Create CoinChange.java

[anill1412]

The Coin Change Problem is a classic dynamic programming (DP) problem where the goal is to find the minimum number of coins required to make a given amount. Given an unlimited supply of certain denominations, you must find the minimum number of coins that sum up to a specified amount. If it’s impossible to make that amount with the given coins, the function should return -1.

Problem Statement:
You are given an integer array coins representing different denominations of coins, and an integer amount representing a total amount of money. The task is to return the minimum number of coins needed to make up that amount.

Example:
Input:

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

3 (11 = 5 + 5 + 1)
Explanation:

To make the amount 11 with the fewest coins, you use two 5-coin denominations and one 1-coin denomination. Approach:
This problem can be solved efficiently using Dynamic Programming. The main idea is to build a DP table where each entry at index i represents the minimum number of coins needed to make the amount i.

Define the State:

Let dp[i] represent the minimum number of coins required to make the amount i. Recurrence Relation:

For each amount i, iterate through each coin c in coins. If i - c >= 0 (meaning the coin can contribute to this amount), update dp[i] as follows: 𝑑
𝑝
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min
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dp[i]=min(dp[i],dp[i−c]+1)
Here, dp[i - c] + 1 represents using one coin of denomination c and the minimum coins needed to make the remaining amount i - c. Base Case:

dp[0] = 0 because no coins are needed to make an amount of 0. Result:

If dp[amount] is still infinity (or a high number), it means it’s impossible to make the amount with the given coins, so return -1. Otherwise, return dp[amount].

[panditakshay402]

kindly follow all the rules from readme.md file