## Interview Question

Senior Software Engineer Interview

-Mountain View, CA

# Given an array of numbers, replace each number with the product of all the numbers in the array except the number itself *without* using division.

17

O(size of array) time & space: First, realize that saying the element should be the product of all other numbers is like saying it is the product of all the numbers to the left, times the product of all the numbers to the right. This is the main idea. Call the original array A, with n elements. Index it with C notation, i.e. from A to A[n - 1]. Create a new array B, also with n elements (can be uninitialized). Then, do this: Accumulator = 1 For i = 0 to n - 2: Accumulator *= A[i] B[i + 1] = Accumulator Accumulator = 1 For i = n - 1 down to 1: Accumulator *= A[i] B[i - 1] *= Accumulator Replace A with B It traverses A twice and executes 2n multiplicates, hence O(n) time It creates an array B with the same size as A, hence O(n) temporary space

Jordan on

11

Create two more arrays. One array contains the products of the elements going upward. That is, B = A, B = A * A, B = B * A, and so on. The other array contains the products of the elements going down. That is, C[n] = A[n], C[n-1] = A[n] * A[n-1], and so on. Now A[i] is simply B[i-1] * C[i+1].

pflau on

7

Here are my 2 cents to do this in memory without creating temporary arrays. The simple solution , if division was allowed, was multiple all the elements of the array i.e. tolal = A*A]*....*A[n-1] now take a loop of array and update element i with A[i] = toal/A[i] Since division is not allowed we have to simulate it. If we say X*Y = Z, it means if X is added Y times it is equal to Z e.g. 2*3 = 6, which also means 2+2+2 = 6. This can be used in reverse to find how mach times X is added to get Z. Here is my C solution, which take pointer to array head A and size of array as input void ArrayMult(int *A, int size) { int total= 1; for(int i=0; i< size; ++i) total *= A[i]; for(int i=0; i< size; ++i) { int temp = total; int cnt = 0; while(temp) { temp -=A[i]; cnt++; } A[i] = cnt; } } Speed in O(n) and space is O(1)

narya on

1

void fill_array ( int* array, size ) { int i; int t1,t2; t1 = array; array = prod(1, size, array ); for(i = 1; i < size; i++){ t2 = array[i]; array[i] = prod(i, array.size(), array)*t1; t1 *= t2; } int prod(start, end, array){ int i; int val(1); for(i = start; i < end; i++ ) val *= array[i]; return val; }

Devin on

2

def without(numbers): lognums = [math.log10(n) for n in numbers] sumlogs = sum(lognums) return [math.pow(10, sumlogs-l) for l in lognums]

xamdam on

2

# A Python solution (requires Python 2.5 or higher): def mult(arr, num): return reduce(lambda x,y: x*y if y!=num else x, arr) arr = [mult(arr,i) for i in arr] # O(n^2) time, O(n) space

rotoiti on

0

#include #define NUM 10 int main() { int i, j = 0; long int val = 1; long A[NUM] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; // Store results in this so results do not interfere with multiplications long prod[NUM]; while(j < NUM) { for(i = 0; i < NUM; i++) { if(j != i) { val *= A[i]; } } prod[j] = val; i = 0; val = 1; j++; } for(i = 0; i < NUM; i++) printf("prod[%d]=%d\n", i, prod[i]); return 0; }

Rohan on