I believe there is a logical math problem with my code, but I cannot put my finger where is it and why

This my code and when i try to test the difference for input of 100 i get 24501794 instead of 25164150, here is my code:

class DifferenceOfSquaresCalculator {

    

    int computeSquareOfSumTo(int input) {
        int sumOfNatural = 0;
        int sumOfNaturalSquared = 0;
        for (int i = 1; i < input; i++){
            sumOfNatural+=i;
        }
        sumOfNaturalSquared = (int) Math.pow(sumOfNatural,2);
        return sumOfNaturalSquared;
    }

    int computeSumOfSquaresTo(int input) {
        int sumOfSquaredNaturals = 0;
        for (int i = 1; i < input; i++){
            i = (int) Math.pow(i, 2);
            sumOfSquaredNaturals+=i;
        }
        return sumOfSquaredNaturals;
    }

    int computeDifferenceOfSquares(int input) {
        int difference = computeSquareOfSumTo(input) - computeSumOfSquaresTo(input);

        return difference;
    }

}


</details>


# 答案1
**得分**: 1

你的代码存在两个问题。

首先，你在计算序列时不包括最后一个数字：

```for (int i = 1; i &lt; input; i++)```
应该改成
```for (int i = 1; i &lt;= input; i++)```

其次，在你的 `computeSumOfSquaresTo` 中，你在循环内部改变了循环变量 `i`。可以尝试以下修改：

int computeSumOfSquaresTo(int input) {
int sumOfSquaredNaturals = 0;
for (int i = 1; i <= input; i++) {
sumOfSquaredNaturals += i * i;
}
return sumOfSquaredNaturals;
}

你还可以使用更简单的方法，使用 StreamAPI：

int computeSquareOfSum(int input) {
int sum = IntStream.rangeClosed(1, input).sum();
return sum * sum;
}

int computeSumOfSquares(int input) {
return IntStream.rangeClosed(1, input).map(i -> i*i).sum();
}

或者，你可以使用一个函数来实现相同的结果：

int computeDifferenceOfSquares(int input) {
int sum = IntStream.rangeClosed(1, input).sum();
int sumOfSquares = IntStream.rangeClosed(1, input).map(i -> i * i).sum();
return sum * sum - sumOfSquares;
}

<details>
<summary>英文:</summary>

You have two problems with this code. 

At first, you count the series excluding the last number:

```for (int i = 1; i &lt; input; i++)```
should be
```for (int i = 1; i &lt;= input; i++)```

At second, in your `computeSumOfSquaresTo` you are changing the loop variable `i` inside the loop. 
Try this instead:

int computeSumOfSquaresTo(int input) {
int sumOfSquaredNaturals = 0;
for (int i = 1; i <= input; i++) {
sumOfSquaredNaturals += i * i;
}
return sumOfSquaredNaturals;
}

You can also use a simpler approach using StreamAPI:

int computeSquareOfSum(int input) {
int sum = IntStream.rangeClosed(1, input).sum();
return sum * sum;
}

int computeSumOfSquares(int input) {
return IntStream.rangeClosed(1, input).map(i -> i*i).sum();
}

or, with same result, you may use just one function:

int computeDifferenceOfSquares(int input) {
int sum = IntStream.rangeClosed(1, input).sum();
int sumOfSquares = IntStream.rangeClosed(1, input).map(i -> i * i).sum();
return sum * sum - sumOfSquares;
}

</details>