Merge pull request #165 from BrianLusina/feat/algorithms-greedy-min-no-of-pushes

feat(algorithms, greedy): minimum number of pushes to type word

Author: BrianLusina

DIRECTORY.md

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+from collections import Counter
+import heapq
+
+
+def minimum_pushes_greedy_with_sorting(word: str) -> int:
+    # frequency vector of size 26 that stores the count of each letter in the word
+    # Space complexity here is O(1) because we have a constant space for the given list, i.e. 26
+    frequency = [0] * 26
+
+    # Iterate through each character and increment the count in the frequency at the index corresponding to char - "a"
+    # since we know from the given constraints that we will have lowercase English letters, this will work fine
+    # This is an O(n) operation, as each character in the word is iterated through
+    for char in word:
+        frequency[ord(char) - ord("a")] += 1
+
+    # Sort the frequencies in descending order to prioritize letters with higher counts
+    # O(n log(n)) operation to handle sorting, with a space complexity of O(n) as Python uses in-memory space to handle
+    # the sorting using timsort
+    frequency.sort(reverse=True)
+
+    # total number of key presses required
+    total_pushes = 0
+
+    # iterate through the sorted frequency
+    for i in range(26):
+        # if the frequency of a letter is zero, break the loop as there are no more letters to process
+        if frequency[i] == 0:
+            break
+        # calculate the number of pushes for each letter based on its position in the sorted list (i / 8 + 1) * frequency[i]
+        total_pushes += (i // 8 + 1) * frequency[i]
+
+    return total_pushes
+
+
+def minimum_pushes_heap(word: str) -> int:
+    # frequency_map to store the count of each letter
+    frequency_map = Counter(word)
+
+    # Priority queue/max heap to store frequencies in descending order
+    frequency_queue = [-freq for freq in frequency_map.values()]
+    heapq.heapify(frequency_queue)
+
+    # total number of key presses required
+    total_pushes = 0
+    index = 0
+
+    # iterate through the sorted frequency_map
+    while frequency_queue:
+        total_pushes += (1 + (index // 8)) * -heapq.heappop(frequency_queue)
+        index += 1
+
+    return total_pushes