最大长度双调子阵列 |设置 2（O(n) 时间和 O(1) 空间）

给定一个包含 n 个正整数的数组 A[0 ... n-1]，如果存在 ak 且 i <= k <= j 满足 A[i] = .. A[j，则子数组 A[i ... j] 是双调的– 1] > = A[j]。编写一个函数数组为参数并返回最大长度双调子数组的长度的函数。

我们在下面的帖子中讨论了 O(n) 时间和 O(n) 空间方法。
最大长度双调子阵列 |设置 1（O(n) 时间和 O(n) 空间）
在这组中，我们将讨论占用恒定额外空间的解决方案。
这个想法是检查从 A[i] 开始的最长双调子数组。从 A[i] 开始，我们首先检查上升结束，然后检查下降结束。当沿着当前子数组的斜率下降时，当它找到两个相等的值时，通过记录下一个开始位置来考虑双调子数组的重叠。如果这个子数组的长度大于 max_len，我们将更新 max_len。我们继续这个过程，直到到达数组的末尾。

C++

// C++ program to find length of longest bitonic
// subarray. O(n) time and O(1) extra space
#include 
using namespace std;
 
// Function to find length of longest bitonic
// subarray
int bitonic(int *A, int n)
{
    // if A is empty
    if (n == 0)
        return 0;
         
    // initializing max_len
    int maxLen=1;
         
    int start=0;
    int nextStart=0;
         
    int j =0;
    while (j < n-1)
    {
        // look for end of ascent      
        while (j=A[j+1]){
                 
            // adjusting nextStart;
            // this will be necessarily executed at least once,
            // when we detect the start of the descent
            if (jA[j+1])
                nextStart=j+1;
                 
            j++;
        }
             
        // updating maxLen, if required
        maxLen = max(maxLen,j-(start-1));
             
        start=nextStart;
    }
         
    return maxLen;
}
 
int main()
{
    int A[] = {12, 4, 78, 90, 45, 23};
    int n = sizeof(A)/sizeof(A[0]);
    printf("Length of max length Bitonic "
            "Subarray is %d", bitonic(A, n));
    return 0;
}

Java

// Java program to find length of longest bitonic
// subarray O(n) time and O(1) extra space
 
public class MaxLengthBitonic
{
    // Method to find length of longest bitonic
    // subarray
    static int maxLenBitonic(int[] A,int n)
    {
        // if A is empty
        if (n == 0)
            return 0;
         
        // initializing max_len
        int maxLen=1;
         
        int start=0;
        int nextStart=0;
         
        int j =0;
        while (j < n-1)
        {
            // look for end of ascent      
            while (j=A[j+1]){
                 
                // adjusting nextStart;
                // this will be necessarily executed at least once,
                // when we detect the start of the descent
                if (jA[j+1])
                    nextStart=j+1;
                 
                j++;
            }
             
            // updating maxLen, if required
            maxLen = Math.max(maxLen,j-(start-1));
             
            start=nextStart;
        }
         
        return maxLen;
    }
     
    public static void  main(String[] args)
    {
        int A[] = {12, 4, 78, 90, 45, 23};
        System.out.println("Length of maximal length bitonic " +
                            "subarray is " + maxLenBitonic(A,A.length));
 
    }
}
// This code is contributed by Markus Schott

Python3

# Python3 program to find length of longest bitonic
# subarray. O(n) time and O(1) extra space
 
# Function to find length of longest
# bitonic subarray
def bitonic(A, n):
 
    # if A is empty
    if (n == 0):
        return 0;
         
    # initializing max_len
    maxLen = 1;
         
    start = 0;
    nextStart = 0;
         
    j = 0;
    while (j < n - 1):
     
        # look for end of ascent    
        while (j < n - 1 and A[j] <= A[j + 1]):
            j = j + 1;
             
        # look for end of descent
        while (j < n - 1 and A[j] >= A[j + 1]):
                 
            # adjusting nextStart;
            # this will be necessarily executed
            # at least once, when we detect the
            # start of the descent
            if (j < n - 1 and A[j] > A[j + 1]):
                nextStart = j + 1;
                 
            j = j + 1;
         
        # updating maxLen, if required
        maxLen = max(maxLen, j - (start - 1));
             
        start = nextStart;
     
    return maxLen;
 
# Driver Code
A = [12, 4, 78, 90, 45, 23];
n = len(A);
print("Length of max length Bitonic Subarray is",
                                  bitonic(A, n));
 
# This code is contributed by Shivi_Aggarwal

C#

// C# program to find length of longest bitonic
// subarray O(n) time and O(1) extra space
using System;
 
class MaxLengthBitonic
{
    // Method to find length of
    // longest bitonic subarray
    static int maxLenBitonic(int[] A, int n)
    {
        // if A is empty
        if (n == 0)
            return 0;
         
        // initializing max_len
        int maxLen = 1;
         
        int start = 0;
        int nextStart = 0;
         
        int j = 0;
        while (j < n-1)
        {
            // look for end of ascent    
            while (j < n-1 && A[j] <= A[j+1])
                j++;
             
            // look for end of descent    
            while (j < n-1 && A[j] >= A[j+1]){
                 
                // adjusting nextStart;
                // this will be necessarily executed at least once,
                // when we detect the start of the descent
                if (j < n-1 && A[j] > A[j+1])
                    nextStart=j + 1;
                 
                j++;
            }
             
            // updating maxLen, if required
            maxLen = Math.Max(maxLen, j - (start - 1));
             
            start=nextStart;
        }
        return maxLen;
    }
     
    public static void Main()
    {
        int []A = {12, 4, 78, 90, 45, 23};
        Console.Write("Length of maximal length bitonic " +
                      "subarray is " + maxLenBitonic(A, A.Length));
    }
}
 
// This code is contributed by nitin mittal.

PHP

= $A[$j + 1])
        {
                 
            // adjusting nextStart;
            // this will be necessarily
            // executed at least once,
            // when we detect the start
            // of the descent
            if ($j < $n - 1 && $A[$j] >
                          $A[$j + 1])
                $nextStart = $j + 1;
            $j++;
        }
             
        // updating maxLen,
        // if required
        $maxLen = max($maxLen, $j - ($start - 1));
        $start = $nextStart;
    }
         
    return $maxLen;
}
 
    // Driver Code
    $A = array(12, 4, 78, 90, 45, 23);
    $n = sizeof($A);
    echo "Length of max length Bitonic "
        ,"Subarray is ", bitonic($A, $n);
 
// This code is contributed by nitin mittal.
?>

Javascript

 
// JavaScript program to find length of
// longest bitonic subarray.
// O(n) time and O(1) extra space
 
// Function to find length of
// longest bitonic subarray
function bitonic(A, n) {
 
    // if A is empty
    if (n == 0)
        return 0;
 
    // initializing max_len
    let maxLen = 1;
 
    let start = 0;
    let nextStart = 0;
 
    let j = 0;
    while (j < n - 1) {
 
        // look for end of ascent   
        while (j < n - 1 &&
            A[j] <= A[j + 1])
            j++;
 
        // look for end of descent   
        while (j < n - 1 &&
            A[j] >= A[j + 1]) {
 
            // adjusting nextStart;
            // this will be necessarily
            // executed at least once,
            // when we detect the start
            // of the descent
            if (j < n - 1 && A[j] >
                A[j + 1])
                nextStart = j + 1;
            j++;
        }
 
        // updating maxLen,
        // if required
        maxLen = Math.max(maxLen, j - (start - 1));
        start = nextStart;
    }
 
    return maxLen;
}
 
// Driver Code
let A = new Array(12, 4, 78, 90, 45, 23);
let n = A.length;
document.write("Length of max length Bitonic "
    + "Subarray is " + bitonic(A, n));
 
// This code is contributed by gfgking
 

输出：

Length of max length bitonic subarray is 5