322. Coin Change

322/memo.md

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+# 322. Coin Change
+
+そのまま思いついた方法として、メモ化再帰を実装: sol1.py
+- 一発で通ったので気持ち良い
+
+再帰関数を使わずに書く
+
+- 動的計画法:
+
+- 最短経路と考えればBFSで書ける
+- tableを保持したsol3.pyを書いたが、coinをソートすれば早期breakができること、levelがそのまま答えになることに気づき、改良: sol4.py
+
+## 計算量
+amount = O(n), len(coins) = O(m)
+### sol1.py
+- 時間計算量 O(nm), 空間計算量 O(n) （=スタックフレーム、キャッシュ）
+### sol2.py
+- 時間計算量 O(nm), 空間計算量 O(n)
+### sol4.py
+- 時間計算量 O(nm), 空間計算量 O(n)
+
+
+動的計画法
+https://www.slideshare.net/slideshow/ss-3578511/3578511#1
+
+自分のsol2.pyはもらうDP
+
+https://github.com/TORUS0818/leetcode/pull/42#discussion_r1904039471
+> -1 の扱いが気に入らなかったので Generator 使うのは考えてみました。
+
+https://github.com/mamo3gr/arai60/blob/322_coin-change/322_coin-change/memo.md
+> 再帰＋メモ化で、amount - coin でできる最小枚数をGeneratorで返させて、min(gen, default=-1) で最小値を取る。 自分もそれぞれ配列に入れてから min は思いついたが、最後に配列を舐めるのもなあ…と思って止めた。Generatorなら消費しながらminを取ってくれそう。
+
+generatorなら作れない場合の無効値を流さず書くことができる（minを取るときにリストを作る必要もない）
+minにdefaultがあることも知らなかった
+

322/sol1.py

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+import functools
+
+
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        @functools.cache
+        def minimum_coins(target_amount):
+            if target_amount == 0:
+                return 0
+            if target_amount < 0:
+                return float("inf")
+            return min([minimum_coins(target_amount - coin) + 1 for coin in coins])
+
+        num_changes = minimum_coins(amount)
+        return -1 if num_changes == float("inf") else num_changes

322/sol2.py

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+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        num_changes = [float("inf")] * (amount + 1)
+        num_changes[0] = 0
+        for target_amount in range(1, amount + 1):
+            for coin in coins:
+                if target_amount - coin >= 0:
+                    num_changes[target_amount] = min(
+                        num_changes[target_amount],
+                        num_changes[target_amount - coin] + 1,
+                    )
+
+        return -1 if num_changes[amount] == float("inf") else num_changes[amount]

322/sol2_revised.py

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+import math
+
+
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        num_changes = [float("inf")] * (
+            amount + 1
+        )  # the minimum number of coins required to make up amount i
+        num_changes[0] = 0
+        for target_amount in range(1, amount + 1):
+            for coin in coins:
+                if target_amount - coin >= 0:
+                    num_changes[target_amount] = min(
+                        num_changes[target_amount],
+                        num_changes[target_amount - coin] + 1,
+                    )
+
+        return -1 if math.inf(num_changes[amount]) else num_changes[amount]

322/sol3.py

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+from collections import deque
+
+
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        minimum_coins = [float("inf")] * (amount + 1)
+        minimum_coins[0] = 0
+        coins_sorted = sorted(coins)
+
+        frontier = deque([0])
+        visited = {0}
+
+        while frontier:
+            current_sum = frontier.popleft()
+            for coin in coins_sorted:
+                next_sum = current_sum + coin
+                if next_sum in visited or next_sum > amount:
+                    continue
+                minimum_coins[next_sum] = min(
+                    minimum_coins[next_sum], minimum_coins[current_sum] + 1
+                )
+                frontier.append(next_sum)
+                visited.add(current_sum)
+
+        return -1 if minimum_coins[amount] == float("inf") else minimum_coins[amount]

322/sol3_revised.py

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+from collections import deque
+import math
+
+
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        minimum_coins = [float("inf")] * (amount + 1)
+        minimum_coins[0] = 0
+        coins_sorted = sorted(coins)
+
+        frontier = deque([0])
+        visited_sum = {0}
+
+        while frontier:
+            current_sum = frontier.popleft()
+            for coin in coins_sorted:
+                next_sum = current_sum + coin
+                if next_sum in visited_sum or next_sum > amount:
+                    continue
+                minimum_coins[next_sum] = min(
+                    minimum_coins[next_sum], minimum_coins[current_sum] + 1
+                )
+                frontier.append(next_sum)
+                visited_sum.add(current_sum)
+
+        return -1 if math.isinf(minimum_coins[amount]) else minimum_coins[amount]

322/sol4.py

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+from collections import deque
+
+
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        if amount == 0:
+            return 0
+
+        coins_sorted = sorted(coins)
+        visited = [False] * (amount + 1)
+        visited[0] = True
+
+        frontier = deque([0])
+        steps = 0
+
+        while frontier:
+            steps += 1
+            len_current_frontier = len(frontier)
+            for _ in range(len_current_frontier):
+                current_sum = frontier.popleft()
+                for coin in coins_sorted:
+                    next_sum = current_sum + coin
+                    if next_sum > amount:
+                        break
+                    if visited[next_sum]:
+                        continue
+                    if next_sum == amount:
+                        return steps
+                    visited[next_sum] = True
+                    frontier.append(next_sum)
+
+        return -1