Count of K-countdowns in an Array

Last Updated : 20 May, 2021

Given an array arr[] of length N and a number K, the task is to count the number of K-countdowns in the array.

A contiguous subarray is said to be a K-countdown if it is of length K and contains the integers K, K-1, K-2, ..., 2, 1 in that order. For example, [4, 3, 2, 1] is 4-countdown and [6, 5, 4, 3, 2, 1] is a 6-countdown.

Examples:

Input: K = 2, arr[] = {3 2 1 2 2 1}
Output: 2
Explanation: Here, K=2 so the array has 2 2-Countdowns(2, 1). One countdown is from index 1 to 2 and the other is from index 4 to 5.
Input: K = 3, arr[] = {4 3 2 1 5 3 2 1}
Output: 2
Explanation: Here, K=3 so the array has 2 3-Countdowns(3, 2, 1)

Approach: The given array is traversed and every time the number K is encountered, it is checked if all the numbers K, K-1, K-2, ... up to 1 are sequentially present in the array or not. If yes, the count is increased by 1. If the next number takes it out of sequence, then the next occurrence of K is looked for.
Below is the implementation of the above approach:

C++

// C++ code for the above program.

#include <bits/stdc++.h>
using namespace std;

// Function to to count the
// number of K-countdowns for
// multiple queries
int countKCountdown(int arr[],
                    int N,
                    int K)
{

    // flag which stores the
    // current value of value
    // in the countdown
    int flag = -1;

    // count of K-countdowns
    int count = 0;

    // Loop to iterate over the
    // elements of the array
    for (int i = 0; i < N; i++) {

        // condition check if
        // the elements
        // of the array is
        // equal to K
        if (arr[i] == K)
            flag = K;

        // condition check if
        // the elements
        // of the array is in
        // continuous order
        if (arr[i] == flag)
            flag--;

        // condition check if
        // the elements
        // of the array are not
        // in continuous order
        else
            flag = -1;

        // condition check to
        // increment the counter
        // if the there is a
        // K-countdown present
        // in the array
        if (flag == 0)
            count++;
    }

    // returning the count of
    // K-countdowns
    return count;
}

// Driver Code
int main()
{
    int N = 8;
    int K = 3;
    int arr[N] = { 4, 3, 2, 1,
                   5, 3, 2, 1 };

    // Function Call
    cout << countKCountdown(arr, N, K);
}

Java

// Java code for the above program.
class GFG{
    
// Function to to count the 
// number of K-countdowns for 
// multiple queries 
public static int countKCountdown(int arr[], 
                                  int N, int K) 
{ 
    
    // Flag which stores the 
    // current value of value 
    // in the countdown 
    int flag = -1; 
    
    // Count of K-countdowns 
    int count = 0; 
    
    // Loop to iterate over the 
    // elements of the array 
    for(int i = 0; i < N; i++) 
    {
       
       // Condition check if the
       // elements of the array is 
       // equal to K 
       if (arr[i] == K) 
           flag = K; 
           
       // Condition check if the
       // elements of the array is 
       // in continuous order 
       if (arr[i] == flag) 
           flag--; 
       
       // Condition check if the
       // elements of the array are 
       // not in continuous order 
       else
           flag = -1; 
       
       // Condition check to increment 
       // the counter if the there is a 
       // K-countdown present in the array 
       if (flag == 0) 
           count++; 
    } 
    
    // Returning the count of 
    // K-countdowns 
    return count; 
} 

// Driver code
public static void main(String[] args) 
{
    int N = 8; 
    int K = 3; 
    int arr[] = { 4, 3, 2, 1, 5, 3, 2, 1 }; 
    
    System.out.print(countKCountdown(arr, N, K));
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 code for the above program.

# Function to to count the
# number of K-countdowns for
# multiple queries
def countKCountdown(arr, N, K):

    # flag which stores the
    # current value of value
    # in the countdown
    flag = -1;

    # count of K-countdowns
    count = 0;

    # Loop to iterate over the
    # elements of the array
    for i in range(0, N):

        # condition check if
        # the elements
        # of the array is
        # equal to K
        if (arr[i] == K):
            flag = K;

        # condition check if
        # the elements
        # of the array is in
        # continuous order
        if (arr[i] == flag):
            flag -= 1;

        # condition check if
        # the elements
        # of the array are not
        # in continuous order
        else:
            flag = -1;

        # condition check to
        # increment the counter
        # if the there is a
        # K-countdown present
        # in the array
        if (flag == 0):
            count += 1;
    
    # returning the count of
    # K-countdowns
    return count;

# Driver Code
N = 8;
K = 3;
arr = [ 4, 3, 2, 1,
        5, 3, 2, 1 ];

# Function Call
print(countKCountdown(arr, N, K))

# This code is contributed by Akanksha_Rai

// C# code for the above program.
using System;
class GFG{
    
// Function to to count the 
// number of K-countdowns for 
// multiple queries 
public static int countKCountdown(int []arr, 
                                  int N, int K) 
{ 
    
    // Flag which stores the 
    // current value of value 
    // in the countdown 
    int flag = -1; 
    
    // Count of K-countdowns 
    int count = 0; 
    
    // Loop to iterate over the 
    // elements of the array 
    for(int i = 0; i < N; i++) 
    {
        
    // Condition check if the
    // elements of the array is 
    // equal to K 
    if (arr[i] == K) 
        flag = K; 
            
    // Condition check if the
    // elements of the array is 
    // in continuous order 
    if (arr[i] == flag) 
        flag--; 
        
    // Condition check if the
    // elements of the array are 
    // not in continuous order 
    else
        flag = -1; 
        
    // Condition check to increment 
    // the counter if the there is a 
    // K-countdown present in the array 
    if (flag == 0) 
        count++; 
    } 
    
    // Returning the count of 
    // K-countdowns 
    return count; 
} 

// Driver code
public static void Main() 
{
    int N = 8; 
    int K = 3; 
    int []arr = { 4, 3, 2, 1, 5, 3, 2, 1 }; 
    
    Console.Write(countKCountdown(arr, N, K));
}
}

// This code is contributed by Akanksha_Rai

JavaScript

<script>
//Javascript code for the above program.

// Function to to count the
// number of K-countdowns for
// multiple queries
function countKCountdown( arr, N, K)
{

    // flag which stores the
    // current value of value
    // in the countdown
    var flag = -1;

    // count of K-countdowns
    var count = 0;

    // Loop to iterate over the
    // elements of the array
    for (var i = 0; i < N; i++) {

        // condition check if
        // the elements
        // of the array is
        // equal to K
        if (arr[i] == K)
            flag = K;

        // condition check if
        // the elements
        // of the array is in
        // continuous order
        if (arr[i] == flag)
            flag--;

        // condition check if
        // the elements
        // of the array are not
        // in continuous order
        else
            flag = -1;

        // condition check to
        // increment the counter
        // if the there is a
        // K-countdown present
        // in the array
        if (flag == 0)
            count++;
    }

    // returning the count of
    // K-countdowns
    return count;
}

var N = 8;
var K = 3;
var arr = [ 4, 3, 2, 1, 5, 3, 2, 1 ];
// Function Call
document.write( countKCountdown(arr, N, K));

// This code is contributed by SoumikMondal
</script>

Output:

Time Complexity: O(N)
Auxiliary Space Complexity: O(1)

Analysis of Algorithms

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