给定数组arr [],其中包含N个整数以及两个整数X和Y。考虑N个线段,其中每个线段的起点和终点分别为arr [i] – X和arr [i] +Y 。
给定另一个数组M个点的b [] 。任务是将这些点分配给段,以使已分配点的段数最大。请注意,一个点最多可以分配给1个线段。
例子:
Input: arr[] = {1, 5}, b = {1, 1, 2}, X = 1, Y = 4
Output: 1
Line Segments are [1-X, 1+Y] , [5-X, 5+Y] i.e. [0, 5] and [4, 9]
The point 1 can be assigned to the first segment [0, 5]
No points can be assigned to the second segment.
So 2 can also be assigned to the first segment but it will not maximize the no. of segment.
So the answer is 1.
Input: arr[] = {1, 2, 3, 4}, b = {1, 3, 5}, X = 0, Y = 0
Output: 2
方法:对两个输入数组进行排序。现在,对于每个段,我们尝试为其分配可能的第一个未分配点。如果当前线段在当前点之前结束,则意味着我们将无法为其分配任何点,因为其前面的所有点都大于当前点,并且线段已经结束。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the maximum number of segments
int countPoints(int n, int m, vector a,
vector b, int x, int y)
{
// Sort both the vectors
sort(a.begin(), a.end());
sort(b.begin(), b.end());
// Initially pointing to the first element of b[]
int j = 0;
int count = 0;
for (int i = 0; i < n; i++) {
// Try to find a match in b[]
while (j < m) {
// The segment ends before b[j]
if (a[i] + y < b[j])
break;
// The point lies within the segment
if (b[j] >= a[i] - x && b[j] <= a[i] + y) {
count++;
j++;
break;
}
// The segment starts after b[j]
else
j++;
}
}
// Return the required count
return count;
}
// Driver code
int main()
{
int x = 1, y = 4;
vector a = { 1, 5 };
int n = a.size();
vector b = { 1, 1, 2 };
int m = a.size();
cout << countPoints(n, m, a, b, x, y);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
// Function to return the
// maximum number of segments
static int countPoints(int n, int m, int a[],
int[] b, int x, int y)
{
// Sort both the vectors
Arrays.sort(a);
Arrays.sort(b);
// Initially pointing to the first element of b[]
int j = 0;
int count = 0;
for (int i = 0; i < n; i++)
{
// Try to find a match in b[]
while (j < m)
{
// The segment ends before b[j]
if (a[i] + y < b[j])
break;
// The point lies within the segment
if (b[j] >= a[i] - x && b[j] <= a[i] + y)
{
count++;
j++;
break;
}
// The segment starts after b[j]
else
j++;
}
}
// Return the required count
return count;
}
// Driver code
public static void main(String args[])
{
int x = 1, y = 4;
int[] a = { 1, 5 };
int n = a.length;
int[] b = { 1, 1, 2 };
int m = a.length;
System.out.println(countPoints(n, m, a, b, x, y));
}
}
// This code is contributed by
// Surendra_Gangwar
Python3
# Python3 implementation of the approach
# Function to return the maximum
# number of segments
def countPoints(n, m, a, b, x, y):
# Sort both the vectors
a.sort()
b.sort()
# Initially pointing to the first
# element of b[]
j, count = 0, 0
for i in range(0, n):
# Try to find a match in b[]
while j < m:
# The segment ends before b[j]
if a[i] + y < b[j]:
break
# The point lies within the segment
if (b[j] >= a[i] - x and
b[j] <= a[i] + y):
count += 1
j += 1
break
# The segment starts after b[j]
else:
j += 1
# Return the required count
return count
# Driver code
if __name__ == "__main__":
x, y = 1, 4
a = [1, 5]
n = len(a)
b = [1, 1, 2]
m = len(b)
print(countPoints(n, m, a, b, x, y))
# This code is contributed by Rituraj Jain
C#
// C# implementation of the approach
using System;
class GFG
{
// Function to return the
// maximum number of segments
static int countPoints(int n, int m, int []a,
int []b, int x, int y)
{
// Sort both the vectors
Array.Sort(a);
Array.Sort(b);
// Initially pointing to the
// first element of b[]
int j = 0;
int count = 0;
for (int i = 0; i < n; i++)
{
// Try to find a match in b[]
while (j < m)
{
// The segment ends before b[j]
if (a[i] + y < b[j])
break;
// The point lies within the segment
if (b[j] >= a[i] - x && b[j] <= a[i] + y)
{
count++;
j++;
break;
}
// The segment starts after b[j]
else
j++;
}
}
// Return the required count
return count;
}
// Driver code
public static void Main()
{
int x = 1, y = 4;
int[] a = {1, 5};
int n = a.Length;
int[] b = {1, 1, 2};
int m = a.Length;
Console.WriteLine(countPoints(n, m, a, b, x, y));
}
}
// This code is contributed by Ryuga
PHP
= $a[$i] - $x &&
$b[$j] <= $a[$i] + $y)
{
$count++;
$j++;
break;
}
// The segment starts after b[j]
else
$j++;
}
}
// Return the required count
return $count;
}
// Driver code
$x = 1;
$y = 4;
$a = array( 1, 5 );
$n = count($a);
$b = array( 1, 1, 2 );
$m = count($b);
echo countPoints($n, $m, $a, $b, $x, $y);
// This code is contributed by Arnab Kundu
?>
1
时间复杂度: O(N * log(N))
辅助空间: O(1)