# Ball Moves - Google Top Interview Questions

### Problem Statement :

```You are given a list of integers nums containing 0s and 1s where a 0 means the cell is empty and 1 means there's a ball there.

Return a new list of integers A of the same length where A[i] is set to the total distance required to move all the balls to A[i]. The distance to move a ball in index j to index i is defined to be abs(j - i).

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [1, 1, 0, 1]

Output

[4, 3, 4, 5]

Explanation

A = abs(0 - 0) + abs(1 - 0) + abs(3 - 0)

A = abs(0 - 1) + abs(1 - 1) + abs(3 - 1)

A = abs(0 - 2) + abs(1 - 2) + abs(3 - 2)

A = abs(0 - 3) + abs(1 - 3) + abs(3 - 3)

For example, to move all the balls to A we need to move the ball at index 0 to 1 for distance of 1 and
move the ball at index 3 to 1 for distance of 2.```

### Solution :

```                        ```Solution in C++ :

vector<int> solve(vector<int>& nums) {
int totalDistance = 0;
int n = nums.size();
int ballsToTheRight = 0;
for (int i = 0; i < n; i++) {
if (nums[i] == 0) continue;
totalDistance += i;
ballsToTheRight++;
}
int ballsToTheLeft = 0;
for (int i = 0; i < n; i++) {
if (nums[i]) {
ballsToTheLeft++;
ballsToTheRight--;
}
nums[i] = totalDistance;
totalDistance -= ballsToTheRight - ballsToTheLeft;
}
return nums;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public int[] solve(int[] nums) {
int sum = 0, ct = 0;
int[] pf = new int[nums.length];
for (int i = 0; i < nums.length; i++) {
sum += ct;
ct += nums[i];
pf[i] = sum;
}
sum = ct = 0;
for (int i = nums.length - 1; i > -1; i--) {
sum += ct;
ct += nums[i];
pf[i] += sum;
}
return pf;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, nums):

suffixSum = [0 for _ in range(len(nums))]
prefixSum = [0 for _ in range(len(nums))]

prefixCount = 0
for i in range(len(nums)):
prefixSum[i] = prefixCount + (prefixSum[i - 1] if i - 1 >= 0 else 0)
if nums[i] == 1:
prefixCount += 1

suffixCount = 0
for i in range(len(nums) - 1, -1, -1):
suffixSum[i] = suffixCount + (suffixSum[i + 1] if len(nums) > i + 1 else 0)
if nums[i] == 1:
suffixCount += 1

res = [prefixSum[i] + suffixSum[i] for i in range(len(nums))]

return res```
```

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