Unlimited Supply: Coin Change

When an item can be used again and again, taking it keeps you on the same item. One small change to take-or-skip solves fewest coins and number of ways.

10 min 2 videos Quiz Pro

Change one rule from the last lesson: each item can be used any number of times. Now taking item i keeps you on i, because you may take it again.

	Take	Skip
Each item once	`f(i + 1, rem − w[i])`	`f(i + 1, rem)`
Unlimited supply	`f(i, rem − w[i])`	`f(i + 1, rem)`

That’s the whole difference. The state and the memo size stay the same.

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Fewest coins
Number of ways

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Item 33 of 44 · updated 2026-10-13