给定一个由N个非负整数组成的数组arr [] ,任务是为每个索引找到一个整数K ,以使数组中至少K个整数直到该索引大于或等于K。
注意:考虑基于1的索引
例子:
Input: arr[] = {3, 0, 6, 1, 5}
Output: K = {1, 1, 2, 2, 3}
Explanation:
At index 1, there is 1 number greater than or equal to 1 in the array i.e. 3. So K value for elements upto index 1 is 1.
At index 2, there is 1 number greater than or equal to 1 in the array i.e. 3. So K value for elements upto index 2 is 1.
At index 3, there are 2 numbers greater than or equal to 2 in the array i.e. 3 and 6. So K value for elements upto index 3 is 2.
At index 4, there are 2 numbers greater than or equal to 2 in the array i.e. 3 and 6. So K value for elements upto index 4 is 2.
At index 5, there are 3 numbers greater than or equal to 3 in the array i.e. 3, 6 and 5. So K value for elements up to index 5 is 3.
Input: arr[] = {9, 10, 7, 5, 0, 10, 2, 0}
Output: K = {1, 2, 3, 4, 4, 5, 5, 5}
天真的方法:
最简单的方法是使用给定链接的文章中使用的有效方法,找到数组[0,i]范围内所有元素的K值,其中i是数组arr []的索引。这里。
时间复杂度: O(N 2 )
空间复杂度: O(N)
高效方法:
这个想法是使用Multiset(红黑树)。多重集按排序顺序存储值,这有助于检查多重集中的当前最小值是否大于或等于其大小。如果是,则整数K的值将是多集的大小。
以下是实施步骤:
- 将数组从索引0遍历到N-1。
- 对于每个索引,将元素插入多重集并检查多重集中的最小值是否小于多重集的大小。
- 如果为true,则擦除起始元素并打印多集的大小。
- 如果为false,则只需打印多重集的大小即可。
- 多重集的大小是每个索引i所需的K值。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Function to find the K-value
// for every index in the array
int print_h_index(int arr[], int N)
{
// Multiset to store the array
// in the form of red-black tree
multiset ms;
// Iterating over the array
for (int i = 0; i < N; i++) {
// Inserting the current
// value in the multiset
ms.insert(arr[i]);
// Condition to check if
// the smallest value
// in the set is less than
// it's size
if (*ms.begin()
< ms.size()) {
// Erase the smallest
// value
ms.erase(ms.begin());
}
// h-index value will be
// the size of the multiset
cout << ms.size() << " ";
}
}
// Driver Code
int main()
{
// array
int arr[] = { 9, 10, 7, 5, 0,
10, 2, 0 };
// Size of the array
int N = sizeof(arr)
/ sizeof(arr[0]);
// function call
print_h_index(arr, N);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG{
// Function to find the K-value
// for every index in the array
static void print_h_index(int arr[], int N)
{
// Multiset to store the array
// in the form of red-black tree
List ms = new ArrayList();
// Iterating over the array
for(int i = 0; i < N; i++)
{
// Inserting the current
// value in the multiset
ms.add(arr[i]);
// Condition to check if
// the smallest value
// in the set is less than
// it's size
int t = Collections.min(ms);
if (t < ms.size())
{
// Erase the smallest
// value
ms.remove(ms.indexOf(t));
}
// h-index value will be
// the size of the multiset
System.out.print(ms.size() + " ");
}
}
// Driver code
public static void main(String[] args)
{
// Array
int arr[] = { 9, 10, 7, 5, 0,
10, 2, 0 };
// Size of the array
int N = arr.length;
// Function call
print_h_index(arr, N);
}
}
// This code is contributed by offbeat
Python3
# Python3 program for the above approach
# Function to find the K-value
# for every index in the array
def print_h_index(arr, N):
# Multiset to store the array
# in the form of red-black tree
ms = []
# Iterating over the array
for i in range(N):
# Inserting the current
# value in the multiset
ms.append(arr[i])
ms.sort()
# Condition to check if
# the smallest value
# in the set is less than
# it's size
if (ms[0] < len(ms)):
# Erase the smallest
# value
ms.pop(0)
# h-index value will be
# the size of the multiset
print(len(ms), end = ' ')
# Driver Code
if __name__=='__main__':
# Array
arr = [ 9, 10, 7, 5, 0, 10, 2, 0 ]
# Size of the array
N = len(arr)
# Function call
print_h_index(arr, N)
# This code is contributed by pratham76
C#
// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
// Function to find the K-value
// for every index in the array
static void print_h_index(int []arr, int N)
{
// Multiset to store the array
// in the form of red-black tree
ArrayList ms = new ArrayList();
// Iterating over the array
for(int i = 0; i < N; i++)
{
// Inserting the current
// value in the multiset
ms.Add(arr[i]);
// Condition to check if
// the smallest value
// in the set is less than
// it's size
int t = int.MaxValue;
foreach(int x in ms)
{
if(x < t)
{
t = x;
}
}
if (t < ms.Count)
{
// Erase the smallest
// value
ms.Remove(t);
}
// h-index value will be
// the size of the multiset
Console.Write(ms.Count + " ");
}
}
// Driver code
public static void Main(string[] args)
{
// Array
int []arr = { 9, 10, 7, 5, 0,
10, 2, 0 };
// Size of the array
int N = arr.Length;
// Function call
print_h_index(arr, N);
}
}
// This code is contributed by rutvik_56
1 2 3 4 4 5 5 5
时间复杂度: O(N * log(N))
辅助空间复杂度: O(N)
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