From 89dcb28ce14561bdb0d712bfa4165105f66c00d1 Mon Sep 17 00:00:00 2001 From: nkeke21 Date: Sat, 12 Nov 2022 12:12:39 +0400 Subject: [PATCH 1/3] Fixes MaxRect problem --- MagicMatrix.md | 87 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 87 insertions(+) create mode 100644 MagicMatrix.md diff --git a/MagicMatrix.md b/MagicMatrix.md new file mode 100644 index 0000000..4ab3332 --- /dev/null +++ b/MagicMatrix.md @@ -0,0 +1,87 @@ +# MagicMatrix + +პრობლემა: +``` +მატრიცას ეწოდება მაგიური თუკი ის კვადრატულია(n x n-ზე) და მასში არის ყველა +რიცხვი 1-დან n^2-ის ჩათვლით. თქვენი მიზანია დაწეროთ magicMatrix მეთოდი +რომელიც შეამოწმებს არის თუ არა მატრიცა მაგიური და თუკი მაგიურია მაშინ +დააბრუნებს true-ს თუ არა მაშინ false-ს. + +``` + + + +## პირობის გააზრება: + +ამ ამოცანის პირობაში ყურადღება უნდა მივაქციოთ ორ მნიშვნელოვან პირობას + +* პირველ რიგში მატრიცა უნდა იყოს კვადრატული(უნდა შევამოწმოთ არის, თუ არა ის კვადარატული). +* თუ ის კვადრატულია, მაშინ უნდა შევამოწმოთ სწორად არის თუ არა ის შევსებული. + + + +## პრობლემის გადაჭრის გზა: + +* პირველ რიგში გავაკეთოთ მეთოდი `private boolean magicMatrix(int[][] inp)` , რომელიც დააბრუნებს `true` - ს +ან `false` -ს (იმისდა მიხედვით, არის თუ არა ჩვენი მატრიცა კვადრატული). + +* როგორც ზემოთ მოგახსენეთ, ჯერ უნდა შევამოწმოთ, არის თუ არა ეს მატრიცა კვადრატული შემდეგი შემოწმებით: + +```java +if (inp.length == 0 || inp.length != inp[0].length) { + return false; +} +``` +-სადაც, `inp.length` არის row -ს სიგრძე, ხოლო `inp[0].length` collumn-ის სიგრძე. + +შესაბამისად, ამ პირობის გაგება`inp.length != inp[0].length` არ უნდა იყოს რთული(ამით ვამოწმებთ, არის თუ არა row - ს სიგრძე collumn - ის სიგრძის ტოლი). +ამ შემთხვევაში ყურადღება უნდა მივაქციოთ შემოწმებას: `inp.length == 0`. თუ ამ პირობას არ შევამოწმებთ, მაშინ `inp.length != inp[0].length` დაიქრაშება, +რადგან ინფორმაციის წაკითხვას ვცდილობთ იქიდან, რაც არ არის. + +* დავუშვათ, row - ს სიგრძე collumn - ის სიგრძის ტოლია. მაშ ისღა დაგვრჩენია შევამოწმოთ, სწორად არის შევსებული თუ არა ეს მატრიცი. + + + +## სწორად არის თუ არა მატრიცა შევსებული: + +* row == collumn + +* გადავუყვეთ მატრიცის თითოეულ ელემენტს (ანუ ჯერ შევამოწმოთ პირველი row - ს ელემენტები, შემდეგ მეორესი და აშ) და ვნახოთ სწორი ინფორმაცია წერია, თუ არა: + +```java +for (int r = 0; r < inp.length; r++) { + for (int c = 0; c < inp[0].length; c++) { + int rightNum = r * inp.length + c + 1; + if (inp[r][c] != rightNum) { + return false; + } + } +} +``` +`int rightNum` გვიჩვენებს თუ რა რიცხვი უნდა ეწეროს კონკრეტულ ადგილას მატრიცაში, იმ შემთხვევაში თუ ის magic მატრიცაა. + +```java +int rightNum = r * inp.length + c + 1; +``` +მოდი ეს ნაწილი უფრო დეტალურად გავიაროთ. დავუშვათ გვაქვს 3 x 3 მატრიცა. პირველ რიგში ჩვენი მეთოდი შევა პირველ `for` ციკლში და შეამოწმებს პირველ row - ს +ელემენტებს: + +ვთ: `inp[0][0] = 1; inp[0][1] = 2; inp[0][2] = 3;` +როცა, c == 0, rightNum == 1. როცა, c == 1, rightNum == 2. როცა, c == 2, rightNum == 3; +შემდეგ სვეტების შემთხვევაში rightNum -ს კიდევ ემატება წინა row - ების ელემენტებს შორის უდიდესი. + +`inp[r][c] != rightNum` - თუ კონკრეტულ ადგილას არასწორი რიცხვი წერია უნდა დავაბრუნოთ `false`. + +* იმ შემთხვევაში, თუ ჩვენ მეთოდის ბოლოში გავედით, ანუ ყველაფერი კარგადაა და უნდა დავაბრუნოთ `true`. + + +## შესაძლო ხარვეზები: + +* თუ არ შევამოწმებთ მატრიცის length, შესაძლოა დაიქრაშოს ჩვენი პროგრამა, რადგან collumn - ის სიგრძის გაგებისას(როცა მატრიცის length == 0), ჩვენი პროგრამა ეცდება +წაიკითხოს ინფორმაცია არარსებული რაღაციდან. + +* შემდეგი ძალიან მნიშვნელო ხარვეზი შეილება იყოს `int rightNum` ის დათვლისას (აუცილებლად სწორად უნდა იქნეს გამოთვლილი). + +* `r * inp.length` ამის მაგივრად შეგვეძლო დაგვეწერა წინა row - ს ბოლო ელემენტის მნიშვნელობა, თუმცა მაშინ პირველ row ში ჩვენი პროგრამა დაიქრაშებოდა, ამიტომ ესეც უნდა +გაგვეთვალისწინებინა. + From dcd767073af196c5b23c8f3bf92307c3d0d51d57 Mon Sep 17 00:00:00 2001 From: nkeke21 Date: Sat, 12 Nov 2022 12:29:30 +0400 Subject: [PATCH 2/3] Fixes MaxRect --- MagicMatrix.md | 87 -------------------------------------------------- 1 file changed, 87 deletions(-) delete mode 100644 MagicMatrix.md diff --git a/MagicMatrix.md b/MagicMatrix.md deleted file mode 100644 index 4ab3332..0000000 --- a/MagicMatrix.md +++ /dev/null @@ -1,87 +0,0 @@ -# MagicMatrix - -პრობლემა: -``` -მატრიცას ეწოდება მაგიური თუკი ის კვადრატულია(n x n-ზე) და მასში არის ყველა -რიცხვი 1-დან n^2-ის ჩათვლით. თქვენი მიზანია დაწეროთ magicMatrix მეთოდი -რომელიც შეამოწმებს არის თუ არა მატრიცა მაგიური და თუკი მაგიურია მაშინ -დააბრუნებს true-ს თუ არა მაშინ false-ს. - -``` - - - -## პირობის გააზრება: - -ამ ამოცანის პირობაში ყურადღება უნდა მივაქციოთ ორ მნიშვნელოვან პირობას - -* პირველ რიგში მატრიცა უნდა იყოს კვადრატული(უნდა შევამოწმოთ არის, თუ არა ის კვადარატული). -* თუ ის კვადრატულია, მაშინ უნდა შევამოწმოთ სწორად არის თუ არა ის შევსებული. - - - -## პრობლემის გადაჭრის გზა: - -* პირველ რიგში გავაკეთოთ მეთოდი `private boolean magicMatrix(int[][] inp)` , რომელიც დააბრუნებს `true` - ს -ან `false` -ს (იმისდა მიხედვით, არის თუ არა ჩვენი მატრიცა კვადრატული). - -* როგორც ზემოთ მოგახსენეთ, ჯერ უნდა შევამოწმოთ, არის თუ არა ეს მატრიცა კვადრატული შემდეგი შემოწმებით: - -```java -if (inp.length == 0 || inp.length != inp[0].length) { - return false; -} -``` --სადაც, `inp.length` არის row -ს სიგრძე, ხოლო `inp[0].length` collumn-ის სიგრძე. - -შესაბამისად, ამ პირობის გაგება`inp.length != inp[0].length` არ უნდა იყოს რთული(ამით ვამოწმებთ, არის თუ არა row - ს სიგრძე collumn - ის სიგრძის ტოლი). -ამ შემთხვევაში ყურადღება უნდა მივაქციოთ შემოწმებას: `inp.length == 0`. თუ ამ პირობას არ შევამოწმებთ, მაშინ `inp.length != inp[0].length` დაიქრაშება, -რადგან ინფორმაციის წაკითხვას ვცდილობთ იქიდან, რაც არ არის. - -* დავუშვათ, row - ს სიგრძე collumn - ის სიგრძის ტოლია. მაშ ისღა დაგვრჩენია შევამოწმოთ, სწორად არის შევსებული თუ არა ეს მატრიცი. - - - -## სწორად არის თუ არა მატრიცა შევსებული: - -* row == collumn - -* გადავუყვეთ მატრიცის თითოეულ ელემენტს (ანუ ჯერ შევამოწმოთ პირველი row - ს ელემენტები, შემდეგ მეორესი და აშ) და ვნახოთ სწორი ინფორმაცია წერია, თუ არა: - -```java -for (int r = 0; r < inp.length; r++) { - for (int c = 0; c < inp[0].length; c++) { - int rightNum = r * inp.length + c + 1; - if (inp[r][c] != rightNum) { - return false; - } - } -} -``` -`int rightNum` გვიჩვენებს თუ რა რიცხვი უნდა ეწეროს კონკრეტულ ადგილას მატრიცაში, იმ შემთხვევაში თუ ის magic მატრიცაა. - -```java -int rightNum = r * inp.length + c + 1; -``` -მოდი ეს ნაწილი უფრო დეტალურად გავიაროთ. დავუშვათ გვაქვს 3 x 3 მატრიცა. პირველ რიგში ჩვენი მეთოდი შევა პირველ `for` ციკლში და შეამოწმებს პირველ row - ს -ელემენტებს: - -ვთ: `inp[0][0] = 1; inp[0][1] = 2; inp[0][2] = 3;` -როცა, c == 0, rightNum == 1. როცა, c == 1, rightNum == 2. როცა, c == 2, rightNum == 3; -შემდეგ სვეტების შემთხვევაში rightNum -ს კიდევ ემატება წინა row - ების ელემენტებს შორის უდიდესი. - -`inp[r][c] != rightNum` - თუ კონკრეტულ ადგილას არასწორი რიცხვი წერია უნდა დავაბრუნოთ `false`. - -* იმ შემთხვევაში, თუ ჩვენ მეთოდის ბოლოში გავედით, ანუ ყველაფერი კარგადაა და უნდა დავაბრუნოთ `true`. - - -## შესაძლო ხარვეზები: - -* თუ არ შევამოწმებთ მატრიცის length, შესაძლოა დაიქრაშოს ჩვენი პროგრამა, რადგან collumn - ის სიგრძის გაგებისას(როცა მატრიცის length == 0), ჩვენი პროგრამა ეცდება -წაიკითხოს ინფორმაცია არარსებული რაღაციდან. - -* შემდეგი ძალიან მნიშვნელო ხარვეზი შეილება იყოს `int rightNum` ის დათვლისას (აუცილებლად სწორად უნდა იქნეს გამოთვლილი). - -* `r * inp.length` ამის მაგივრად შეგვეძლო დაგვეწერა წინა row - ს ბოლო ელემენტის მნიშვნელობა, თუმცა მაშინ პირველ row ში ჩვენი პროგრამა დაიქრაშებოდა, ამიტომ ესეც უნდა -გაგვეთვალისწინებინა. - From 71fcc4c07ad2ad5955536fe8dadae215f4c702f9 Mon Sep 17 00:00:00 2001 From: nkeke21 Date: Sat, 12 Nov 2022 12:35:45 +0400 Subject: [PATCH 3/3] Fixes MaxRect problem --- MaxRect.java | 41 +++++++++++++ MaxRect.md | 117 ++++++++++++++++++++++++++++++++++++ checkForAllPoints.png | Bin 0 -> 250154 bytes diagonalPoints.png | Bin 0 -> 249026 bytes errorInCheckingElements.png | Bin 0 -> 250154 bytes 5 files changed, 158 insertions(+) create mode 100644 MaxRect.java create mode 100644 MaxRect.md create mode 100644 checkForAllPoints.png create mode 100644 diagonalPoints.png create mode 100644 errorInCheckingElements.png diff --git a/MaxRect.java b/MaxRect.java new file mode 100644 index 0000000..c619ab9 --- /dev/null +++ b/MaxRect.java @@ -0,0 +1,41 @@ +import acm.program.ConsoleProgram; + +public class MaxRect extends ConsoleProgram { + + private int maxRect(int[][] arr) { + int max = 0; + for (int r = 0; r < arr.length; r++) { + for (int c = 0; c < arr[r].length; c++) { + + if (arr[r][c] == 1) { + for (int i = r; i < arr.length; i++) { + for (int j = c; j < arr[i].length; j++) { + + if (arr[i][j] == 1) { + if (allOnes(arr, r, c, i, j)) { + if ((i - r + 1) * (j - c + 1) > max) { + max = (i - r + 1) * (j - c + 1); + } + } + } + + } + } + } + + } + } + return max; + } + + private boolean allOnes(int[][] arr, int r, int c, int i, int j) { + for (int k = r; k <= i; k++) { + for (int p = c; p <= j; p++) { + if (arr[k][p] != 1) { + return false; + } + } + } + return true; + } +} \ No newline at end of file diff --git a/MaxRect.md b/MaxRect.md new file mode 100644 index 0000000..56dae61 --- /dev/null +++ b/MaxRect.md @@ -0,0 +1,117 @@ +# MaxRect + +პრობლემა: +``` + გადმოგეცემათ nxm-ზე მატრიცა რომელშიც მხოლოდ 0-ები და 1-ები წერია. მეთოდმა +უნდა დააბრუნოს ამ მატრიცის ყველაზე დიდი ქვემართკუთხედის +ზომა(ელემენტების რაოდენობა) რომელიც მხოლოდ 1-ებისგან შედგება. +მაგალითად: + + 01100100 + 01111100 + 00111100 + 00111100 + + ამ მატრიცაში ყველაზე დიდი შიდა მართკუთხედი, რომელიც სულ ერთიანებისგან +შედგება არის 12 ზომის: + + 01 1001 00 + 01*1111*00 + 00*1111*00 + 00*1111*00 + + შესაბამისად ამ მატრიცაზე მეთოდმა უნდა დააბრუნოს 12. ჩათვალეთ რომ +გადმოცემულ მატრიცაში ერთი უჯრა მაინც იქნება რომელშიც წერია 1. + +``` + +## პროლბლემის გააზრება: + +* ჩვენ გადმოცემულ მატრიცაში უნდა ვიპოვოთ ისეთი მართკუთხედი, რომელიც შედგენილი იქნება მხოლოდ ერთიანებისაგან, მაგ: +``` + 111 1 11 + 111 1 11 +``` + +* ამ ამოცანაში მთავარია მოვიფიქროთ, თუ როგორ ვიპოვოთ ასეთი მართკუთხედები, კოდის დაწერა კი არც ისე რთულია. + +## პრობლემის გადაჭრის გზა: + +* მე გთავაზობთ შემდეგს: + +* გადავუყვეთ მატრიცის თითოეულ ელემენტს და თითოეულისათვის გავაკეთოთ შემდეგი რამ: + +* დავიმახსოვროთ მოცემული წერტილი. შემდეგ ამ წერტილიდან მარჯვნივ და ქვემოთ გადავუყვეთ სხვა წერტილებს. ალბათ გაინტერესებთ, თუ რას წარმოადგენენ ეს სხვა წერტილები?! ეს სხვა წერტილები არიან დამახსოვრებული წერტილის მოპირდაპირე წერტილები მართკუთხედში. იხილეთ სურათი: checkForAllPoints.png, რომელშიც განხილულია თუ როგორ ვიქცევით პირველი წერტილისათვის მატრიცაში. ანალოგიური მიდგომაა სხვა წერტილებზეც. + +* დამახსოვრებული წერტილი და "ის რაღაც სხვა წერტილი" რომ შევაერთოთ მართკუთხედში მივიღებთ დიაგონალს. ეს ყველაფერი რომ უკეთ წარმოიდგინოთ, ნახეთ სურათი: diagonalPoints.png. + +* შემდეგ უნდა შევამოწმოთ არის თუ არა ამ მოცემულ სამკუთხედში სულ ერთიანები. თუ პასუხი არის `true` უნდა შევამოწმოთ ამ მართკუთხედის ფართობი არის თუ არა მეტი მანამდე შემოწმებულ მართკუთხედების ფართობებზე. თუ პასუხი არის `false`, არაფერს ვაკეთებთ და გადავდივართ შემდეგ წერტილზე. + +## კოდის რეალიზაცია: + +* პირბელ რიგში, შევქმნათ მეთოდი რომელიც გვიბრუნებს მაქსიმალური ფართობის მქონე მართკუთხედის ფართობს, `private int maxRect(int[][] arr)`, რომელსაც გადავცემთ მატრიცას. + +* მივყვეთ "პრობლემის გადაჭრის გზაში" მოცემულ ნაბიჯებს და დავწეროთ შესაბამისი კოდი. + +* გადავუყვეთ მატრიცის თითოეულ ელემენტს: +```java + for (int r = 0; r < arr.length; r++) { + for (int c = 0; c < arr[r].length; c++) { +``` +სადაც r არის შესაბამისი სტრიქონის ნომერი და c არის შესაბამისი სვეტის ნომერი. + +* დავიმახსოვროთ მოცემული წერტილი: +```java + if (arr[r][c] == 1) { +``` + თუ მოცემული წერტილი 1 ის ტოლი არაა ჩვენ არ გვაინტერესებს ეს წერტილი და გადავდივართ შემდეგ წერტილზე, რადგან რა დიდი მართკუთხედის წერტილიც არ უნდა იყოს ეს წერტილი, ამ მართკუთხედში ყველა ელემენტი 1 ის ტოლი არ გამოვა. + +* ვიპოვოთ მეორე წერტილი, რომელიც ამჟამად მყოფი ელემენტის ან მარჯვნივ დგას ან ქვემოთ: +```java + for (int i = r; i < arr.length; i++) { + for (int j = c; j < arr[i].length; j++) { +``` + შევამოწმოთ არის თუ არა ეს მეორე წერტილიც 1 ის ტოლი. თუ არაა, მაშინ ჩვენ ამ ორი წერტილით მოჭიმული მართკუთხედიც არ გვაინტერესებს ზემოთხსენებული მიზეზის გამო. + +```java + if (arr[i][j] == 1) { +``` +სადაც i და j წარმოადგენენ მეორე წერტილისთვის სტრიქონის ნომერს და სვეტის ნომერს. + +* შევამოწმოთ არის თუ არა ამ ორი წერტილით მოჭიმულ მართკუთხედში ყველა ერთიანი. +```java + if (allOnes(arr, r, c, i, j)) { +``` + მეთოდი, `allOnes(arr, r, c, i, j)`, გადაუყვება ამ ორ წერტილით მოჭიმულ მართკუთხედში ყველა ელემენტს და თუ იპოვის 0 ს აბრუნებს `false`, ხოლო თუ 0 იანი არ გვხვდება, აბრუნებს `true` ს. კოდი საკმაოდ მარტივია: + +```java + for (int k = r; k <= i; k++) { + for (int p = c; p <= j; p++) { + if (arr[k][p] != 1) { + return false; + } + } + } + return true; +``` + გადაუყვება სტრიქონებს r დან i მდე და სვეტებს c დან j მდე. r <= i, c <= j. + +* ახლა უნდა შევამოწმოთ არის თუ არა ეს მართკუთხედი მაქსიმალური ფართობის მქონე. +```java + if ((i - r + 1) * (j - c + 1) > max) { + max = (i - r + 1) * (j - c + 1); + } +``` + max არის რაღაც ცვლადი, რომელშიც ვინახავთ მაქსიმალური ფართობის მქონე მართკუთხედის ფართობს. + + იმის მიხვედრას თუ როგორ ვიგებთ გვერდებს, ეს საკმაოდ მარტივია. `i - r` და `j - c`. თუმცა გაგიკვირდებათ, თუ რატომ ვუმატებთ თითოეულ გვერდს კიდევ ერთს. რომ წარმოვიდგინოთ მხოლოდ წერტილი და კოდში დაგვეწერა `(i - r) * (j - c)`, პასუხს ამ შემთხვევისათვის მივიღებდით ნულს, როდესაც რეალურად ის ერთის ტოლია. ან რო გვქონოდა წერტილების გვერდიგვერდ, მაშინ პასუხი გამოგვივიდოდა 0 და აშ. ამიტომ ამ ზემოხსენებულ მონაცემებს დამატებით უნდა დავუმატოთ კიდევ ერთი. + +### შესაძლო ხარვეზები: + +* ერთი ხარვეზი უკვე მოგახსენეთ "კოდის რეალიზაციაში", როდესაც ვისაუბრეთ, თუ რატომ ჭირდებოდა ზემოხსენებულ მონაცემებს ერთის დამატება. + +* მეორე ხარვეზი შესაძლოა ყოფილიყო შემდეგი: `(r - i + 1)`, რაც არასწორია რადგან r <= i და ზოგ შემთხვევაში ეს უარყოფით რიცხვს მოგვცემდა, რაც არასწორია. ამის გამოსწორება შეიძლება თუ დავწერთ `(i - r + 1)` ან ავიღებთ სხვაობის მოდულს. ანალოგიურად ვიქცევით სვეტებზეც. + +* ზოგმა შეიძლება ჩათვალოს, რომ i > r, რაც არასწორია, რადგან ამით ჩვენ ვუარყოფთ ისეთ მაგალითებს, როგორებიცაა: 1x1, 1x2, 1x5 და აშ. ანალოგიურად სვეტებზეც. + +* შემოწმების დროსაც, როდესაც ვამოწმებთ არის თუ არა მოცემულ მართკუთხედში ყველა ერთიანი, ჩვენ უნდა გავითვალისწინოთ ის წერტილებიც, რომლებიც ამ მართკუთხედს ჭიმავენ, რადგან წინააღმდეგ შემთხვევაში ჩვენ ჩავთვლით, რომ ამ წერტილების ზევით, ქვემოთ, და გვერდზე ერთიანები წერია, რაც არასწორია, რადგან ჩვენ მხოლოდ ვიცით, რომ ეს წერტილები არიან მხოლოდ და მხოლოდ ერთიანების ტოლი. სურათი, რომ უკეთ წარმოიდგინოთ, ნახეთ სურათი: errorInCheckingElements.png. diff --git a/checkForAllPoints.png b/checkForAllPoints.png new file mode 100644 index 0000000000000000000000000000000000000000..75b11ef839b7331ea07dea80770087e3c5d91e65 GIT binary patch literal 250154 zcmZ6zc|6qZ_Xpf^mkOyUWUDMwS;mrmhBnEPxudc+vRBB?ES5@0wldZ*QkG=jw;5zG zSto>S!x&6oVVUi7KIb~uIq&m6?@Q>v2HKn_&Yw7N-~gx2-P?u- z4jdUcaNw~1v7^8vpT4D=0zdxoxT*8t81UtL%=RttH@~NriKmf^y{C_ryWIhY7cS0r 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