检查给定矩阵是否为汉克尔
原文:https://www . geesforgeks . org/check-given-matrix-Hankel-not/
给定大小为n×n的矩阵 m[][] 。任务是检查给定的矩阵是否是汉克尔矩阵。 在线性代数中，以赫尔曼·汉克尔命名的汉克尔矩阵(或称目录矩阵)是一个正方形矩阵，其中从左到右的每条斜对角都是常数。 示例:
输入: n = 4， m[][] = { {1，2，3，5}， {2，3，5，8}， {3，5，8，0}， {5，8，0，9 } }； 输出:是 所有对角线{1}、{2，2}、{3，3，3}、{5，5，5，5}、{8，8，8}、{9}都有常数值。 所以给定的矩阵是汉克尔矩阵。
输入: n = 3， m[][] = { {1，2，3}， {2，3，5}， {3，9，8 } }； 输出:否
注意，一个矩阵要成为汉克尔矩阵，它必须是这样的形式，
a0 a1 a2 a3
a1 a2 a3 a4
a2 a3 a4 a5
a3 a4 a5 a6
因此，为了检查给定的矩阵是否是 Hankel 矩阵，我们需要检查每个 m[i][j] == a i + j 。现在，一个 i + j 可以定义为:
m[i+j][0], if i + j < n
ai + j =
m[i + j - n + 1][n-1], otherwise
下面是上述方法的实现:
C++
// C++ Program to check if given matrix is
// Hankel Matrix or not.
#include <bits/stdc++.h>
using namespace std;
#define N 4
// Function to check if given matrix is Hankel
// Matrix or not.
bool checkHankelMatrix(int n, int m[N][N])
{
// for each row
for (int i = 0; i < n; i++) {
// for each column
for (int j = 0; j < n; j++) {
// checking if i + j is less than n
if (i + j < n) {
// checking if the element is equal to the
// corresponding diagonal constant
if (m[i][j] != m[i + j][0])
return false;
}
else {
// checking if the element is equal to the
// corresponding diagonal constant
if (m[i][j] != m[i + j - n + 1][n - 1])
return false;
}
}
}
return true;
}
// Drivers code
int main()
{
int n = 4;
int m[N][N] = {
{ 1, 2, 3, 5 },
{ 2, 3, 5, 8 },
{ 3, 5, 8, 0 },
{ 5, 8, 0, 9 }
};
checkHankelMatrix(n, m) ? (cout << "Yes")
: (cout << "No");
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to check if given matrix is
// Hankel Matrix or not.
import java.io.*;
import java.util.*;
class GFG {
// Function to check if given matrix
// is Hankel Matrix or not.
static boolean checkHankelMatrix(int n,
int m[][])
{
// for each row
for (int i = 0; i < n; i++) {
// for each column
for (int j = 0; j < n; j++) {
// checking if i + j is less
// than n
if (i + j < n) {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i][j] != m[i + j][0])
return false;
}
else {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i][j] !=
m[i + j - n + 1][n - 1])
return false;
}
}
}
return true;
}
// Drivers code
public static void main(String args[])
{
int n = 4;
int m[][] = {
{ 1, 2, 3, 5 },
{ 2, 3, 5, 8 },
{ 3, 5, 8, 0 },
{ 5, 8, 0, 9 }
};
if(checkHankelMatrix(n, m))
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by Anuj_67.
Python 3
# Python 3 Program to check if given matrix is
# Hankel Matrix or not.
N = 4
# Function to check if given matrix is Hankel
# Matrix or not.
def checkHankelMatrix(n, m):
# for each row
for i in range( 0, n):
# for each column
for j in range( 0, n):
# checking if i + j is less
# than n
if (i + j < n):
# checking if the element is
# equal to the corresponding
# diagonal constant
if (m[i][j] != m[i + j][0]):
return False
else :
# checking if the element is
# equal to the corresponding
# diagonal constant
if (m[i][j] !=
m[i + j - n + 1][n - 1]):
return False
return True
# Drivers code
n = 4
m =[[1, 2, 3, 5,],
[2, 3, 5, 8,],
[3, 5, 8, 0,],
[5, 8, 0, 9]]
(print("Yes") if checkHankelMatrix(n, m)
else print("No"))
# This code is contributed by Smitha.
C
// C# Program to check if given matrix is
// Hankel Matrix or not.
using System;
class GFG {
// Function to check if given matrix
// is Hankel Matrix or not.
static bool checkHankelMatrix(int n,
int [,]m)
{
// for each row
for (int i = 0; i < n; i++) {
// for each column
for (int j = 0; j < n; j++) {
// checking if i + j is less
// than n
if (i + j < n) {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i, j] != m[i + j, 0])
return false;
}
else {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i,j] != m[i + j - n
+ 1, n - 1])
return false;
}
}
}
return true;
}
// Drivers code
public static void Main()
{
int n = 4;
int [,]m = {
{ 1, 2, 3, 5 },
{ 2, 3, 5, 8 },
{ 3, 5, 8, 0 },
{ 5, 8, 0, 9 }
};
if(checkHankelMatrix(n, m))
Console.Write("Yes");
else
Console.Write("No");
}
}
// This code is contributed by Anuj_67.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to check if given matrix is
// Hankel Matrix or not.
$N = 4;
// Function to check if
// given matrix is Hankel
// Matrix or not.
function checkHankelMatrix( $n, $m)
{
// for each row
for($i = 0; $i < $n; $i++) {
// for each column
for ($j = 0;$j < $n; $j++) {
// checking if i + j
// is less than n
if ($i + $j < $n) {
// checking if the element
// is equal to the corresponding
// diagonal constant
if ($m[$i][$j] != $m[$i + $j][0])
return false;
}
else {
// checking if the element
// is equal to the
// corresponding diagonal constant
if ($m[$i][$j] != $m[$i + $j -
$n + 1][$n - 1])
return false;
}
}
}
return true;
}
// Driver code
$n = 4;
$m = array(array( 1, 2, 3, 5 ),
array( 2, 3, 5, 8 ),
array( 3, 5, 8, 0 ),
array( 5, 8, 0, 9 ));
if(checkHankelMatrix($n, $m))
echo "Yes";
else
echo "No";
// This code is contributed by Anuj_67.
?>
java 描述语言
<script>
// Java script Program to check if given matrix is
// Hankel Matrix or not.
// Function to check if given matrix
// is Hankel Matrix or not.
function checkHankelMatrix(n,m)
{
// for each row
for (let i = 0; i < n; i++) {
// for each column
for (let j = 0; j < n; j++) {
// checking if i + j is less
// than n
if (i + j < n) {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i][j] != m[i + j][0])
return false;
}
else {
// checking if the element
// is equal to the
// corresponding diagonal
// constant
if (m[i][j] !=
m[i + j - n + 1][n - 1])
return false;
}
}
}
return true;
}
// Drivers code
let n = 4;
let m = [
[1, 2, 3, 5 ],
[ 2, 3, 5, 8] ,
[ 3, 5, 8, 0 ],
[ 5, 8, 0, 9 ]
];
if(checkHankelMatrix(n, m))
document.write("Yes");
else
document.write("No");
//this code is contributed by mohan pavan pulamolu
</script>
Output
Yes
时间复杂度:O(N2) 辅助空间: O(1)
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