Why it matters

Hirschberg saves memory. Understanding shapes bio DP.

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The architecture

Compute midpoint of alignment via O(m+n) space DP.

Recurse on two halves.

Hirschberg's algorithmForward + backwardO(m+n) spaceFind midpointof alignmentRecurse halvesD&CHirschberg 1975; standard for long-sequence alignment; O(mn) time O(m+n) space
Hirschberg.
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How it works end to end

Same alignment quality as full-space.

Similar time complexity.

Standard for long sequences.