Minimum Coin Change
Let's solve the Minimum Coin Change problem using Dynamic Programming.
Statement
You’re given an integer total
and a list of integers called coins
. The integers inside the coins
represent the coin denominations, and total
is the total amount of money.
You have to return the minimum number of coins that can make up the total
amount by using any combination of the available coins. If the amount can’t be made up, return 1
. If the total amount is 0
, return 0
.
Note: You may assume that we have an infinite number of each kind of coin.
Let’s say, we have $3$ coins (1, 2, 3) and want to make a total amount of $5$. The minimum number of coins required to make this total is $2$ coins, such that (2 + 3 = 5).
Constraints:

$1 \leq$
coins.length
$\leq 12$ 
$1 \leq$
coins[i]
$\leq 2^{31} 1$ 
$0 \leq$
total
$\leq 1000$
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