Subarray Sum - Why Initialize with 0

Why start with $freq[0] = 1$? Consider array $[3]$ with $k = 3$.

After processing:

• $prefixSum = 3$
• We look for $prefixSum - k = 0$ in the map
• If $0$ wasn't in the map, we'd miss this valid subarray

The prefix sum $0$ represents the empty prefix (sum before index $0$). A subarray from index $0$ to $j$ has sum $prefix[j] - prefix[-1] = prefix[j] - 0 = prefix[j]$.