Minimum Coin Combination

This problem focuses on finding the minimum number of stamps needed to reach a specific postage value, a classic dynamic programming challenge. Mastering this demonstrates understanding of optimization techniques and problem decomposition, crucial skills for software engineers.

dynamic-programmingoptimizationminimumarray

Problem Statement

A postal service wants to determine the fewest number of stamps needed to achieve a particular postage value. You are given an array representing the denominations of available stamps and a target postage value. Write a function that returns the minimum number of stamps required to reach the target. If it's impossible to reach the target value with the given stamp denominations, return -1.

Example 1

Input: stamps = [1, 5, 10, 25], target = 37

Output: 3

The optimal solution uses one 25-cent stamp, one 10-cent stamp, and two 1-cent stamps, totaling 3 stamps.

Example 2

Input: stamps = [3, 5], target = 2

Output: -1

It is impossible to reach the target value of 2 using only stamps with denominations of 3 and 5.

Constraints

-1 <= stamps.length <= 12
-1 <= stamps[i] <= 1000
-0 <= target <= 10000
-All values in stamps are unique.

Brute Force Approach

The brute force approach involves trying every possible combination of stamps to see if any combination sums to the target postage. Imagine trying every possible way to fill a backpack with items, without any strategy. This is highly inefficient because you'll explore many invalid and redundant combinations. Time complexity is exponential, space complexity is minimal.

TimeO(n^target)

SpaceO(1)

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