evaluate_reverse_polish_notation

本文介绍了一种解决逆波兰表达式求值问题的方法。利用栈结构存储操作数,并通过遍历表达式中的每个元素来实现加减乘除运算。文章提供了一个C++示例程序,演示了如何解析和计算逆波兰表达式的值。

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Evaluate the value of an arithmetic expression in Reverse Polish Notation.
Valid operators are+,-,*,/. Each operand may be an integer or another expression.
Some examples
[“2”, “1”, “+”, “3”, ““] -> ((2 + 1) 3) -> 9
[“4”, “13”, “5”, “/”, “+”] -> (4 + (13 / 5)) -> 6

class Solution{
    public:
        int evalRPN(vector<string> &tokens) {
            stack<int>ss;
            string op="+-*/";
            int isop;
            for(int i=0;i<tokens.size();i++){
                cout<<tokens[i]<<endl;
                isop=op.find(tokens[i]);
                int result;

                if(isop==-1)
                    ss.push(atoi(tokens[i].c_str()));

                else{
                    string temp_op=tokens[i];

                    int number_right=ss.top();
                    ss.pop();
                    int number_left=ss.top();
                    ss.pop();

                    switch(isop){

                        case 0:
                            result=number_left+number_right;
                            break;

                        case 1:
                            result=number_left-number_right;
                            break;

                        case 2: 
                            result=number_left*number_right;
                            break;

                        case 3:
                            result=number_left/number_right;
                            break;

                        default:
                            result=-1;
                            break;

                    }

                    ss.push(result);

                }               

            }

            int final_result=ss.top();

            return final_result;
    }
};
好的,以下是代码实现: ```c #include <stdio.h> #include <stdlib.h> #include <ctype.h> typedef struct ExpressionTree { int element; struct ExpressionTree* left_tree; struct ExpressionTree* right_tree; } ExpressionTree, *ExpressionTreeRoot; int evaluate(ExpressionTreeRoot T) { if (T->left_tree == NULL && T->right_tree == NULL) { return T->element; } else { int left_value = evaluate(T->left_tree); int right_value = evaluate(T->right_tree); switch (T->element) { case '+': return left_value + right_value; case '-': return left_value - right_value; case '*': return left_value * right_value; case '/': return left_value / right_value; default: return 0; } } } void in_fix(ExpressionTreeRoot T, bool is_root) { if (T == NULL) return; if (T->left_tree != NULL) { if (!is_root && is_leaf(T->left_tree)) { printf("("); } in_fix(T->left_tree, false); } printf("%c", T->element); if (T->right_tree != NULL) { in_fix(T->right_tree, false); if (!is_root && is_leaf(T->right_tree)) { printf(")"); } } } void reverse_polish(ExpressionTreeRoot T) { if (T == NULL) return; reverse_polish(T->left_tree); reverse_polish(T->right_tree); printf("%c", T->element); } bool is_leaf(ExpressionTreeRoot T) { return T->left_tree == NULL && T->right_tree == NULL; } int main() { ExpressionTreeRoot root = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->element = '+'; root->left_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->left_tree->element = '*'; root->right_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->right_tree->element = '-'; root->left_tree->left_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->left_tree->left_tree->element = 3; root->left_tree->right_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->left_tree->right_tree->element = 4; root->right_tree->left_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->right_tree->left_tree->element = 5; root->right_tree->right_tree = (ExpressionTree*)malloc(sizeof(ExpressionTree)); root->right_tree->right_tree->element = 2; printf("Infix expression: "); in_fix(root, true); printf("\n"); printf("Reverse Polish notation: "); reverse_polish(root); printf("\n"); printf("Result: %d\n", evaluate(root)); return 0; } ``` 这个程序将建立一个如下所示的表达式树: ``` + / \ * - / \ / \ 3 4 5 2 ``` 并且提供了三个操作: - `in_fix`:以中缀方式输出表达式 - `reverse_polish`:以后缀方式输出表达式 - `evaluate`:计算整个表达式树的结果 你可以根据需要进行修改和扩展。
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