# Longest alternating (positive and negative) subarray starting at every index

A subarray is called alternating if any two consecutive numbers in it have opposite signs (i.e. one of them should be negative, whereas the other should be positive).

Given an array of n integers. For each index i, we need to find the length if the longest alternating subarray starting at i.

Examples:

```Input : a[] = {1, -5, 1, -5}
Output : For index 0, {1, -5, 1, -5} = 4
index 1, {-5, 1, -5} = 3
index 2, {1, -5} = 2
index 3, {-5} = 1.

Input :a[] = {-5, -1, -1, 2, -2, -3}
Output : index 0 = 1,
index 1 = 1,
index 2 = 3,
index 3 = 2,
index 4 = 1,
index 5 = 1,
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A Naive approach is to use two loops in which we traverse the whole array starting from every index i (0 to n-1) and calculate the length of the alternating subarray.
Time Complexity: O(n2).

Efficient Approach:
Observe that when a[i] and a[i+1] have opposite signs, count[i] will be 1 more than count[i+1]. Otherwise when they have same sign count[i] will be 1.

We use Dynamic Programming here.

 `// CPP program to find longest alternating ` `// subarray starting from every index. ` `#include ` `using` `namespace` `std; ` ` `  `void` `longestAlternating(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `count[n]; ` ` `  `    ``// Fill count[] from end.  ` `    ``count[n - 1] = 1; ` `    ``for` `(``int` `i = n - 2; i >= 0; i--) { ` `        ``if` `(arr[i] * arr[i + 1] < 0) ` `            ``count[i] = count[i + 1] + 1; ` `        ``else` `            ``count[i] = 1; ` `    ``} ` ` `  `    ``// Print result ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << count[i] << ``" "``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[] = { -5, -1, -1, 2, -2, -3 }; ` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a); ` `    ``longestAlternating(a, n); ` `    ``return` `0; ` `} `

 `// Java program to find longest alternating ` `// subarray starting from every index. ` `import` `java.util.*; ` ` `  `class` `Longest{ ` `     `  `    ``public` `static` `void` `longestAlternating(``int` `arr[],  ` `                                             ``int` `n) ` `    ``{ ` `        ``int``[] count = ``new` `int``[n]; ` ` `  `        ``// Fill count[] from end.  ` `        ``count[n - ``1``] = ``1``; ` `        ``for` `(``int` `i = n - ``2``; i >= ``0``; i--) { ` `            ``if` `(arr[i] * arr[i + ``1``] < ``0``) ` `                ``count[i] = count[i + ``1``] + ``1``; ` `            ``else` `                ``count[i] = ``1``; ` `        ``} ` ` `  `        ``// Print result ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``System.out.print(count[i] + ``" "``); ` `    ``} ` `     `  `    ``// driver program ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `a[] = { -``5``, -``1``, -``1``, ``2``, -``2``, -``3` `}; ` `        ``int` `n = ``6``; ` `        ``longestAlternating(a, n); ` `    ``} ` `} ` ` `  `// This code is contributed by rishabh_jain `

 `# Python3 program to find longest alternating ` `# subarray starting from every index. ` ` `  `def` `longestAlternating(arr, n) : ` `    ``count ``=` `[``None``] ``*` `n ` ` `  `    ``# Fill count[] from end.  ` `    ``count[n ``-` `1``] ``=` `1` `    ``i ``=` `n ``-` `2` `     `  `    ``while` `i >``=` `0` `: ` `        ``if` `(arr[i] ``*` `arr[i ``+` `1``] < ``0``) : ` `            ``count[i] ``=` `count[i ``+` `1``] ``+` `1` `        ``else` `: ` `            ``count[i] ``=` `1``; ` `        ``i ``=` `i ``-` `1` ` `  `    ``i ``=` `0` `     `  `    ``# Print result ` `    ``while` `i < n : ` `        ``print` `(count[i], end ``=` `" "``) ` `        ``i ``=` `i ``+` `1` ` `  `# Driver Code ` `a ``=` `[ ``-``5``, ``-``1``, ``-``1``, ``2``, ``-``2``, ``-``3` `] ` `n ``=` `len``(a) ` `longestAlternating(a, n); ` ` `  ` `  `# This code is contributed by rishabh_jain  `

 `//C# program to find longest alternating ` `// subarray starting from every index. ` `using` `System; ` ` `  `class` `Longest ` `{ ` `     `  `    ``public` `static` `void` `longestAlternating(``int` `[]arr,  ` `                                            ``int` `n) ` `    ``{ ` `        ``int``[] count = ``new` `int``[n]; ` ` `  `        ``// Fill count[] from end.  ` `        ``count[n - 1] = 1; ` `        ``for` `(``int` `i = n - 2; i >= 0; i--)  ` `        ``{ ` `            ``if` `(arr[i] * arr[i + 1] < 0) ` `                ``count[i] = count[i + 1] + 1; ` `            ``else` `                ``count[i] = 1; ` `        ``} ` ` `  `        ``// Print result ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``Console.Write(count[i] + ``" "``); ` `    ``} ` `     `  `    ``// Driver program ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]a = { -5, -1, -1, 2, -2, -3 }; ` `        ``int` `n = 6; ` `        ``longestAlternating(a, n); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m `

 `= 0; ``\$i``--)  ` `    ``{ ` `        ``if` `(``\$arr``[``\$i``] * ``\$arr``[``\$i` `+ 1] < 0) ` `            ``\$count``[``\$i``] = ``\$count``[``\$i` `+ 1] + 1; ` `        ``else` `            ``\$count``[``\$i``] = 1; ` `    ``} ` ` `  `    ``// Print result ` `    ``for` `( ``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``echo` `\$count``[``\$i``] , ``" "``; ` `} ` ` `  `    ``// Driver code ` `    ``\$a` `= ``array``( -5, -1, -1, 2, -2, -3 ); ` `    ``\$n` `=``count``(``\$a``); ` `    ``longestAlternating(``\$a``, ``\$n``); ` ` `  `// This code is contributed by anuj_67. ` `?> `

Output:
```1 1 3 2 1 1
```

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