Minimum Size Subarray Sum

Expand, then shrink greedily

For positive integers, maintain a window [left,right] and its sum. Extend right one element at a time. Whenever the sum is at least target, record the current length and move left rightward, subtracting values, until the sum falls below target. The shortest valid window ending at a fixed right is found by this maximal safe shrink, so taking the minimum across all right endpoints is correct.

State the assumption

Positivity is what makes the method work: removing a left value can only reduce the sum, so a window that is too small cannot become valid without moving right. With negative values, use a prefix-sum deque algorithm instead. Each element enters and leaves the window at most once, giving O(n) time and O(1) extra space. Initialize the answer to an impossible sentinel and convert it to zero or -1 according to the problem statement. Test a one-element answer, no qualifying subarray, a window that needs multiple left removals, and target equal to the total sum.