[main] added mincoins

Author: cthacker-udel

pythonProblems/dp/mincoins.py

@@ -2,14 +2,33 @@
 
 
 def min_coins(n: int, coins: List[int]):
-    dp = [0] * n
-    for i in range(n):  # iterate through all the potential targets 0...n
+    """_summary_
+
+    Args:
+        n (int): _description_
+        coins (List[int]): _description_
+    """
+    dp = [0] + ([float('inf')] * n)
+    for i in range(n + 1):  # iterate through all the potential coin value targets 0...n
+        # iterate through all potential coins in the list and apply it to the sub-problems,
         for j in range(len(coins)):
-            dp[i] = min(dp[i], dp[i - j]) + 1
-    return min(dp)
+            # checking if the subproblem before it has less steps, then add one to the final result
+            # checking if the current target - the coin we're on right now has been solved,
+            if (i - coins[j]) < 0:
+                # if it has not, then we continue
+                continue
+            # dp[i] represents the current potential target coin value
+            # dp[i - coins[j]] represents the subproblem of the potential target coin value - the current coin
+            # check the current target we're on, check if the current target has less steps
+            dp[i] = min(dp[i], dp[i - coins[j]] + 1)
+            # then the subproblem of the current target - the coin we're on currently (aka previous subproblem), then add one to that result
+            # because we are evaluating a previous subproblem and in order to reach the current target we add one step to it.
+    print(dp[n] if dp[n] != float('inf') else -1)
 
 
 if __name__ == '__main__':
-    coins = [1, 5, 7]
-    target = 11
-    print(min_coins(target, coins))
+    first_line = input()
+    target = int(first_line.split(" ")[1])
+    arr_line = input()
+    arr = [int(x) for x in arr_line.split(" ")]
+    min_coins(target, arr)