkStack start

PushLinkStack end

PostfixExpression[11] =

PostfixExpression[12] = +

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

OpData = 15

PushLinkStack start

PushLinkStack end

PostfixExpression[13] =

PostfixExpression[14] = 1

PushData 01 = 1

In while, PostfixExpression[15] = 0

PushData 02 = 10

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf206d0

LinkStack->Count = 2

TraStackNode = 0xf206d0, TraStackNode->Data = 10

TraStackNode = 0xf207b0, TraStackNode->Data = 15

PrintLinkStack end

PostfixExpression[16] =

PostfixExpression[17] = 2

PushData 01 = 2

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf20580

LinkStack->Count = 3

TraStackNode = 0xf20580, TraStackNode->Data = 2

TraStackNode = 0xf206d0, TraStackNode->Data = 10

TraStackNode = 0xf207b0, TraStackNode->Data = 15

PrintLinkStack end

PostfixExpression[18] =

PostfixExpression[19] = /

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

OpData = 5

PushLinkStack start

PushLinkStack end

PostfixExpression[20] =

PostfixExpression[21] = +

PopLinkStack start

PopLinkStack end

PopLinkStack start

PopLinkStack end

OpData = 20

PushLinkStack start

PushLinkStack end

PrintLinkStack start

LinkStack->Top = 0xf205f0

LinkStack->Count = 1

TraStackNode = 0xf205f0, TraStackNode->Data = 20

PrintLinkStack end

PopLinkStack start

PopLinkStack end

*ResData1 = 20

In OpPostfixFunc, ResData2 = 20

In RPNString, ResData = 20

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