Sum of Square Numbers

本文介绍了一种算法,用于判断是否存在两个整数a和b,使得它们的平方和等于给定的非负整数c。通过计算从0到sqrt(c)之间的所有可能组合来寻找答案。

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题目描述:

Given a non-negative integer c, your task is to decide whether there're two integers a and b such that a2 + b2 = c.

Example 1:

Input: 5
Output: True
Explanation: 1 * 1 + 2 * 2 = 5

Example 2:

Input: 3
Output: False

思路:

int x=sqrt(c);
    int start=0;
    int end=x;
    计算 start的平方+end的平方 num
    如果 num>c,end减1
    如果 num<c,start加1
    直到num==c或者start>end


代码:

  bool judgeSquareSum(int c) {
        if (c<0)
            return false;
        int x=sqrt(c);
        int begin=0;
        int end=x;
        while(begin<=end)
        {
            int sum=begin*begin+end*end;
            if (sum==c)
                return true;
            if (sum>c)
                end=end-1;
            else if (sum<c)
                begin=begin+1;
        }
        return false;
    }

用C语言解决下列问题:Kirill wants to weave the very beautiful blanket consisting of n×m of the same size square patches of some colors. He matched some non-negative integer to each color. Thus, in our problem, the blanket can be considered a B matrix of size n×m consisting of non-negative integers. Kirill considers that the blanket is very beautiful, if for each submatrix A of size 4×4 of the matrix B is true: A11⊕A12⊕A21⊕A22=A33⊕A34⊕A43⊕A44, A13⊕A14⊕A23⊕A24=A31⊕A32⊕A41⊕A42, where ⊕ means bitwise exclusive OR Kirill asks you to help her weave a very beautiful blanket, and as colorful as possible! He gives you two integers n and m . Your task is to generate a matrix B of size n×m , which corresponds to a very beautiful blanket and in which the number of different numbers maximized. Input The first line of input data contains one integer number t (1≤t≤1000 ) — the number of test cases. The single line of each test case contains two integers n and m (4≤n,m≤200) — the size of matrix B . It is guaranteed that the sum of n⋅m does not exceed 2⋅105 . Output For each test case, in first line output one integer cnt (1≤cnt≤n⋅m) — the maximum number of different numbers in the matrix. Then output the matrix B (0≤Bij<263) of size n×m . If there are several correct matrices, it is allowed to output any one. It can be shown that if there exists a matrix with an optimal number of distinct numbers, then there exists among suitable matrices such a B that (0≤Bij<263) .
03-10
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