702737. Balance with respect to an array
Balance with respect to an array
Summary
The problem is about finding the balance point in a given array. The balance point is defined as the index at which the sum of elements on the left side equals the sum of elements on the right side, considering all elements up to that point.
Detailed Explanation
To solve this problem, we can use a two-pointer approach. Initialize two pointers, left and right, at the beginning and end of the array, respectively. Calculate the sum of elements from the start to left (inclusive) and from right to the end (exclusive).
Move the pointer that has the smaller sum towards the other. This is because we want to minimize the distance between the two sums.
When the two pointers meet, it means we have found the balance point. If the array is already balanced, the pointers will not move.
Here's a step-by-step breakdown:
- Initialize
leftandrightat 0 andn-1, respectively. - Calculate
sum_leftas the sum of elements from start toleft. - Calculate
sum_rightas the sum of elements fromrightto end (exclusive). - If
sum_left <= sum_right, movelefttowardsright. Otherwise, moverighttowardsleft. - Repeat steps 2-4 until
leftandrightmeet. - The meeting point is the balance point.
Time complexity: O(n), where n is the length of the array. We only need to traverse the array once.
Space complexity: O(1). We don't use any extra space that scales with the input size.
Optimized Solutions
Java
public int findBalance(int[] arr) {
int left = 0, right = arr.length - 1;
while (left <= right) {
int sum_left = 0, sum_right = 0;
for (int i = 0; i <= left; i++) {
sum_left += arr[i];
}
for (int i = right; i < arr.length; i++) {
sum_right += arr[i];
}
if (sum_left <= sum_right) {
left++;
} else {
right--;
}
}
return left;
}