Coin Change

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Problem

Given an array of coin denominations and a target amount, return the fewest number of coins needed to make up that amount using unlimited coins of each denomination. Return -1 if the amount cannot be made.

Examples

Example 1

Input:coins = [1,2,5], amount = 11

Output:3

11 = 5 + 5 + 1.

Example 2

Input:coins = [2], amount = 3

Output:-1

Constraints

1 <= coins.length <= 12

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How to approach it: the 1-D Dynamic Programming pattern

Break a problem into overlapping subproblems along a single dimension — like "the answer up to index i" — solve each one once, and reuse the result instead of recomputing it.

Look for this pattern when

A greedy or purely recursive approach recomputes the same subproblem repeatedly.
The problem asks for a count, a minimum/maximum, or a yes/no reachability over a sequence, where the answer at position `i` depends on answers at earlier positions.

Read the full 1-D Dynamic Programming guide →

Video walkthroughs

Original problem on LeetCode ↗