Balanced Array

Balanced array can mean equal left and right sums, equal numbers of categories, or a partition after one operation, so request the exact definition before coding. For an equal-sum pivot, compute total once, maintain leftSum, and at index i test leftSum equals total minus leftSum minus nums[i]. Then add nums[i] to leftSum. That invariant makes each index a constant-time decision and handles negative values, unlike a two-pointer approach that depends on nonnegative elements. If the task instead concerns equal counts of two symbols, maintain a signed prefix difference and store earliest positions for each difference. Discuss whether an empty side is allowed and whether integer totals can overflow. Dry run with no pivot, pivot at either end, negative values, and repeated values. The equal-sum pivot method is O(n) time and O(1) extra space; a prefix map for longest balanced subarray is O(n) expected time and O(n) space.