本文概述
给出一个包含N个整数和另一个k≤N的整数的数组arr[],任务是找到每个大小为k的子数组的最大元素。
例子:
Input: arr[] = {9, 7, 2, 4, 6, 8, 2, 1, 5}
k = 3
Output: 9 7 6 8 8 8 5
Explanation:
Window 1: {9, 7, 2}, max = 9
Window 2: {7, 2, 4}, max = 7
Window 3: {2, 4, 6}, max = 6
Window 4: {4, 6, 8}, max = 8
Window 5: {6, 8, 2}, max = 8
Window 6: {8, 2, 1}, max = 8
Window 7: {2, 1, 5}, max = 5
Input: arr[] = {6, 7, 5, 2, 1, 7, 2, 1, 10}
k = 2
Output: 7 7 5 2 7 7 2 10
Explanation:
Window 1: {6, 7}, max = 7
Window 2: {7, 5}, max = 7
Window 3: {5, 2}, max = 5
Window 4: {2, 1}, max = 2
Window 5: {1, 7}, max = 7
Window 6: {7, 2}, max = 7
Window 7: {2, 1}, max = 2
Window 8: {1, 10}, max = 10
先决条件: 下一个更大的元素
方法:
对于每个索引,计算子数组从这个索引开始时当前元素最大的索引,即对于每个索引i,一个索引j≥i,使max(a[i], a[i + 1],…a[j]) = a[i]。我们把它命名为max_upto[i]。
然后,通过检查从i到i + k - 1, max_upto[i]≥i + k - 1(该窗口的最后一个索引)的每个索引,可以找到长度为k的子数组中从第i个索引开始的最大元素。
栈数据结构可以用来在一个窗口中存储值,即最后访问的或之前插入的元素将在顶部(与当前元素的索引最近的元素)。
算法:
- 创建一个数组max_upto和一个用于存储索引的堆栈。在堆栈中压入0。
- 运行从索引1到索引n-1的循环。
- 从堆栈中弹出所有索引, 其中哪些元素(array 展开)小于当前元素并更新max_upto 展开 = i – 1然后将i插入堆栈。
- 从堆栈中弹出所有索引并分配max_upto 展开 = n – 1.
- 创建一个变量j = 0
- 运行从0到n – k的循环, 循环计数器为i
- 运行一个嵌套循环, 直到j <i或max_upto [j] <i + k – 1, 在每次迭代中递增j。
- 打印第j个数组元素。
实现
C ++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to print the maximum for
// every k size sub-array
void print_max( int a[], int n, int k)
{
// max_upto array stores the index
// upto which the maximum element is a[i]
// i.e. max(a[i], a[i + 1], ... a[max_upto[i]]) = a[i]
int max_upto[n];
// Update max_upto array similar to
// finding next greater element
stack< int > s;
s.push(0);
for ( int i = 1; i < n; i++) {
while (!s.empty() && a展开 < a[i]) {
max_upto展开 = i - 1;
s.pop();
}
s.push(i);
}
while (!s.empty()) {
max_upto展开 = n - 1;
s.pop();
}
int j = 0;
for ( int i = 0; i <= n - k; i++) {
// j < i is to check whether the
// jth element is outside the window
while (j < i || max_upto[j] < i + k - 1)
j++;
cout << a[j] << " " ;
}
cout << endl;
}
// Driver code
int main()
{
int a[] = { 9, 7, 2, 4, 6, 8, 2, 1, 5 };
int n = sizeof (a) / sizeof ( int );
int k = 3;
print_max(a, n, k);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
// Function to print the maximum for
// every k size sub-array
static void print_max( int a[], int n, int k)
{
// max_upto array stores the index
// upto which the maximum element is a[i]
// i.e. max(a[i], a[i + 1], ... a[max_upto[i]]) = a[i]
int [] max_upto = new int [n];
// Update max_upto array similar to
// finding next greater element
Stack<Integer> s = new Stack<>();
s.push( 0 );
for ( int i = 1 ; i < n; i++)
{
while (!s.empty() && a展开 < a[i])
{
max_upto展开 = i - 1 ;
s.pop();
}
s.push(i);
}
while (!s.empty())
{
max_upto展开 = n - 1 ;
s.pop();
}
int j = 0 ;
for ( int i = 0 ; i <= n - k; i++)
{
// j < i is to check whether the
// jth element is outside the window
while (j < i || max_upto[j] < i + k - 1 )
{
j++;
}
System.out.print(a[j] + " " );
}
System.out.println();
}
// Driver code
public static void main(String[] args)
{
int a[] = { 9 , 7 , 2 , 4 , 6 , 8 , 2 , 1 , 5 };
int n = a.length;
int k = 3 ;
print_max(a, n, k);
}
}
// This code has been contributed by 29AjayKumar
Python3
# Python3 implementation of the approach
# Function to print the maximum for
# every k size sub-array
def print_max(a, n, k):
# max_upto array stores the index
# upto which the maximum element is a[i]
# i.e. max(a[i], a[i + 1], ... a[max_upto[i]]) = a[i]
max_upto = [ 0 for i in range (n)]
# Update max_upto array similar to
# finding next greater element
s = []
s.append( 0 )
for i in range ( 1 , n):
while ( len (s) > 0 and a展开] < a[i]):
max_upto展开] = i - 1
del s[ - 1 ]
s.append(i)
while ( len (s) > 0 ):
max_upto展开] = n - 1
del s[ - 1 ]
j = 0
for i in range (n - k + 1 ):
# j < i is to check whether the
# jth element is outside the window
while (j < i or max_upto[j] < i + k - 1 ):
j + = 1
print (a[j], end = " " )
print ()
# Driver code
a = [ 9 , 7 , 2 , 4 , 6 , 8 , 2 , 1 , 5 ]
n = len (a)
k = 3
print_max(a, n, k)
# This code is contributed by mohit kumar
C#
// C# implementation of the approach
using System;
using System.Collections.Generic;
class GFG
{
// Function to print the maximum for
// every k size sub-array
static void print_max( int []a, int n, int k)
{
// max_upto array stores the index
// upto which the maximum element is a[i]
// i.e. max(a[i], a[i + 1], ... a[max_upto[i]]) = a[i]
int [] max_upto = new int [n];
// Update max_upto array similar to
// finding next greater element
Stack< int > s = new Stack< int >();
s.Push(0);
for ( int i = 1; i < n; i++)
{
while (s.Count!=0 && a展开 < a[i])
{
max_upto展开 = i - 1;
s.Pop();
}
s.Push(i);
}
while (s.Count!=0)
{
max_upto展开 = n - 1;
s.Pop();
}
int j = 0;
for ( int i = 0; i <= n - k; i++)
{
// j < i is to check whether the
// jth element is outside the window
while (j < i || max_upto[j] < i + k - 1)
{
j++;
}
Console.Write(a[j] + " " );
}
Console.WriteLine();
}
// Driver code
public static void Main(String[] args)
{
int []a = {9, 7, 2, 4, 6, 8, 2, 1, 5};
int n = a.Length;
int k = 3;
print_max(a, n, k);
}
}
// This code has been contributed by 29AjayKumar
输出如下:
9 7 6 8 8 8 5
复杂度分析:
- 时间复杂度:O(n)。
仅需要两次遍历数组。因此, 时间复杂度为O(n)。 - 空间复杂度:O(n)。
需要两个大小为n的额外空间。