给定一个尺寸为2 x n的矩形网格。我们需要找出最大和,以使没有两个选择的数字在垂直,对角线或水平方向上相邻。
例子:
Input: 1 4 5
2 0 0
Output: 7
If we start from 1 then we can add only 5 or 0.
So max_sum = 6 in this case.
If we select 2 then also we can add only 5 or 0.
So max_sum = 7 in this case.
If we select from 4 or 0 then there is no further
elements can be added.
So, Max sum is 7.
Input: 1 2 3 4 5
6 7 8 9 10
Output: 24
方法:
此问题是最大和的扩展,因此没有两个元素相邻。唯一要更改的是获取特定列的两行的最大元素。考虑到两种情况,我们逐列遍历并保持最大和。
1)包含当前列的元素。在这种情况下,我们在当前列中最多使用两个元素。
2)当前列的一个元素被排除(或不包括)
下面是上述步骤的实现。
C++
// C++ program to find maximum sum in a grid such that
// no two elements are adjacent.
#include
#define MAX 1000
using namespace std;
// Function to find max sum without adjacent
int maxSum(int grid[2][MAX], int n)
{
// Sum including maximum element of first column
int incl = max(grid[0][0], grid[1][0]);
// Not including first column's element
int excl = 0, excl_new;
// Traverse for further elements
for (int i = 1; i
Java
// Java Code for Maximum sum in a 2 x n grid
// such that no two elements are adjacent
import java.util.*;
class GFG {
// Function to find max sum without adjacent
public static int maxSum(int grid[][], int n)
{
// Sum including maximum element of first
// column
int incl = Math.max(grid[0][0], grid[1][0]);
// Not including first column's element
int excl = 0, excl_new;
// Traverse for further elements
for (int i = 1; i < n; i++ )
{
// Update max_sum on including or
// excluding of previous column
excl_new = Math.max(excl, incl);
// Include current column. Add maximum element
// from both row of current column
incl = excl + Math.max(grid[0][i], grid[1][i]);
// If current column doesn't to be included
excl = excl_new;
}
// Return maximum of excl and incl
// As that will be the maximum sum
return Math.max(excl, incl);
}
/* Driver program to test above function */
public static void main(String[] args)
{
int grid[][] = {{ 1, 2, 3, 4, 5},
{ 6, 7, 8, 9, 10}};
int n = 5;
System.out.println(maxSum(grid, n));
}
}
// This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 program to find maximum sum in a grid such that
# no two elements are adjacent.
# Function to find max sum without adjacent
def maxSum(grid, n) :
# Sum including maximum element of first column
incl = max(grid[0][0], grid[1][0])
# Not including first column's element
excl = 0
# Traverse for further elements
for i in range(1, n) :
# Update max_sum on including or excluding
# of previous column
excl_new = max(excl, incl)
# Include current column. Add maximum element
# from both row of current column
incl = excl + max(grid[0][i], grid[1][i])
# If current column doesn't to be included
excl = excl_new
# Return maximum of excl and incl
# As that will be the maximum sum
return max(excl, incl)
# Driver code
if __name__ == "__main__" :
grid = [ [ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10] ]
n = 5
print(maxSum(grid, n))
// This code is contributed by Ryuga
C#
// C# program Code for Maximum sum
// in a 2 x n grid such that no two
// elements are adjacent
using System;
class GFG
{
// Function to find max sum
// without adjacent
public static int maxSum(int [,]grid, int n)
{
// Sum including maximum element
// of first column
int incl = Math.Max(grid[0, 0],
grid[1, 0]);
// Not including first column's
// element
int excl = 0, excl_new;
// Traverse for further elements
for (int i = 1; i < n; i++ )
{
// Update max_sum on including or
// excluding of previous column
excl_new = Math.Max(excl, incl);
// Include current column. Add
// maximum element from both
// row of current column
incl = excl + Math.Max(grid[0, i],
grid[1, i]);
// If current column doesn't
// to be included
excl = excl_new;
}
// Return maximum of excl and incl
// As that will be the maximum sum
return Math.Max(excl, incl);
}
// Driver Code
public static void Main(String[] args)
{
int [,]grid = {{ 1, 2, 3, 4, 5},
{ 6, 7, 8, 9, 10}};
int n = 5;
Console.Write(maxSum(grid, n));
}
}
// This code is contributed
// by PrinciRaj1992
PHP
输出:
24