用0至9这10个数字组成一位数、两位数、三位数、四位数各一个,使它们都是非零的完全平方数.例如1,36,784,9025就是满足条件的一种分法,用matlab输出所有符合要求的数
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要找到由0到9这10个数字组成的每一位上都为非零的完全平方数,我们需要遍历所有的可能组合。对于一位数,这是从1到9;对于两位数,是从10到99;三位数是从100到999;四位数是从1000到9999。然后检查每个数是否是完全平方数。
以下是一个简单的Matlab代码片段,用于生成并检查这些数字:
```matlab
function isPerfectSquare = checkPerfectSquares()
% Define the ranges of numbers to check
oneDigitRange = 1:9;
twoDigitRange = 10:99;
threeDigitRange = 100:999;
fourDigitRange = 1000:9999;
% Initialize an empty cell array to store perfect squares
perfectSquares = {};
% Check each range for perfect squares
for i = 1:length(oneDigitRange)
num = oneDigitRange(i);
if isqrt(num)^2 == num
perfectSquares{end+1} = num;
end
end
for i = 1:length(twoDigitRange)
num = twoDigitRange(i);
if isqrt(num)^2 == num
perfectSquares{end+1} = num;
end
end
for i = 1:length(threeDigitRange)
num = threeDigitRange(i);
if isqrt(num)^2 == num
perfectSquares{end+1} = num;
end
end
for i = 1:length(fourDigitRange)
num = fourDigitRange(i);
if isqrt(num)^2 == num
perfectSquares{end+1} = num;
end
end
% Display the perfect squares
disp(perfectSquares);
% Function to check if a number is a perfect square using sqrt() function with round-off
function isSquare = isqrt(n)
isSquare = floor(sqrt(double(n)))^2 == n;
end
end
```
运行这个`checkPerfectSquares()`函数后,Matlab将会输出所有符合条件的一位数、两位数、三位数和四位数完全平方数。
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