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Maximum size of sub-array that satisfies the given condition in C++ program
In this problem, we are given an array arr[] of n integers. Our task is to create a program to find the maximum size of sub-array that satisfies the given condition.
Problem Description − We need to find the length of largest subarray that satisfies any one of the below condition,
arr[k] > arr[k+1], if k is odd and arr[k] < arr[k+1], if k is even. For all elements of the subarray.
arr[k] < arr[k+1], if k is odd and arr[k] > arr[k+1], if k is even. For all elements of the subarray.
Here, k is the index of the element of the subarray in arr[].
Let’s take an example to understand the problem,
Input
arr[] = {7, 3, 1, 5, 4, 2, 9}Output
4
Explanation
The subarray {3, 1, 5, 4} satisfies the condition 1.
k = 1(odd), arr[k] > arr[k+1], 3 > 1
k = 2(even), arr[k] < arr[k+1], 1 < 5
k = 3(odd), arr[k] > arr[k+1], 5 > 4Solution Approach
We can see from the example that for any of the conditions to be true. The subarray should have alternate greater-smaller elements i.e. if 1st > 2nd, then 2nd > 3rd, and so on.
Now, for ease of calculation, we will create a relation array indicating this relationship. The following is how we will be tailoring the relation array,
If arr[i] == arr[i + 1],relArr[i] = ‘E’ If arr[i] > arr[i + 1],relArr[i] = ‘G’ If arr[i] < arr[i + 1],relArr[i] = ‘S’
Using this array we can easily find the max subarray size. Subarray to be considered will have alternate ‘G’ and ‘S’.
Example
Program to illustrate the working of our solution,
#include<iostream>
using namespace std;
char findRel(int a, int b) {
if(a > b)
return 'G';
else if(a < b)
return 'S';
return 'E';
}
int calcMaxSubArray(int arr[], int n) {
int maxLen = 1;
int len = 1;
char c = findRel(arr[0], arr[1]);
for(int i = 1; i <= n−1; i++){
if(c == 'S' && findRel(arr[i], arr[i + 1]) == 'G')
len++;
else if(c == 'G' && findRel(arr[i], arr[i + 1]) == 'S')
len++;
else {
if(maxLen < (len + 1))
maxLen = (len + 1);
len = 1;
}
c = findRel(arr[i], arr[i+1]);
}
return maxLen;
}
int main() {
int arr[] = {7, 3, 1, 5, 4, 2, 9};
int n = sizeof(arr) / sizeof(arr[0]);
cout<<"The maximum size of sub−array that satisfies the given
condition is "<<calcMaxSubArray(arr, n);
}Output
The maximum size of sub-array that satisfies the given condition is 4
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