给定一个由一对平衡括号组成的字符串str ，任务是根据以下规则计算给定字符串的分数：
- “ () ”的得分为 1。
- “ xy ” 的分数为x + y ，其中x和y是单独的一对平衡括号。
- “ (x) ”的得分是x 的两倍(即)， x 的 2 * 得分。
例子：
Input: str = “()()”
Output: 2
Explanation: There are are two individual psirs of balanced parenthesis “() ()”. Therefore, score = score of “()” + score of “()” = 1 + 1 = 2
Input: str = “(())”
Output: 2
Explanation: Since the input is of the form “(x)”, the total score = 2 * score of “()” = 2 * 1 = 2
方法：使用Stack可以解决这个问题。我们的想法是遍历字符串的字符。对于每个第i个字符，检查字符是否为‘(‘ 。如果为真，则将该字符插入堆栈。否则，计算内括号的分数并将分数的两倍插入堆栈。遵循解决问题的步骤如下：
- 初始化一个堆栈来存储当前遍历的字符或内平衡括号的分数。
- 迭代字符串str的字符。对于每个第i个字符，检查以下条件：
- 如果当前字符是否为‘(‘ 。如果发现为真，则将当前字符压入堆栈。
- 否则，检查栈顶元素是否为‘(‘ 。如果发现为真，则将“1”插入栈中，代表内平衡括号的分数。
- 否则，将堆栈的顶部元素加倍并将获得的值压入堆栈。
- 最后，打印得到的总分。
下面是上述方法的实现：
C++
// C++ program to implement
// the above approach
#include
#include
using namespace std;
// Function to calculate
// score of parentheses
long long scoreOfParentheses(string S)
{
stack s;
// Stores index of
// character of string
int i = 0;
// Stores total scores
// obtained from the string
long long ans = 0;
// Iterate over characters
// of the string
while (i < S.length()) {
// If s[i] is '('
if (S[i] == '(')
s.push("(");
else {
// If top element of
// stack is '('
if (s.top() == "(") {
s.pop();
s.push("1");
}
else {
// Stores score of
// inner parentheses
long long count = 0;
// Calculate score of
// inner parentheses
while (s.top() != "(") {
// Update count
count += stoi(s.top());
s.pop();
}
// Pop from stack
s.pop();
// Insert score of
// inner parentheses
s.push(to_string(2 * count));
}
}
// Update i
i++;
}
// Calculate score
// of the string
while (!s.empty()) {
// Update ans
ans += stoi(s.top());
s.pop();
}
return ans;
}
// Driver Code
int main()
{
string S1 = "(()(()))";
cout << scoreOfParentheses(S1) << endl;
return 0;
} Java
// Java program to implement
// the above approach
import java.util.*;
class GFG
{
// Function to calculate
// score of parentheses
static long scoreOfParentheses(String S)
{
Stack s = new Stack<>();
// Stores index of
// character of String
int i = 0;
// Stores total scores
// obtained from the String
long ans = 0;
// Iterate over characters
// of the String
while (i < S.length())
{
// If s[i] is '('
if (S.charAt(i) == '(')
s.add("(");
else
{
// If top element of
// stack is '('
if (s.peek() == "(")
{
s.pop();
s.add("1");
}
else
{
// Stores score of
// inner parentheses
long count = 0;
// Calculate score of
// inner parentheses
while (s.peek() != "(")
{
// Update count
count += Integer.parseInt(s.peek());
s.pop();
}
// Pop from stack
s.pop();
// Insert score of
// inner parentheses
s.add(String.valueOf(2 * count));
}
}
// Update i
i++;
}
// Calculate score
// of the String
while (!s.isEmpty())
{
// Update ans
ans += Integer.parseInt(s.peek());
s.pop();
}
return ans;
}
// Driver Code
public static void main(String[] args)
{
String S1 = "(()(()))";
System.out.print(scoreOfParentheses(S1) +"\n");
}
}
// This code is contributed by 29AjayKumar. Python3
# Python3 program to implement
# the above approach
# Function to calculate
# score of parentheses
def scoreOfParentheses(S):
s = []
# Stores index of
# character of string
i = 0
# Stores total scores
# obtained from the string
ans = 0
# Iterate over characters
# of the string
while (i < len(S)):
# If s[i] is '('
if (S[i] == '('):
s.append("(")
else:
# If top element of
# stack is '('
if (s[-1] == "("):
s.pop()
s.append("1")
else:
# Stores score of
# inner parentheses
count = 0
# Calculate score of
# inner parentheses
while (s[-1] != "("):
# Update count
count += int(s[-1])
s.pop()
# Pop from stack
s.pop()
# Insert score of
# inner parentheses
s.append(str(2 * count))
# Update i
i += 1
# Calculate score
# of the string
while len(s) > 0:
# Update ans
ans += int(s[-1])
s.pop()
return ans
# Driver Code
if __name__ == '__main__':
S1 = "(()(()))"
print(scoreOfParentheses(S1))
# This code is contributed by mohit kumar 29C#
// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
class GFG
{
// Function to calculate
// score of parentheses
static long scoreOfParentheses(String S)
{
Stack s = new Stack();
// Stores index of
// character of String
int i = 0;
// Stores total scores
// obtained from the String
long ans = 0;
// Iterate over characters
// of the String
while (i < S.Length)
{
// If s[i] is '('
if (S[i] == '(')
s.Push("(");
else
{
// If top element of
// stack is '('
if (s.Peek() == "(")
{
s.Pop();
s.Push("1");
}
else
{
// Stores score of
// inner parentheses
long count = 0;
// Calculate score of
// inner parentheses
while (s.Peek() != "(")
{
// Update count
count += Int32.Parse(s.Peek());
s.Pop();
}
// Pop from stack
s.Pop();
// Insert score of
// inner parentheses
s.Push(String.Join("", 2 * count));
}
}
// Update i
i++;
}
// Calculate score
// of the String
while (s.Count != 0)
{
// Update ans
ans += Int32.Parse(s.Peek());
s.Pop();
}
return ans;
}
// Driver Code
public static void Main(String[] args)
{
String S1 = "(()(()))";
Console.Write(scoreOfParentheses(S1) +"\n");
}
}
// This code is contributed by 29AjayKumar 输出：
6时间复杂度： O(N)
辅助空间： O(N)
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