在一串 N 个字符中插入两对括号的方法数量
给定一个长度为 N 的字符串 str ，任务是找出在给定字符串中只插入 2 对括号的方法，这样得到的字符串仍然有效。 例:
输入: str = "ab" 输出: 6 ((a))b、(a)(b)、(a)(b)、(a(b))、a((b)) 共 6 路。 输入: str = "aab" 输出: 20
方法:可以观察到，对于绳子的长度 1、2、3、…、N 一系列将形成为 1、6、20、50、105、196、336、540、… ，其 N th 术语为(N+1)2*((N+1)2–1 以下是上述方法的实施:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to return the number of ways
// to insert the bracket pairs
int cntWays(string str, int n)
{
int x = n + 1;
int ways = x * x * (x * x - 1) / 12;
return ways;
}
// Driver code
int main()
{
string str = "ab";
int n = str.length();
cout << cntWays(str, n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java implementation of the approach
import java.util.*;
class GFG
{
// Function to return the number of ways
// to insert the bracket pairs
static int cntWays(String str, int n)
{
int x = n + 1;
int ways = x * x * (x * x - 1) / 12;
return ways;
}
// Driver code
public static void main(String []args)
{
String str = "ab";
int n = str.length();
System.out.println(cntWays(str, n));
}
}
// This code is contributed by Rajput-Ji
Python 3
# Python3 implementation of the approach
# Function to return the number of ways
# to insert the bracket pairs
def cntWays(string, n) :
x = n + 1;
ways = x * x * (x * x - 1) // 12;
return ways;
# Driver code
if __name__ == "__main__" :
string = "ab";
n = len(string);
print(cntWays(string, n));
# This code is contributed by AnkitRai01
C
// C# implementation of the approach
using System;
class GFG
{
// Function to return the number of ways
// to insert the bracket pairs
static int cntWays(String str, int n)
{
int x = n + 1;
int ways = x * x * (x * x - 1) / 12;
return ways;
}
// Driver code
public static void Main(String []args)
{
String str = "ab";
int n = str.Length;
Console.WriteLine(cntWays(str, n));
}
}
// This code is contributed by Rajput-Ji
java 描述语言
<script>
// Javascript implementation of the approach
// Function to return the number of ways
// to insert the bracket pairs
function cntWays(str, n)
{
var x = n + 1;
var ways = x * x * (x * x - 1) / 12;
return ways;
}
// Driver code
var str = "ab";
var n = str.length;
document.write(cntWays(str, n));
// This code is contributed by rutvik_56.
</script>
Output:
6
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