给定一个nxn矩阵，其中包含0到n 2 -1范围内的所有数字。问题是要计算严格按递增顺序重新排列矩阵中所有数字所需的总能量，即重新排列后，第一行包含从0到n-1的’n’个数字，然后第二行包含从n到2n- 1，依此类推，直到最后一行或第n行。可以从当前位置向左，向右，顶部或底部四个方向中的任何一个方向移动数字，以到达最终修改的矩阵中的目标。将号码从当前位置转移到所需目的地的移动步骤数是该号码移动所需的能量。例如，在4 x 4矩阵中，数字“ 6”出现在位置(2，3)。它在修改后的矩阵中的目标位置是(1，1)。因此，“ 6”向左移动2步，向上移动1步到达位置(1，1)。共移动了3步，因此“ 6”所需的能量为3个单位。这样，我们必须总结所有数字的移动/重新排列所需的所有能量。
例子 ：
Input : mat[][] = { {3, 0},
{2, 1} }
Output : 4 units
For number '3':
Move it one step right and one step down.
Total 2 steps thus energy required = 2 units.
For number '0':
Move it one step left.
Total 1 step thus energy required = 1 unit.
For number '1':
Move it one step up.
Total 1 step thus energy required = 1 unit.
Total energy required = 4 units.
Input : mat[][] = { {4, 7, 10, 3},
{8, 5, 6, 1},
{9, 11, 10, 2},
{15, 13, 14, 12} }
Output : 22 units
算法：
calculateEnergy(mat, n)
Declare i_des, j_des, q
Initialize tot_energy = 0
for i = 0 to n-1
for j = 0 to n-1
q = mat[i][j] / n
i_des = q
j_des = mat[i][j] - (n * q)
tot_energy += abs(i_des - i) + abs(j_des - j)
return tot_energy
C++
// C++ implementation to find the total energy
// required to rearrange the numbers
#include
using namespace std;
#define SIZE 100
// function to find the total energy
// required to rearrange the numbers
int calculateEnergy(int mat[SIZE][SIZE], int n)
{
int i_des, j_des, q;
int tot_energy = 0;
// nested loops to access the elements
// of the given matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// store quotient
q = mat[i][j] / n;
// final destination location (i_des, j_des) of
// the element mat[i][j] is being calculated
i_des = q;
j_des = mat[i][j] - (n * q);
// energy required for the movement of the
// element mat[i][j] is calculated and then
// accumulated in the 'tot_energy'
tot_energy += abs(i_des - i) + abs(j_des - j);
}
}
// required total energy
return tot_energy;
}
// Driver program to test above
int main()
{
int mat[SIZE][SIZE] = { { 4, 7, 0, 3 },
{ 8, 5, 6, 1 },
{ 9, 11, 10, 2 },
{ 15, 13, 14, 12 } };
int n = 4;
cout << "Total energy required = "
<< calculateEnergy(mat, n) << " units";
return 0;
} Java
// Java implementation to find
// the total energy required
// to rearrange the numbers
import java.util.*;
import java.lang.*;
public class GfG{
private final static int SIZE = 100;
// function to find the total energy
// required to rearrange the numbers
public static int calculateEnergy(int mat[][],
int n)
{
int i_des, j_des, q;
int tot_energy = 0;
// nested loops to access the elements
// of the given matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// store quotient
q = mat[i][j] / n;
// final destination location
// (i_des, j_des) of
// the element mat[i][j] is
// being calculated
i_des = q;
j_des = mat[i][j] - (n * q);
// energy required for the
// movement of the
// element mat[i][j] is
// calculated and then
// accumulated in the 'tot_energy'
tot_energy += Math.abs(i_des - i) +
Math.abs(j_des - j);
}
}
// required total energy
return tot_energy;
}
// Driver function
public static void main(String argc[]){
int[][] mat = new int[][] {{ 4, 7, 0, 3 },
{ 8, 5, 6, 1 },
{ 9, 11, 10, 2 },
{ 15, 13, 14, 12 }};
int n = 4;
System.out.println("Total energy required = "
+ calculateEnergy(mat, n) + " units");
}
}
// This code is contributed by Sagar ShuklaPython3
# implementation to find the total
# energy required to rearrange the
# numbers
n = 4
# function to find the total energy
# required to rearrange the numbers
def calculateEnergy(mat,n):
tot_energy = 0
# nested loops to access the
# elements of the given matrix
for i in range(n):
for j in range(n):
#store quotient
q = mat[i][j]//n
# final destination location
# (i_des, j_des) of the
# element mat[i][j] is being
# calculated
i_des = q
j_des = mat[i][j]- (n*q)
# energy required for the
# movement of the element
# mat[i][j] is calculated
# and then accumulated in
# the 'tot_energy'
tot_energy += (abs(i_des-i)
+ abs(j_des-j))
# required total energy
return tot_energy
# Driver Program
mat = [[4, 7, 0, 3],
[8, 5, 6, 1],
[9, 11, 10, 2],
[15, 13, 14, 12]]
print("Total energy required = ",
calculateEnergy(mat,n), "units")
# This code is contributed by Shrikant13.C#
// C# implementation to find
// the total energy required
// to rearrange the numbers
using System;
class GFG {
// function to find the total energy
// required to rearrange the numbers
public static int calculateEnergy(int[, ] mat,
int n)
{
int i_des, j_des, q;
int tot_energy = 0;
// nested loops to access the elements
// of the given matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// store quotient
q = mat[i, j] / n;
// final destination location
// (i_des, j_des) of
// the element mat[i][j] is
// being calculated
i_des = q;
j_des = mat[i, j] - (n * q);
// energy required for the
// movement of the
// element mat[i][j] is
// calculated and then
// accumulated in the 'tot_energy'
tot_energy += Math.Abs(i_des - i) +
Math.Abs(j_des - j);
}
}
// required total energy
return tot_energy;
}
// Driver function
public static void Main()
{
int[, ] mat = new int[, ]{ { 4, 7, 0, 3 },
{ 8, 5, 6, 1 },
{ 9, 11, 10, 2 },
{ 15, 13, 14, 12 } };
int n = 4;
Console.Write("Total energy required = " +
calculateEnergy(mat, n) + " units");
}
}
// This code is contributed by Sam007PHP
输出 ：
Total energy required = 22 units
时间复杂度： O(n 2 )