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📜  检查数组是否形成增减序列,反之亦然

📅  最后修改于: 2021-05-13 22:49:33             🧑  作者: Mango

给定N个整数的数组arr [] ,任务是查找该数组是否可以分为2个子数组,以使第一个子数组严格增加而第二个子数组严格减少,反之亦然。如果给定的数组可以分割,则打印“是”,否则打印“否”
例子:

幼稚的方法:幼稚的想法是将数组在每个可能的索引处划分为两个子数组,并显式检查第一个子数组是否严格增加,第二个子数组是否严格减少,反之亦然。如果我们可以破坏任何子数组,则打印“是”,否则打印“否”
时间复杂度: O(N 2 )
辅助空间: O(1)
高效方法:要优化上述方法,请遍历数组并检查严格递增的序列,然后检查严格递减的子序列,反之亦然。步骤如下:

  1. 如果arr [1]> arr [0],则检查严格增加然后严格减少为:
    • 检查每对连续的对,直到在任何索引i arr [i + 1]小于arr [i]为止。
    • 现在,从索引i +1开始,检查每个连续的对,直到数组结尾为止,是否arr [i +1]小于arr [i]。如果在任何索引i处, arr [i]均小于arr [i + 1],则中断循环。
    • 如果我们在上述步骤中结束,则打印“是”,否则打印“否”
  2. 如果arr [1]
  3. 检查每对连续的对,直到在任何索引i arr [i + 1]大于arr [i]为止。
  4. 现在,从索引i +1开始,检查每个连续的对,直到数组结尾为止,是否arr [i +1]大于arr [i]。如果在任何索引i处, arr [i]均大于arr [i + 1],则中断循环。
  5. 如果我们在上述步骤中结束,则打印“是”,否则打印“否”

下面是上述方法的实现:

C++
// C++ program for the above approach
#include 
using namespace std;
  
// Function to check if the given array
// forms an increasing decreasing
// sequence or vice versa
bool canMake(int n, int ar[])
{
    // Base Case
    if (n == 1)
        return true;
    else {
  
        // First subarray is
        // stricly increasing
        if (ar[0] < ar[1]) {
  
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n
                   && ar[i - 1] < ar[i]) {
                i++;
            }
  
            // Check for strictly
            // decreasing condition
            // & find the break point
            while (i + 1 < n
                   && ar[i] > ar[i + 1]) {
                i++;
            }
  
            // If i is equal to
            // length of array
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // First subarray is
        // strictly Decreasing
        else if (ar[0] > ar[1]) {
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n
                   && ar[i - 1] > ar[i]) {
                i++;
            }
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i + 1 < n
                   && ar[i] < ar[i + 1]) {
                i++;
            }
  
            // If i is equal to
            // length of array - 1
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // Condition if ar[0] == ar[1]
        else {
            for (int i = 2; i < n; i++) {
                if (ar[i - 1] <= ar[i])
                    return false;
            }
            return true;
        }
    }
}
  
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 1, 2, 3, 4, 5 };
    int n = sizeof arr / sizeof arr[0];
  
    // Function Call
    if (canMake(n, arr)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
  
    return 0;
}


Java
// Java program for the above approach
import java.util.*;
class GFG{
  
// Function to check if the given array
// forms an increasing decreasing
// sequence or vice versa
static boolean canMake(int n, int ar[])
{
    // Base Case
    if (n == 1)
        return true;
    else 
    {
  
        // First subarray is
        // stricly increasing
        if (ar[0] < ar[1]) 
        {
  
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n && ar[i - 1] < ar[i]) 
            {
                i++;
            }
  
            // Check for strictly
            // decreasing condition
            // & find the break point
            while (i + 1 < n && ar[i] > ar[i + 1])
            {
                i++;
            }
  
            // If i is equal to
            // length of array
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // First subarray is
        // strictly Decreasing
        else if (ar[0] > ar[1]) 
        {
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n && ar[i - 1] > ar[i]) 
            {
                i++;
            }
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i + 1 < n && ar[i] < ar[i + 1]) 
            {
                i++;
            }
  
            // If i is equal to
            // length of array - 1
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // Condition if ar[0] == ar[1]
        else 
        {
            for (int i = 2; i < n; i++)
            {
                if (ar[i - 1] <= ar[i])
                    return false;
            }
            return true;
        }
    }
}
  
// Driver Code
public static void main(String[] args)
{
    // Given array arr[]
    int arr[] = { 1, 2, 3, 4, 5 };
    int n = arr.length;
  
    // Function Call
    if (!canMake(n, arr)) {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
  
// This code is contributed by Rohit_ranjan


Python3
# Python3 program for the above approach
  
# Function to check if the given array
# forms an increasing decreasing
# sequence or vice versa
def canMake(n, ar):
      
    # Base Case
    if (n == 1):
        return True;
    else:
  
        # First subarray is
        # stricly increasing
        if (ar[0] < ar[1]):
  
            i = 1;
  
            # Check for strictly
            # increasing condition
            # & find the break point
            while (i < n and ar[i - 1] < ar[i]):
                i += 1;
  
            # Check for strictly
            # decreasing condition
            # & find the break point
            while (i + 1 < n and ar[i] > ar[i + 1]):
                i += 1;
  
            # If i is equal to
            # length of array
            if (i >= n - 1):
                return True;
            else:
                return False;
  
        # First subarray is
        # strictly Decreasing
        elif (ar[0] > ar[1]):
            i = 1;
  
            # Check for strictly
            # increasing condition
            # & find the break point
            while (i < n and ar[i - 1] > ar[i]):
                i += 1;
  
            # Check for strictly
            # increasing condition
            # & find the break point
            while (i + 1 < n and ar[i] < ar[i + 1]):
                i += 1;
  
            # If i is equal to
            # length of array - 1
            if (i >= n - 1):
                return True;
            else:
                return False;
  
        # Condition if ar[0] == ar[1]
        else:
            for i in range(2, n):
                if (ar[i - 1] <= ar[i]):
                    return False;
  
            return True;
  
# Driver Code
  
# Given array arr
arr = [1, 2, 3, 4, 5];
n = len(arr);
  
# Function Call
if (canMake(n, arr)==False):
    print("Yes");
else:
    print("No");
  
# This code is contributed by PrinciRaj1992


C#
// C# program for the above approach
using System;
class GFG{
  
// Function to check if the given array
// forms an increasing decreasing
// sequence or vice versa
static bool canMake(int n, int []ar)
{
    // Base Case
    if (n == 1)
        return true;
    else 
    {
  
        // First subarray is
        // stricly increasing
        if (ar[0] < ar[1]) 
        {
  
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n && ar[i - 1] < ar[i]) 
            {
                i++;
            }
  
            // Check for strictly
            // decreasing condition
            // & find the break point
            while (i + 1 < n && ar[i] > ar[i + 1])
            {
                i++;
            }
  
            // If i is equal to
            // length of array
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // First subarray is
        // strictly Decreasing
        else if (ar[0] > ar[1]) 
        {
            int i = 1;
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i < n && ar[i - 1] > ar[i]) 
            {
                i++;
            }
  
            // Check for strictly
            // increasing condition
            // & find the break point
            while (i + 1 < n && ar[i] < ar[i + 1]) 
            {
                i++;
            }
  
            // If i is equal to
            // length of array - 1
            if (i >= n - 1)
                return true;
            else
                return false;
        }
  
        // Condition if ar[0] == ar[1]
        else 
        {
            for (int i = 2; i < n; i++)
            {
                if (ar[i - 1] <= ar[i])
                    return false;
            }
            return true;
        }
    }
}
  
// Driver Code
public static void Main(String[] args)
{
    // Given array []arr
    int []arr = { 1, 2, 3, 4, 5 };
    int n = arr.Length;
  
    // Function Call
    if (!canMake(n, arr))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
  
// This code is contributed by Rajput-Ji


输出:
No





时间复杂度: O(N)
辅助空间: O(1)