## Array of products of all other numbers

Given an array $A$ of size $N$, return another resulting array $B$ of the same size $N$, where $B[i]$ is the products of all numbers in $A$ except for $A[i]$.
EXAMPLE:
INPUT: $A$ = [1,2,3,4]
OUTPUT: $B$ = [24, 12, 8, 6]

My initial thoughts:
We can first compute the products of everything, in the example, this is 1*2*3*4 = 24. Then for each element in the resulting array, we divide the total products by that element in the original array, that is: 24 = 24/1; 12 = 24/2; 8 = 24/3; 6 = 24/4. We need to be careful with the edge cases: where there are zero(s). We cannot divide by zero. Hence, we modify the algorithm. We first compute the products of non-zeros and count the number of zeros in $A$. Then for position $i$ in $B$, if $A[i]=0$, we check if there are at least 2 zeros, if yes, $B[i]=0$. If not, $B[i]$ should be equal to the products of non-zeros. If $A[i]\ne0$, we check if there is at least 1 zero, if yes, $B[i]=0$. Otherwise, $B[i]$ is the product of non-zeros divided by \$A[i]\$.

Codes:

```public static long[] getArrayOfProducts(int[] original) {
int zeroCounts = 0;
long products = 1;
for(int number : original) {
if(number == 0)
zeroCounts++;
else
products *= number;
}

long[] result = new long[original.length];
for(int i = 0; i < result.length; ++i) {
if(original[i] == 0) {
if(zeroCounts > 1)
result[i] = 0;
else
result[i] = products;
} else if(zeroCounts > 0) {
result[i] = 0;
} else {
result[i] = products / original[i];
}
}

return result;
}

Better Solution:
According to the post here:
public static long[] getArrayOfProducts2(int[] original) {
long[] results = new long[original.length];
results[0] = 1;
for(int i = 1; i < original.length; ++i) {
results[i] = results[i-1]*original[i-1];
}

long temp = 1;
for(int i = results.length - 1; i >= 0; --i) {
results[i] *= temp;
temp *= original[i];
}
return results;
}

Notice:
If the product is too large so that we hit integer/long overflow, we need to handle that, probably by introducing additional variables to store temporary products.

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