Lazy Propagation

Some operations shift all breakpoints: 'add $c$ to all elements' shifts the function right by $c$. Instead of updating every breakpoint, track a global offset. Apply lazily when popping. Maintain: $actualValue = heapValue + offset$. When inserting, subtract offset first.

This handles shifts in $O(1)$ instead of $O(n)$. needed for problems with many shift operations. Global shifts are common in Slope Trick problems. Lazy propagation avoids $O(n)$ updates per operation.