给定一个数组元素,其中数组中的每个元素表示圆上已有切口的度(0 <= a [i] <= 359) 。任务是找到使圆弧段大小相等所需的最小额外切割次数。
例子:
Input : arr[] = { 0, 2 }
Output : 178
Input : arr[] = { 30, 60, 180 }
Output : 9
方法:解决上述问题的一种有效方法是找到所有连续的角度差的gcd。该gcd是一个圆形线段的最大角度,然后将获得360 / gcdOb的线段数。但是,已经有N个削减。因此,其他削减将为(360 / gcdObtained)– N。
下面是上述方法的实现:
C++
// CPP program to find the minimum number
// of additional cuts required to make
// circle segments equal sized
#include
using namespace std;
// Function to find the minimum number
// of additional cuts required to make
// circle segments are equal sized
int minimumCuts(int a[], int n)
{
// Sort the array
sort(a, a + n);
// Initial gcd value
int gcd = a[1] - a[0];
int s = gcd;
for (int i = 2; i < n; i++) {
gcd = __gcd(gcd, a[i] - a[i - 1]);
s += a[i] - a[i - 1];
}
// Inlcuding the last segment
if (360 - s > 0)
gcd = __gcd(gcd, 360 - s);
return (360 / gcd) - n;
}
// Driver code
int main()
{
int arr[] = { 30, 60, 180 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << minimumCuts(arr, n);
return 0;
}
Java
// Java program to find the minimum
// number of additional cuts required
// to make circle segments equal sized
import java.util.Arrays;
class GFG
{
// Recursive function to
// return gcd of two nos
static int findgcd(int a, int b)
{
if (b == 0)
return a;
return findgcd(b, a % b);
}
// Function to find the minimum number
// of additional cuts required to make
// circle segments are equal sized
static int minimumCuts(int a[], int n)
{
// Sort the array
Arrays.sort(a);
// Initial gcd value
int gcd = a[1] - a[0];
int s = gcd;
for (int i = 2; i < n; i++)
{
gcd = findgcd(gcd, a[i] - a[i - 1]);
s += a[i] - a[i - 1];
}
// Inlcuding the last segment
if (360 - s > 0)
gcd = findgcd(gcd, 360 - s);
return (360 / gcd) - n;
}
// Driver code
public static void main(String[] args)
{
int[] arr = new int[] { 30, 60, 180 };
int n = arr.length;
System.out.println(minimumCuts(arr, n));
}
}
// This code is contributed by mits
Python 3
# Python 3 program to find the minimum number
# of additional cuts required to make
# circle segments equal sized
import math
# Function to find the minimum number
# of additional cuts required to make
# circle segments are equal sized
def minimumCuts(a, n):
# Sort the array
a.sort()
# Initial gcd value
gcd = a[1] - a[0]
s = gcd
for i in range(2,n) :
gcd = math.gcd(gcd, a[i] - a[i - 1])
s += a[i] - a[i - 1]
# Inlcuding the last segment
if (360 - s > 0):
gcd = math.gcd(gcd, 360 - s)
return (360 // gcd) - n
# Driver code
if __name__ == "__main__":
arr = [ 30, 60, 180 ]
n = len(arr)
print(minimumCuts(arr, n))
C#
// C# program to find the minimum
// number of additional cuts required
// to make circle segments equal sized
using System;
class GFG
{
// Recursive function to
// return gcd of two nos
static int findgcd(int a, int b)
{
if (b == 0)
return a;
return findgcd(b, a % b);
}
// Function to find the minimum number
// of additional cuts required to make
// circle segments are equal sized
static int minimumCuts(int []a, int n)
{
// Sort the array
Array.Sort(a);
// Initial gcd value
int gcd = a[1] - a[0];
int s = gcd;
for (int i = 2; i < n; i++)
{
gcd = findgcd(gcd, a[i] - a[i - 1]);
s += a[i] - a[i - 1];
}
// Inlcuding the last segment
if (360 - s > 0)
gcd = findgcd(gcd, 360 - s);
return (360 / gcd) - n;
}
// Driver Code
static void Main()
{
int[] arr = new int[] { 30, 60, 180 };
int n = arr.Length;
Console.WriteLine(minimumCuts(arr, n));
}
// This code is contributed by ANKITRAI1
}
PHP
0)
$gcd = findgcd($gcd, 360 - $s);
return (360 / $gcd) - $n;
}
// Driver Code
$arr = array(30, 60, 180);
$n = sizeof($arr);
echo (minimumCuts($arr, $n));
// This code is contributed by ajit
?>
Javascript
输出:
9