SDE - 1

You are given an array of n integers (a1, a2,....,an), you need to find if the array contains a pythagorean triplet or not.

An array is said to have a pythagorean triplet if there exists three integers x,y and z in the array such that x^2 + y^2 = z^2.

Note

1. The integers x,y and z might not be distinct , but they should be present at different locations in the array i.e if a[i] = x, a[j] = y and a[k] = z, then i,j and k should be pairwise distinct.
2. The integers a,b and c can be present in any order in the given array.

Ninja has been given two baskets of apples containing ‘A’ and ‘B’ apples each. Also, he has been given extra ‘C’ apples separately.

This apple will be gifted to the Ninja’s best buddies; Ninja wants to do some partiality so that the number of apples in the first basket is strictly greater than the number of apples in the second basket.

The ninja can do it using extra ‘C’ apples, he must have to use all the extra apples and transfer them in both the first and second basket.

Your task is to help Ninja by calculating a number of possible arrangements of apples so that the resultant configuration is feasible for Ninja to do the partiality.

EXAMPLE:

Input: 'A' = 5, 'B' = 3, 'C' = 4

Output: 3

Here only three possible combinations are:

(7, 5) Transfer 2 apples to the first basket and 2 apples to the second basket.
(9, 3) Transfer 4 apples to the first basket and 0 apples to the second basket.
(8, 4) Transfer 3 apples to the first basket and 1 apple to the second basket.

Only above combinations for (A, B) satisfies the condition that all 'C'  apples are used and ('A' > 'B')

We have a collection of 'N' stones, each stone has a positive integer weight.

On each turn, we choose the two heaviest stones and smash them together. Suppose the stones have weights 'x' and 'y' with 'x' <= 'y'. The result of this smash will be:

1. If 'x' == 'y', both stones are totally destroyed;

2. If 'x' != 'y', the stone of weight 'x' is totally destroyed, and the stone of weight 'y' has a new weight equal to 'y - x'.

In the end, there is at most 1 stone left. Return the weight of this stone or 0 if there are no stones left.

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