DP-1

coin_change.py

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+"""
+time - o(n)
+space - o(n)
+create an array whose length is same as amount set the zeroth index as 0. For every coin
+calculate the number of ways we can achieve the amount by taking previous amount and adding 1
+if we are able to get the target amount with the given coins then the array's amount index will
+have a value and not the default value (+inf in this case)
+"""
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')]*(amount+1)
+        dp[0] = 0
+        for coin in coins:
+            for i in range(coin, amount+1):
+                dp[i] = min(dp[i], dp[i-coin]+1)
+        if dp[amount]!=float('inf'):
+            return dp[amount]
+        return -1
+

house_robber.py

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+"""
+time - o(n)
+space - o(n)
+create a list and add whether to rob or not to rob (what is the amount made for each decision)
+when we calculate the value for robbing a house, we take previous index's not to rob value
+and add the value.
+if we choose not to rob, we look at what's maximum in the previous index, 
+finally the last index has the max value we can rob
+"""
+class Solution:
+    def rob(self, nums: List[int]) -> int:
+        robbed=[]
+        for i in range(len(nums)):
+            if not robbed:
+                robbed.append((nums[i],0)) #(choose_t0_rob,choose_not_to_rob)
+            else:
+                choose_to_rob=nums[i] + robbed[i-1][1]
+                choose_not_to_rob = max(robbed[i-1][1],robbed[i-1][0])
+                robbed.append((choose_to_rob,choose_not_to_rob))
+        return max(robbed[-1])