Ņemot vērā skaitļu režģi, atrodiet maksimālā garuma čūsku secību un izdrukājiet. Ja ir vairākas čūsku sekvences, ar maksimālo garumu izdrukājiet kādu no tām.
Čūskas secību veido blakus esošie skaitļi tīklā tā, lai katram skaitlim būtu labajā pusē esošais numurs vai numurs, kas zemāks par to, ir +1 vai -1 tā vērtība. Piemēram, ja režģī atrodaties vietā (x y), varat vai nu pārvietoties pa labi, t.i., (x y+1), ja šis skaitlis ir ± 1, vai pārvietoties uz leju, t.i. (x+1 y), ja šis skaitlis ir ± 1.
For example 9 6 5 2 8 7 6 5 7 3 1 6 1 1 1 7 In above grid the longest snake sequence is: (9 8 7 6 5 6 7)
Zemāk attēlā parādīti visi iespējamie ceļi:
Mēs ļoti iesakām samazināt savu pārlūkprogrammu un vispirms izmēģināt to pats.
Ideja ir izmantot dinamisko programmēšanu. Katrā matricas šūnā mēs saglabājam maksimālo čūskas garumu, kas beidzas ar pašreizējo šūnām. Maksimālā garuma čūsku secībai būs maksimālā vērtība. Maksimālās vērtības šūna atbilst čūskas astei. Lai izdrukātu čūsku, mums ir jāatstāj atpakaļ no astes līdz Snake’s Head.
Let T[i][i] represent maximum length of a snake which ends at cell (i j) then for given matrix M the DP relation is defined as T[0][0] = 0 T[i][j] = max(T[i][j] T[i][j - 1] + 1) if M[i][j] = M[i][j - 1] ± 1 T[i][j] = max(T[i][j] T[i - 1][j] + 1) if M[i][j] = M[i - 1][j] ± 1
Zemāk ir idejas ieviešana
C++// C++ program to find maximum length // Snake sequence and print it #include
// Java program to find maximum length // Snake sequence and print it import java.util.*; class GFG { static int M = 4; static int N = 4; static class Point { int x y; public Point(int x int y) { this.x = x; this.y = y; } }; // Function to find maximum length Snake sequence path // (i j) corresponds to tail of the snake static List<Point> findPath(int grid[][] int mat[][] int i int j) { List<Point> path = new LinkedList<>(); Point pt = new Point(i j); path.add(0 pt); while (grid[i][j] != 0) { if (i > 0 && grid[i][j] - 1 == grid[i - 1][j]) { pt = new Point(i - 1 j); path.add(0 pt); i--; } else if (j > 0 && grid[i][j] - 1 == grid[i][j - 1]) { pt = new Point(i j - 1); path.add(0 pt); j--; } } return path; } // Function to find maximum length Snake sequence static void findSnakeSequence(int mat[][]) { // table to store results of subproblems int [][]lookup = new int[M][N]; // initialize by 0 // stores maximum length of Snake sequence int max_len = 0; // store coordinates to snake's tail int max_row = 0; int max_col = 0; // fill the table in bottom-up fashion for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) { // do except for (0 0) cell if (i != 0 || j != 0) { // look above if (i > 0 && Math.abs(mat[i - 1][j] - mat[i][j]) == 1) { lookup[i][j] = Math.max(lookup[i][j] lookup[i - 1][j] + 1); if (max_len < lookup[i][j]) { max_len = lookup[i][j]; max_row = i; max_col = j; } } // look left if (j > 0 && Math.abs(mat[i][j - 1] - mat[i][j]) == 1) { lookup[i][j] = Math.max(lookup[i][j] lookup[i][j - 1] + 1); if (max_len < lookup[i][j]) { max_len = lookup[i][j]; max_row = i; max_col = j; } } } } } System.out.print('Maximum length of Snake ' + 'sequence is: ' + max_len + 'n'); // find maximum length Snake sequence path List<Point> path = findPath(lookup mat max_row max_col); System.out.print('Snake sequence is:'); for (Point it : path) System.out.print('n' + mat[it.x][it.y] + ' (' + it.x + ' ' + it.y + ')'); } // Driver code public static void main(String[] args) { int mat[][] = {{9 6 5 2} {8 7 6 5} {7 3 1 6} {1 1 1 7}}; findSnakeSequence(mat); } } // This code is contributed by 29AjayKumar
// C# program to find maximum length // Snake sequence and print it using System; using System.Collections.Generic; class GFG { static int M = 4; static int N = 4; public class Point { public int x y; public Point(int x int y) { this.x = x; this.y = y; } }; // Function to find maximum length Snake sequence path // (i j) corresponds to tail of the snake static List<Point> findPath(int[ ] grid int[ ] mat int i int j) { List<Point> path = new List<Point>(); Point pt = new Point(i j); path.Insert(0 pt); while (grid[i j] != 0) { if (i > 0 && grid[i j] - 1 == grid[i - 1 j]) { pt = new Point(i - 1 j); path.Insert(0 pt); i--; } else if (j > 0 && grid[i j] - 1 == grid[i j - 1]) { pt = new Point(i j - 1); path.Insert(0 pt); j--; } } return path; } // Function to find maximum length Snake sequence static void findSnakeSequence(int[ ] mat) { // table to store results of subproblems int[ ] lookup = new int[M N]; // initialize by 0 // stores maximum length of Snake sequence int max_len = 0; // store coordinates to snake's tail int max_row = 0; int max_col = 0; // fill the table in bottom-up fashion for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) { // do except for (0 0) cell if (i != 0 || j != 0) { // look above if (i > 0 && Math.Abs(mat[i - 1 j] - mat[i j]) == 1) { lookup[i j] = Math.Max( lookup[i j] lookup[i - 1 j] + 1); if (max_len < lookup[i j]) { max_len = lookup[i j]; max_row = i; max_col = j; } } // look left if (j > 0 && Math.Abs(mat[i j - 1] - mat[i j]) == 1) { lookup[i j] = Math.Max( lookup[i j] lookup[i j - 1] + 1); if (max_len < lookup[i j]) { max_len = lookup[i j]; max_row = i; max_col = j; } } } } } Console.Write('Maximum length of Snake ' + 'sequence is: ' + max_len + 'n'); // find maximum length Snake sequence path List<Point> path = findPath(lookup mat max_row max_col); Console.Write('Snake sequence is:'); foreach(Point it in path) Console.Write('n' + mat[it.x it.y] + ' (' + it.x + ' ' + it.y + ')'); } // Driver code public static void Main(String[] args) { int[ ] mat = { { 9 6 5 2 } { 8 7 6 5 } { 7 3 1 6 } { 1 1 1 7 } }; findSnakeSequence(mat); } } // This code is contributed by Princi Singh
def snakesequence(S m n): sequence = {} DP = [[1 for x in range(m+1)] for x in range(n+1)] a b maximum = 0 0 0 position = [0 0] for i in range(0 n+1): for j in range(0 m+1): a b = 0 0 p = 'initial' if(i > 0 and abs(S[i][j] - S[i-1][j]) == 1): a = DP[i-1][j] if(j > 0 and abs(S[i][j] - S[i][j-1]) == 1): b = DP[i][j-1] if a != 0 and a >= b: p = str(i-1) + ' ' + str(j) elif b != 0: p = str(i) + ' ' + str(j-1) q = str(i) + ' ' + str(j) sequence[q] = p DP[i][j] = DP[i][j] + max(a b) if DP[i][j] >= maximum: maximum = DP[i][j] position[0] = i position[1] = j snakeValues = [] snakePositions = [] snakeValues.append(S[position[0]][position[1]]) check = 'found' str_next = str(position[0]) + ' ' + str(position[1]) findingIndices = sequence[str_next].split() while(check == 'found'): if sequence[str_next] == 'initial': snakePositions.insert(0 str_next) check = 'end' continue findingIndices = sequence[str_next].split() g = int(findingIndices[0]) h = int(findingIndices[1]) snakeValues.insert(0 S[g][h]) snake_position = str(g) + ' ' + str(h) snakePositions.insert(0 str_next) str_next = sequence[str_next] return [snakeValues snakePositions] S = [[9 6 5 2] [8 7 6 5] [7 3 1 6] [1 1 10 7]] m = 3 n = 3 seq = snakesequence(S m n) for i in range(len(seq[0])): print(seq[0][i] '' seq[1][i].split())
function snakesequence(S m n) { let sequence = {} let DP = new Array(n + 1) for (var i = 0; i <= n; i++) DP[i] = new Array(m + 1).fill(1) let a = 0 b = 0 maximum = 0 let position = [0 0] for (var i = 0; i <= n; i++) { for (var j = 0; j <= m; j++) { a = 0 b = 0 let p = 'initial' if(i > 0 && Math.abs(S[i][j] - S[i-1][j]) == 1) a = DP[i-1][j] if(j > 0 && Math.abs(S[i][j] - S[i][j-1]) == 1) b = DP[i][j-1] if (a != 0 && a >= b) p = String(i-1) + ' ' + String(j) else if (b != 0) p = String(i) + ' ' + String(j-1) let q = String(i) + ' ' + String(j) sequence[q] = p DP[i][j] = DP[i][j] + Math.max(a b) if (DP[i][j] >= maximum) { maximum = DP[i][j] position[0] = i position[1] = j } } } let snakeValues = [] let snakePositions = [] snakeValues.push(S[position[0]][position[1]]) let check = 'found' let String_next = String(position[0]) + ' ' + String(position[1]) let findingIndices = sequence[String_next].split(' ') while(check == 'found') { if (sequence[String_next] == 'initial') { snakePositions.unshift(String_next) check = 'end' continue } findingIndices = sequence[String_next].split(' ') let g = parseInt(findingIndices[0]) let h = parseInt(findingIndices[1]) snakeValues.unshift(S[g][h]) let snake_position = String(g) + ' ' + String(h) snakePositions.unshift(String_next) String_next = sequence[String_next] } return [snakeValues snakePositions] } // Driver Code let S = [[9 6 5 2] [8 7 6 5] [7 3 1 6] [1 1 10 7]] let m = 3 let n = 3 let seq = snakesequence(S m n) for (var i = 0; i < seq[0].length; i++) console.log(seq[0][i] + '' seq[1][i].split(' '))
Izvade
Maximum length of Snake sequence is: 6 Snake sequence is: 9 (0 0) 8 (1 0) 7 (1 1) 6 (1 2) 5 (1 3) 6 (2 3) 7 (3 3)
Iepriekš minētā šķīduma laika sarežģītība ir O (m*n). Papildu telpa, ko izmanto ar iepriekš minēto šķīdumu, ir O (m*n). Ja mums nav jāizdrukā čūskas telpa, var vēl vairāk samazināt līdz O (n), jo rezultātu mēs izmantojam tikai no pēdējās rindas.
ievietošanas kārtošanas algoritms