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puzzles/arrays/longest_increasing_subsequence/__init__.py rename to algorithms/dynamic_programming/longest_increasing_subsequence/__init__.py diff --git a/puzzles/arrays/longest_increasing_subsequence/test_longest_increasing_subsequence.py b/algorithms/dynamic_programming/longest_increasing_subsequence/test_longest_increasing_subsequence.py similarity index 100% rename from puzzles/arrays/longest_increasing_subsequence/test_longest_increasing_subsequence.py rename to algorithms/dynamic_programming/longest_increasing_subsequence/test_longest_increasing_subsequence.py diff --git a/algorithms/greedy/minimum_number_of_pushes/README.md b/algorithms/greedy/minimum_number_of_pushes/README.md new file mode 100644 index 00000000..6dd3ba43 --- /dev/null +++ b/algorithms/greedy/minimum_number_of_pushes/README.md @@ -0,0 +1,231 @@ +# Minimum Number of Pushes to Type Word + +You are given a string word containing lowercase English letters. + +Telephone keypads have keys mapped with distinct collections of lowercase English letters, which can be used to form +words by pushing them. For example, the key 2 is mapped with ["a","b","c"], we need to push the key one time to type +"a", two times to type "b", and three times to type "c" . + +It is allowed to remap the keys numbered 2 to 9 to distinct collections of letters. The keys can be remapped to any +amount of letters, but each letter must be mapped to exactly one key. You need to find the minimum number of times the +keys will be pushed to type the string word. + +Return the minimum number of pushes needed to type word after remapping the keys. + +An example mapping of letters to keys on a telephone keypad is given below. Note that 1, *, #, and 0 do not map to any +letters. + +![Example 1](images/examples/minimum_number_of_pushes_to_type_word_ii_sample.png) + +![Example 1](images/examples/minimum_number_of_pushes_to_type_word_ii_example_1.png) + +> Input: word = "abcde" +> Output: 5 +> Explanation: The remapped keypad given in the image provides the minimum cost. +> "a" -> one push on key 2 +> "b" -> one push on key 3 +> "c" -> one push on key 4 +> "d" -> one push on key 5 +> "e" -> one push on key 6 +> Total cost is 1 + 1 + 1 + 1 + 1 = 5. +> It can be shown that no other mapping can provide a lower cost. + +![Example 2](images/examples/minimum_number_of_pushes_to_type_word_ii_example_2.png) + +> Input: word = "xyzxyzxyzxyz" +> Output: 12 +> Explanation: The remapped keypad given in the image provides the minimum cost. +> "x" -> one push on key 2 +> "y" -> one push on key 3 +> "z" -> one push on key 4 +> Total cost is 1 * 4 + 1 * 4 + 1 * 4 = 12 +> It can be shown that no other mapping can provide a lower cost. +> Note that the key 9 is not mapped to any letter: it is not necessary to map letters to every key, but to map all the letters. + +![Example 3](images/examples/minimum_number_of_pushes_to_type_word_ii_example_3.png) + +> Input: word = "aabbccddeeffgghhiiiiii" +> Output: 24 +> Explanation: The remapped keypad given in the image provides the minimum cost. +> "a" -> one push on key 2 +> "b" -> one push on key 3 +> "c" -> one push on key 4 +> "d" -> one push on key 5 +> "e" -> one push on key 6 +> "f" -> one push on key 7 +> "g" -> one push on key 8 +> "h" -> two pushes on key 9 +> "i" -> one push on key 9 +> Total cost is 1 * 2 + 1 * 2 + 1 * 2 + 1 * 2 + 1 * 2 + 1 * 2 + 1 * 2 + 2 * 2 + 6 * 1 = 24. +> It can be shown that no other mapping can provide a lower cost. + +![Example 4](./images/examples/minimum_number_of_pushes_to_type_word_ii_example_4.png) +![Example 5](./images/examples/minimum_number_of_pushes_to_type_word_ii_example_5.png) +![Example 6](./images/examples/minimum_number_of_pushes_to_type_word_ii_example_6.png) + +## Constraints + +- 1 <= `word.length` <= 10^5 +- `word` consists of lowercase English letters + +## Topics + +- Hash Table +- String +- Greedy +- Sorting +- Counting + +## Solution + +1. [Greedy Sorting](#greedy-sorting) +2. [Using a heap](#using-a-heap) + +### Greedy Sorting + +To solve this problem, we use a greedy algorithm approach combined with sorting. Keeping in mind that we have 8 keys +available (2-9), the primary intuition is to remap the keys so the 8 most frequently occurring characters in the given +string are assigned as first key presses, the next most common 8 characters as second key presses, and so on. + +We begin by counting the occurrences of each letter using a counter, which provides the frequency of each distinct +letter. Next, we sort these frequencies in descending order. + +Since there are 8 possible key assignments, we'll divide the frequency rank by 8 to group it as a first, second, or +third key press. Note that dividing the frequencies by 8 will result in 0, 1, and 2. We must add 1 to this group number +to get the actual number of presses required for letters in that group. Multiplying this by the number of times the +character appears in the given string yields the total number of presses for that letter. + +Finally, we will sum the total presses required to type the word. + +This greedy way, combined with sorting by frequency, ensures that each decision (assignment of letters to keys) is +optimal for minimizing key presses. + +#### Algorithm + +- Initialize a frequency vector frequency of size 26 to store the count of each letter in the word. + - Iterate through each character c in word and increment the count in frequency at the index corresponding to c - 'a'. +- Sort the frequency vector in descending order to prioritize letters with higher counts. +- Initialize a variable totalPushes to store the total number of key presses required. +- Iterate through the sorted frequency vector: + - If the frequency of a letter is zero, break the loop as there are no more letters to process. + - Calculate the number of pushes for each letter based on its position in the sorted list: (i / 8 + 1) * frequency[i]. + > the number of pushes required to obtain a single instance of it is (i / 8 + 1). Because there are 8 available + > keys (2 − 9), for the first 8 values of i (i = 0 to i = 7) corresponding to the first 8 frequent letters, + > (i / 8 + 1) will give 1. For the next 8 values of i (i=8 to i=15) corresponding to the next 8 frequent letters, + > (i / 8 + 1) will give 2, and this pattern continues. + - Accumulate this value in totalPushes. +- Return totalPushes as the minimum number of key presses required to type the word. + +![Solution Greedy 1](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_1.png) +![Solution Greedy 2](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_2.png) +![Solution Greedy 3](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_3.png) +![Solution Greedy 4](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_4.png) +![Solution Greedy 5](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_5.png) +![Solution Greedy 6](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_6.png) +![Solution Greedy 7](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_7.png) +![Solution Greedy 8](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_8.png) +![Solution Greedy 9](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_9.png) +![Solution Greedy 10](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_10.png) +![Solution Greedy 11](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_11.png) +![Solution Greedy 12](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_12.png) +![Solution Greedy 13](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_13.png) +![Solution Greedy 14](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_14.png) +![Solution Greedy 15](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_15.png) +![Solution Greedy 16](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_16.png) +![Solution Greedy 17](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_17.png) +![Solution Greedy 18](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_18.png) +![Solution Greedy 19](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_greedy_19.png) + +#### Complexity Analysis + +Let `n` be the length of the string + +##### Time Complexity + +Iterating through the word string to count the frequency of each letter takes `O(n)`. + +Sorting the frequency array, which has a fixed size of 26 (for each letter in the alphabet), takes O(1) because the size +of the array is constant. + +Iterating through the frequency array to compute the total number of presses is O(1) because the array size is constant. + +Overall, the dominant term is O(n) due to the frequency counting step. + +##### Space Complexity + +Frequency array and sorting takes O(1) space, as it always requires space for 26 integers. + +Overall, the space complexity is O(1) because the space used does not depend on the input size. + +--- + +### Using a Heap + +Following the initial approach that used sorting and a greedy strategy, we now explore a similar yet refined method. + +First, we count the frequency of each character in the word using an unordered map (or dictionary), where each key +represents a character, and its value indicates how many times it appears in the word. + +Next, we use a priority queue (or max-heap) to efficiently manage these frequencies. The priority queue enables quick +retrieval of the character with the highest frequency by giving the most frequent characters the highest priority. + +As we process characters from the priority queue, we dynamically assign them to keys based on their frequencies. +Specifically, at each iteration, we extract the character with the highest frequency and assign it to the key with the +least number of characters assigned. + +To facilitate this, we maintain a record of the number of letters assigned to each key press count. This helps us +determine the next available key press count for assigning characters. For instance, once a key press count of 1 is +fully utilized, we proceed to a key press count of 2, and so on. + +We assign the character with the highest frequency to the least costly available key press count, updating our record to +reflect this assignment and marking the key press count as occupied. This process continues until all characters are assigned. + +Finally, we calculate the total number of key presses required by summing the product of each character’s frequency and +its assigned key press count. This gives us the optimal total number of key presses needed to type the word. + +#### Algorithm + +- Create a frequency map frequencyMap to store the count of each letter in the input string word. + - Iterate through word and for each character, increment its count in frequencyMap. +- Create a priority queue frequencyQueue to store the frequencies of letters in descending order. + - Iterate through frequencyMap and push each frequency into frequencyQueue. +- Initialize a variable totalPushes to 0 to keep track of the total number of presses. +- Initialize an index variable index to 0. +- Calculate the total number of presses by processing the frequencies in the priority queue. + - While frequencyQueue is not empty: + - Add the product of (1 + (index / 8)) and the top frequency from frequencyQueue to totalPushes. + - Remove the top element from frequencyQueue. + - Increment index by 1. +- Return totalPushes as the minimum number of presses needed. + +> Note: As shown in Slide 4, when calculating totalPushes, we multiply by 1. This value represents frequencyQueue.top(), +> which is 1 in the visual example. + +![Solution Heap 1](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_1.png) +![Solution Heap 2](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_2.png) +![Solution Heap 3](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_3.png) +![Solution Heap 4](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_4.png) +![Solution Heap 5](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_5.png) +![Solution Heap 6](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_6.png) +![Solution Heap 7](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_7.png) +![Solution Heap 8](./images/solutions/minimum_number_of_pushes_to_type_word_ii_solution_heap_8.png) + +#### Complexity Analysis + +##### Time Complexity + +Iterating through the word string to count the frequency of each letter takes O(n). + +Inserting each frequency into the priority queue and extracting the maximum frequency both operate with a time +complexity of O(klogk), where k represents the number of distinct letters. Each of these operations—insertions, and +extractions—is logarithmic due to the heap structure of the priority queue. However, since the number of distinct +letters is limited to a maximum of 26 (one for each letter in the alphabet), the size of the priority queue remains +constant and thus the time complexity effectively becomes O(1) in practice. + +Overall, the dominant term is O(n) due to the frequency counting step. + +##### Space Complexity + +The frequency map and priority queue take O(26)=O(1) space, as it always requires a fixed space for 26 integers. + +Overall, the space complexity is O(1) because the space used does not depend on the input size. diff --git a/algorithms/greedy/minimum_number_of_pushes/__init__.py b/algorithms/greedy/minimum_number_of_pushes/__init__.py new file mode 100644 index 00000000..d6632d40 --- /dev/null +++ b/algorithms/greedy/minimum_number_of_pushes/__init__.py @@ -0,0 +1,52 @@ +from collections import Counter +import heapq + + +def minimum_pushes_greedy_with_sorting(word: str) -> int: + # frequency vector of size 26 that storees 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 throuch 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 diff --git a/algorithms/greedy/minimum_number_of_pushes/images/examples/minimum_number_of_pushes_to_type_word_ii_example_1.png b/algorithms/greedy/minimum_number_of_pushes/images/examples/minimum_number_of_pushes_to_type_word_ii_example_1.png new file mode 100644 index 0000000000000000000000000000000000000000..742adc350e5272b86c706d838edfe5c84080324f GIT binary patch literal 25179 zcmb@tby!=$w>C;k3ls}24gpG`xNGoID1qV*#jUtYgBOB3#fuepFYb~ALW{e*7b_Hp z8-C|}=R426|6X`@va@HeS!>pwJ!{Q7?}V!;f$^{@u+h-a@Z@Br)zHwMh@uW=EDY2Y zeCjL?)DN(=l$45`l+u$?C>U;LZsPvlZ>7xt(yfUj6 zjD1Si34$0**xcZQ~NS}{S2ozuW~%aB^>iZSykpA)X|CBxv{ek{J=gf~cN~%lA$)Ud0&0H)j99*p& z-9EE4Nu#QovewXX(@|6qHgmM+Ffn&Dwcvo*J3We^i9&=?r}h?ZCa)p(b`Gw>5V1G^ zxkDIr{&<=5&FlZ%;$|!MMn_TQwUnca#cKf$E)K3Y;@GcWzZP{d|17K~E%V>vs9$1l ztlZq3ggH6CeEGuhg_pz8#gda-NJxm2i-(hkhaGhXyQ`;zn+b&7!Ikd6D)~S4NL#p? zxmY{7SvxwseyrET)Y08d?9H1;MgQ~nUv^qRtpBej2iN~@7OH`qk0qSk99*3LQ#VRf z^zo{&iZ#T-PFLF69_1dC4sjkKLDB!*|NklZzZ(CSq|X191yF3 zF5J?(c>d?H2+z<6)9abnvqFr3r4_~B6^A%;bR%>llx-dOXIN)g3V2W3yVJkx zEt38O{{a6Gg!oeZr+SKKUQj{)#uiSi*mtq03a^DxLUdgGC_Rog4(>)H)B)6}3eVk9 zLSSPXf*ri2iG{t6ACDHackl0`gkrlUUZeDsG*9|UdZR4xf=*APgs1~bBvE?QUCV9) z|Dh~+G#vf^Ps6orZRKeEc2?KYr+w-!ry4sn*$ms7AgjTo5k_}=+V;O4va3)=NEt)% z1elgilN*T~z31m6Bp&`saK?ac!%Pobw;L!z1#deoCJKRuuD|(VX_i^Kq9=WXun?Azv1p!6#|MK828-oY08Ij`IrG!EBx03!Ur|FRZpzJVz`UyV<`2 zsfet!STsko&inJK$cl!!(#s3~hYQo~%r8T+qE833$l6$|+G;^4t0ENz7k>)6(KYQt z8D8=lLic`0FH;Wa=ffEhlyl?C5(YkhY>ilBgtk&oEc)_AJ)jpbPQMz^%|TtHkn2`c zR_1`w5f$Onbpadq$VJNDmVSPkqvq`_RucA48b1H(vf1zNj~+U%p4nId%ewO{znl&* zUcf8i(Y8DvwWIYoFxp@K`cUdA6t$EWEB;9z<>-o?-RR#d+@BkV#c!GXU7S>G`BKrR4NSN+br zKaQMBcZXj@NY`NibVjL=NFd&)las%BWkaE8@xI&a^|-mv7g z&$i(C{zU$z%#o$UO&YIXIbI>DR7SMGT)#ol8jC`-+Fv8>(_zVyrmcxN-wSFGu^txAJ&3& z2Hz(oBfEj3o!>Nu++kP>KIXQ}6ubB$2P!^0QZy|8X3SzEKJ7*FUW5hAwH~&V%|O

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zQR)uS&3{mqa%5>u68nc=6~ekT`b~!x|6ko0=xeQK|Chpk>|M)MGtnn9oyw3AJc1q! zQG4)FNQZ`_wuX|8CNa*$zjxe`-V(|55XZnU7#V;#@{(vnGLmvmjeCemMM<>(J?$Ta zv&+I2p(yj8%l~t#QXj*WG`XaWv+V!7i&!V6W3qj?nunE)>3{PniUB0I9v>cNei#zC zc_dn$Jlnt)`O)`&`tAQEpe0&$w)2(Q8qE}?)yc!@Q-I-g&dg}(v%A-(_dKQ4wJqfQ zpAr#Y2Vh(ev_4JrlW@!0bEqtRK46Sy2=lwd-l&_G?xyD}teStyYwfMx> z`e<^^;x~<2l&b$%i>It|MA1ZkEPW2cQuuGx#Ibi-F4YOYy!_uMJ-vpe*ExA}28q@& z|E=0?AS}w1{vwC$zi;XPw;7!XkhgkWIh?QegdauxW%%z0W$=$@Ize6RD+KqbgFTKG zcb}F7Npk7`uSxu;-bwKt4-XI4Zf Date: Mon, 26 Jan 2026 06:23:30 +0000 Subject: [PATCH 2/4] updating DIRECTORY.md --- DIRECTORY.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 0576d0df..4e99d164 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -77,6 +77,8 @@ * [Test Knapsack 01](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/knapsack_01/test_knapsack_01.py) * Longest Common Subsequence * [Test Longest Common Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/longest_common_subsequence/test_longest_common_subsequence.py) + * Longest Increasing Subsequence + * [Test Longest Increasing Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/longest_increasing_subsequence/test_longest_increasing_subsequence.py) * Maximal Square * [Test Maximal Square](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/dynamic_programming/maximal_square/test_maximal_square.py) * Min Distance @@ -155,6 +157,8 @@ * [Test Majority Element](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/majority_element/test_majority_element.py) * Min Arrows * [Test Find Min Arrows](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/min_arrows/test_find_min_arrows.py) + * Minimum Number Of Pushes + * [Test Minimum Number Of Pushes](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/minimum_number_of_pushes/test_minimum_number_of_pushes.py) * Minimum Refuel Stops * [Test Min Refueling Stops](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/minimum_refuel_stops/test_min_refueling_stops.py) * Spread Stones @@ -695,8 +699,6 @@ * [Test Increasing Triplet](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/increasing_triplet_subsequence/test_increasing_triplet.py) * Kid With Greatest No Of Candies * [Test Kids With Greatest Candies](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/kid_with_greatest_no_of_candies/test_kids_with_greatest_candies.py) - * Longest Increasing Subsequence - * [Test Longest Increasing Subsequence](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/longest_increasing_subsequence/test_longest_increasing_subsequence.py) * Longest Subarray Of Ones * [Test Longest Subarray](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/arrays/longest_subarray_of_ones/test_longest_subarray.py) * Lucky Numbers In A Matrix From 6e7e00f3a4b3c1bfb2596639d4289acccdb354cd Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 26 Jan 2026 09:35:56 +0300 Subject: [PATCH 3/4] Update algorithms/greedy/minimum_number_of_pushes/README.md Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/greedy/minimum_number_of_pushes/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/algorithms/greedy/minimum_number_of_pushes/README.md b/algorithms/greedy/minimum_number_of_pushes/README.md index 6dd3ba43..312405bf 100644 --- a/algorithms/greedy/minimum_number_of_pushes/README.md +++ b/algorithms/greedy/minimum_number_of_pushes/README.md @@ -109,7 +109,7 @@ optimal for minimizing key presses. - Iterate through the sorted frequency vector: - If the frequency of a letter is zero, break the loop as there are no more letters to process. - Calculate the number of pushes for each letter based on its position in the sorted list: (i / 8 + 1) * frequency[i]. - > the number of pushes required to obtain a single instance of it is (i / 8 + 1). Because there are 8 available + > the number of pushes required to obtain a single instance of it is (i / 8 + 1). Because there are 8 available > keys (2 − 9), for the first 8 values of i (i = 0 to i = 7) corresponding to the first 8 frequent letters, > (i / 8 + 1) will give 1. For the next 8 values of i (i=8 to i=15) corresponding to the next 8 frequent letters, > (i / 8 + 1) will give 2, and this pattern continues. From c02094f98f8c13eeb6e886abe644c0a02e3f86e6 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Mon, 26 Jan 2026 09:36:09 +0300 Subject: [PATCH 4/4] Update algorithms/greedy/minimum_number_of_pushes/__init__.py Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> --- algorithms/greedy/minimum_number_of_pushes/__init__.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/algorithms/greedy/minimum_number_of_pushes/__init__.py b/algorithms/greedy/minimum_number_of_pushes/__init__.py index d6632d40..a5aed0e7 100644 --- a/algorithms/greedy/minimum_number_of_pushes/__init__.py +++ b/algorithms/greedy/minimum_number_of_pushes/__init__.py @@ -3,11 +3,11 @@ def minimum_pushes_greedy_with_sorting(word: str) -> int: - # frequency vector of size 26 that storees the count of each letter in the word + # 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 throuch each character and increment the count in the frequency at the index corresponding to char - "a" + # 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: