给定一个数字网格，找到最大长度的 Snake 序列并打印它。如果存在多个最大长度的蛇序列，则打印其中任何一个。
蛇形序列由网格中的相邻数字组成，对于每个数字，其右侧或下方的数字为其值的 +1 或 -1。例如，如果您在网格中的位置 (x, y)，如果该数字为 ± 1，您可以向右移动，即 (x, y+1) 或向下移动，即 (x+1, y) 如果该数字是±1。
例如，
9、6、5、2
8、7、6、5
7, 3, 1, 6
1, 1, 1, 7
在上面的网格中，最长的蛇序列是：(9, 8, 7, 6, 5, 6, 7)
下图显示了所有可能的路径——
我们强烈建议您将浏览器最小化，然后自己先尝试一下。
这个想法是使用动态规划。对于矩阵的每个单元格，我们保持以当前单元格结尾的蛇的最大长度。最大长度蛇序列将具有最大值。最大值单元格将对应于蛇的尾巴。为了打印蛇，我们需要从尾部一直回溯到蛇的头部。
设T[i][i]表示在单元格 (i, j) 处结束的蛇的最大长度，然后对于给定的矩阵 M，DP 关系定义为 –
T[0][0] = 0
T[i][j] = max(T[i][j], T[i][j – 1] + 1) 如果 M[i][j] = M[i][j – 1] ± 1
T[i][j] = max(T[i][j], T[i – 1][j] + 1) 如果 M[i][j] = M[i – 1][j] ± 1
下面是这个想法的实现——
C++
// C++ program to find maximum length
// Snake sequence and print it
#include
using namespace std;
#define M 4
#define N 4
struct Point
{
int x, y;
};
// Function to find maximum length Snake sequence path
// (i, j) corresponds to tail of the snake
list findPath(int grid[M][N], int mat[M][N],
int i, int j)
{
list path;
Point pt = {i, j};
path.push_front(pt);
while (grid[i][j] != 0)
{
if (i > 0 &&
grid[i][j] - 1 == grid[i - 1][j])
{
pt = {i - 1, j};
path.push_front(pt);
i--;
}
else if (j > 0 &&
grid[i][j] - 1 == grid[i][j - 1])
{
pt = {i, j - 1};
path.push_front(pt);
j--;
}
}
return path;
}
// Function to find maximum length Snake sequence
void findSnakeSequence(int mat[M][N])
{
// table to store results of subproblems
int lookup[M][N];
// initialize by 0
memset(lookup, 0, sizeof lookup);
// 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 || j)
{
// look above
if (i > 0 &&
abs(mat[i - 1][j] - mat[i][j]) == 1)
{
lookup[i][j] = 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 &&
abs(mat[i][j - 1] - mat[i][j]) == 1)
{
lookup[i][j] = 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;
}
}
}
}
}
cout << "Maximum length of Snake sequence is: "
<< max_len << endl;
// find maximum length Snake sequence path
list path = findPath(lookup, mat, max_row,
max_col);
cout << "Snake sequence is:";
for (auto it = path.begin(); it != path.end(); it++)
cout << endl << mat[it->x][it->y] << " ("
<< it->x << ", " << it->y << ")" ;
}
// Driver code
int main()
{
int mat[M][N] =
{
{9, 6, 5, 2},
{8, 7, 6, 5},
{7, 3, 1, 6},
{1, 1, 1, 7},
};
findSnakeSequence(mat);
return 0;
} Java
// 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 findPath(int grid[][],
int mat[][],
int i, int j)
{
List 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 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
Python3] // 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 findPath(int [,]grid,
int [,]mat,
int i, int j)
{
List path = new List();
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 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 输出 ：
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)
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