给定N个水平线表示由阵列位置[] [大小N,其中位置[I]]表示具有第i个水平行x坐标-从位置[I] [0]至位置[I] [1]和一个整数K,表示可以绘制的最大垂直线数,任务是检查N 条给定的线是否可以与最多K 条垂直线相交。
例子:
Input: N = 4, K = 2, position[][] = [[1, 4], [6, 8], [7, 9], [10, 15]]
Output: NO
Explanation: In the given example, draw lines at [1, 7, 10]. The line drawn at 1 will intersect the first line, the line at position 7 will intersect both the second and third lines, and the line drawn at 10 will intersect the fourth line. Hence, a minimum of 3 rods is required. Hence, it is not possible
Input: N = 5, K = 3, position[][] = [[1, 6], [3, 5], [2, 4], [8, 12], [10, 24]]
Output : YES
方法:这个想法是使用贪心的方法来解决这个问题,通过对positions[][]数组进行排序,并用1条线,交叉尽可能多的线等等。请按照以下步骤解决问题:
- 按升序对数组position[][]进行排序。
- 将变量ans初始化为1以存储答案,将r初始化为position[0][1]以存储终点直到特定点,其他水平线可以与给定的考虑垂直线相交。
- 使用变量迭代范围[1, N] ,例如 I ,并执行以下步骤:
- 如果位置[I] [0]是小于r,则r的值设置为最小R或位置[I] [1]的。
- 否则,将ans的值加1 ,并将r的值设置为position[i][1]。
- 如果k更大 小于等于ans,则打印“YES” ,否则打印“NO” 。
下面是上述方法的实现:
C++14
// C++ program for the above approach
#include
using namespace std;
// Function to check if it is possible
// to intersect n lines using k vertical lines
void findIfPossible(int n, int k,
vector > position)
{
sort(position.begin(), position.end());
int ans = 1;
// Track the point till a particular
// vertical line can intersect
int r = position[0][1];
// Iterate over the range
for (int i = 1; i < n; i++) {
if (position[i][0] <= r) {
r = min(r, position[i][1]);
}
else {
ans++;
r = position[i][1];
}
}
if (k >= ans)
cout << "YES" << endl;
else
cout << "NO" << endl;
}
// Driver Code
int main()
{
int n = 5;
int k = 2;
vector > position = {
{ 2, 5 }, { 4, 6 }, { 7, 16 }, { 9, 10 }, { 10, 17 }
};
findIfPossible(n, k, position);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG
{
// Function to check if it is possible
// to intersect n lines using k vertical lines
static void findIfPossible(int n, int k,
int[][] position)
{
Arrays.sort(position, Comparator.comparingDouble(o -> o[0]));
int ans = 1;
// Track the point till a particular
// vertical line can intersect
int r = position[0][1];
// Iterate over the range
for (int i = 1; i < n; i++) {
if (position[i][0] <= r) {
r = Math.min(r, position[i][1]);
}
else {
ans++;
r = position[i][1];
}
}
if (k >= ans)
System.out.println("YES");
else
System.out.println("NO");
}
// Driver Code
public static void main(String[] args)
{
int n = 5;
int k = 2;
int[][] position = {
{ 2, 5 }, { 4, 6 }, { 7, 16 }, { 9, 10 }, { 10, 17 }
};
findIfPossible(n, k, position);
}
}
// This code is contributed by sanjoy_62.
Python3
# python program for the above approach
# Function to check if it is possible
# to intersect n lines using k vertical lines
def findIfPossible(n, k, position):
position.sort()
ans = 1
# Track the point till a particular
# vertical line can intersect
r = position[0][1]
# Iterate over the range
for i in range(1, n):
if (position[i][0] <= r):
r = min(r, position[i][1])
else:
ans += 1
r = position[i][1]
if (k >= ans):
print("YES")
else:
print("NO")
# Driver Code
n = 5
k = 2
position = [[2, 5], [4, 6], [7, 16], [9, 10], [10, 17]]
findIfPossible(n, k, position)
# This code is contributed by amreshkumar3
C#
// C# program for the above approach
using System;
class GFG{
static void Sort(int[,] arr)
{
for(int i = 0; i < arr.GetLength(0); i++)
{
for(int j = arr.GetLength(1) - 1; j > 0; j--)
{
for(int k = 0; k < j; k++)
{
if (arr[i, k] > arr[i, k + 1])
{
int myTemp = arr[i, k];
arr[i, k] = arr[i, k + 1];
arr[i, k + 1] = myTemp;
}
}
}
}
}
// Function to check if it is possible
// to intersect n lines using k vertical lines
static void findIfPossible(int n, int k,
int[,] position)
{
Sort(position);
int ans = 1;
// Track the point till a particular
// vertical line can intersect
int r = position[0, 1];
// Iterate over the range
for(int i = 1; i < n; i++)
{
if (position[i, 0] <= r)
{
r = Math.Min(r, position[i, 1]);
}
else
{
ans++;
r = position[i, 1];
}
}
if (k >= ans)
Console.Write("YES");
else
Console.Write("NO");
}
// Driver Code
public static void Main(string[] args)
{
int n = 5;
int k = 2;
int[,] position = { { 2, 5 }, { 4, 6 },
{ 7, 16 }, { 9, 10 },
{ 10, 17 } };
findIfPossible(n, k, position);
}
}
// This code is contributed by code_hunt
Javascript
YES
时间复杂度: O(NlogN)
辅助空间: O(1)
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