将数字分成三部分
给定一个非常大的数，把它分解成 3 个整数，这样它们就可以和原来的数相加，并计算出这样做的方法。
示例:
Input : 3
Output : 10
The possible combinations where the sum
of the numbers is equal to 3 are:
0+0+3 = 3
0+3+0 = 3
3+0+0 = 3
0+1+2 = 3
0+2+1 = 3
1+0+2 = 3
1+2+0 = 3
2+0+1 = 3
2+1+0 = 3
1+1+1 = 3
Input : 6
Output : 28
一共 10 种方式，所以回答是 10 种。
天真方法:尝试从 0 到给定数字的所有组合，并检查它们是否加到给定数字，如果是，则将计数增加 1 并继续该过程。
C++
// C++ program to count number of ways to break
// a number in three parts.
#include <bits/stdc++.h>
#define ll long long int
using namespace std;
// Function to count number of ways
// to make the given number n
ll count_of_ways(ll n)
{
ll count = 0;
for (int i = 0; i <= n; i++)
for (int j = 0; j <= n; j++)
for (int k = 0; k <= n; k++)
if (i + j + k == n)
count++;
return count;
}
// Driver Function
int main()
{
ll n = 3;
cout << count_of_ways(n) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to count number of ways to break
// a number in three parts
import java.io.*;
class GFG {
// Function to count number of ways
// to make the given number n
static long count_of_ways(long n)
{
long count = 0;
for (int i = 0; i <= n; i++)
for (int j = 0; j <= n; j++)
for (int k = 0; k <= n; k++)
if (i + j + k == n)
count++;
return count;
}
// driver program
public static void main(String[] args)
{
long n = 3;
System.out.println(count_of_ways(n));
}
}
// Contributed by Pramod Kumar
Python 3
# Python3 program to count number of
# ways to break
# a number in three parts.
# Function to count number of ways
# to make the given number n
def count_of_ways(n):
count = 0
for i in range(0, n+1):
for j in range(0, n+1):
for k in range(0, n+1):
if(i + j + k == n):
count = count + 1
return count
# Driver Function
if __name__=='__main__':
n = 3
print(count_of_ways(n))
# This code is contributed by
# Sanjit_Prasad
C
// C# program to count number of ways
// to break a number in three parts
using System;
class GFG {
// Function to count number of ways
// to make the given number n
static long count_of_ways(long n)
{
long count = 0;
for (int i = 0; i <= n; i++)
for (int j = 0; j <= n; j++)
for (int k = 0; k <= n; k++)
if (i + j + k == n)
count++;
return count;
}
// driver program
public static void Main()
{
long n = 3;
Console.WriteLine(count_of_ways(n));
}
}
// This code is Contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to count number
// of ways to break a number
// in three parts.
// Function to count number of ways
// to make the given number n
function count_of_ways( $n)
{
$count = 0;
for ($i = 0; $i <= $n; $i++)
for ($j = 0; $j <= $n; $j++)
for ($k = 0; $k <= $n; $k++)
if ($i + $j + $k == $n)
$count++;
return $count;
}
// Driver Code
$n = 3;
echo count_of_ways($n);
// This code is Contributed by vt_m.
?>
java 描述语言
<script>
// JavaScript program to count
// number of ways to break
// a number in three parts.
// Function to count number of ways
// to make the given number n
function count_of_ways(n)
{
let count = 0;
for(let i = 0; i <= n; i++)
for(let j = 0; j <= n; j++)
for(let k = 0; k <= n; k++)
if (i + j + k == n)
count++;
return count;
}
// Driver code
let n = 3;
document.write(count_of_ways(n) + "<br>");
// This code is contributed by Surbhi Tyagi.
</script>
输出:
10
时间复杂度: O(n 3
高效方法:如果我们仔细观察测试用例，那么我们会意识到将一个数字 n 分成 3 部分的方法数量等于(n+1) * (n+2) / 2。
C++
// C++ program to count number of ways to break
// a number in three parts.
#include <bits/stdc++.h>
#define ll long long int
using namespace std;
// Function to count number of ways
// to make the given number n
ll count_of_ways(ll n)
{
ll count;
count = (n + 1) * (n + 2) / 2;
return count;
}
// Driver Function
int main()
{
ll n = 3;
cout << count_of_ways(n) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to count number of ways to break
// a number in three parts
import java.io.*;
class GFG {
// Function to count number of ways
// to make the given number n
static long count_of_ways(long n)
{
long count = 0;
count = (n + 1) * (n + 2) / 2;
return count;
}
// driver program
public static void main(String[] args)
{
long n = 3;
System.out.println(count_of_ways(n));
}
}
// Contributed by Pramod Kumar
Python 3
# Python 3 program to count number of
# ways to break a number in three parts.
# Function to count number of ways
# to make the given number n
def count_of_ways(n):
count = 0
count = (n + 1) * (n + 2) // 2
return count
# Driver code
n = 3
print(count_of_ways(n))
# This code is contributed by Shrikant13
C
// C# program to count number of ways to
// break a number in three parts
using System;
class GFG {
// Function to count number of ways
// to make the given number n
static long count_of_ways(long n)
{
long count = 0;
count = (n + 1) * (n + 2) / 2;
return count;
}
// driver program
public static void Main()
{
long n = 3;
Console.WriteLine(count_of_ways(n));
}
}
// This code is Contributed by vt_m.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to count number
// of ways to break a number
// in three parts.
// Function to count number of ways
// to make the given number n
function count_of_ways( $n)
{
$count;
$count = ($n + 1) * ($n + 2) / 2;
return $count;
}
// Driver Code
$n = 3;
echo count_of_ways($n);
// This code is Contributed by vt_m.
?>
java 描述语言
<script>
// javascript program to count number of ways to
// break a number in three parts
// Function to count number of ways
// to make the given number n
function count_of_ways(n)
{
var count = 0;
count = (n + 1) * (n + 2) / 2;
return count;
}
// driver program
var n = 3;
document.write(count_of_ways(n));
// This code is contributed by bunnyram19.
</script>
输出:
10
时间复杂度: O(1)
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