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6.28数论测试
(hao.cpp/c/pas)
【问题描述】
从1− N中找一些数乘起来使得答案是一个完全平方数，求这个完全平方数
最大可能是多少。
【输入格式】
第一行一个数字N。
【输出格式】
一行一个整数代表答案对100000007取模之后的答案。
【样例输入】
7
【样例输出】
144
【样例解释】
但是塔外面有东西。
【数据规模与约定】
对于20%的数据，\begin{equation*}1\leq N\leq 100 \end{equation*}。
对于50%的数据，\begin{equation*}1\leq N\leq 5000 \end{equation*}。
对于70%的数据，\begin{equation*}1\leq N\leq 10^5 \end{equation*}。
对于100%的数据，\begin{equation*}1\leq N\leq 5\times 10^6 \end{equation*}。
思路分析：
1.完全平方数的性质：
\begin{equation*}对于任意完全平方数n，总能写成n=a^b\cdot c^d\cdot\cdots y^z(a, c, f, \cdots , y均为质数，b, d, e, \cdots , z 均为偶数)的形式.\end{equation*}
AC代码：
1 #include<cstdio> 2 #define _____________ 5000000 3 #define ____________ 100000007 4 #define _____________________ for 5 #define ______________________ while 6 #define _______________________ if 7 #define ________________________ return 8 #define _________________________ main 9 #define __________________________ freopen 10 #define ___________________________ "hao.in" 11 #define ____________________________ "r" 12 #define _____________________________ stdin 13 #define ______________________________ "hao.out" 14 #define _______________________________ "w" 15 #define ________________________________ stdout 16 #define _________________________________ scanf 17 #define __________________________________ printf 18 #define ___________________________________ "%d" 19 #define ____________________________________ { 20 #define _____________________________________ } 21 #define ______________________________________ , 22 #define _______________________________________ ; 23 #define ________________________________________ [ 24 #define _________________________________________ ] 25 #define __________________________________________ ( 26 #define ___________________________________________ = 27 #define ____________________________________________ ) 28 #define _____________________________________________ 1 29 #define ______________________________________________ ++ 30 #define _______________________________________________ 2 31 #define ________________________________________________ * 32 #define _________________________________________________ % 33 #define __________________________________________________ & 34 #define ___________________________________________________ / 35 #define ____________________________________________________ <= 36 #define _____________________________________________________ += 37 #define ______________________________________________________ >>= 38 #define _______________________________________________________ + 39 #define ________________________________________________________ /= 40 #define _________________________________________________________ 0 41 #define __________________________________________________________ ! 42 #define ___________________________________________________________ long 43 #define ____________________________________________________________ typedef 44 #define _____________________________________________________________ int 45 #define ______________________________________________________________ void 46 #define _______________________________________________________________ using 47 #define ________________________________________________________________ namespace 48 #define _________________________________________________________________ std 49 #define __________________________________________________________________ += 50 _______________________________________________________________ ________________________________________________________________ _________________________________________________________________ _______________________________________ 51 ____________________________________________________________ ___________________________________________________________ ___________________________________________________________ ____________________ _______________________________________ 52 ____________________________________________________________ _____________________________________________________________ ___________________ _______________________________________ 53 ____________________________________________________________ ______________________________________________________________ __________________ _______________________________________ 54 ___________________ _________ ______________________________________ ___ _______________________________________ 55 ___________________ ____ ________________________________________ _____________ _________________________________________ _______________________________________ 56 ___________________ _ ________________________________________ _____________ _________________________________________ _______________________________________ 57 ___________________ ___________ ________________________________________ _____________ _________________________________________ _______________________________________ 58 ____________________ _____ ___________________________________________ _____________________________________________ _______________________________________ 59 __________________ ______ __________________________________________ ____________________________________________ 60 ____________________________________ 61 _____________________ __________________________________________ ___________________ _______ ___________________________________________ _______________________________________________ _______________________________________ _______ ____________________________________________________ _________ _______________________________________ _______ ______________________________________________ ____________________________________________ 62 _______________________ __________________________________________ __________________________________________________________ ____ ________________________________________ _______ _________________________________________ ____________________________________________ 63 ____________________________________ 64 _ ________________________________________ ______________________________________________ ___ _________________________________________ ___________________________________________ _______ _______________________________________ 65 _____________________ __________________________________________ ___________________ ________ ___________________________________________ _______ _______________________________________________________ _______ _______________________________________ ________ ____________________________________________________ _________ _______________________________________ ________ __________________________________________________________________ _______ ____________________________________________ 66 ____ ________________________________________ ________ _________________________________________ ___________________________________________ _____________________________________________ _______________________________________ 67 _____________________________________ 68 _____________________________________ 69 __________________ ______________ __________________________________________ ____________________________________________ 70 ____________________________________ 71 _____________________ __________________________________________ ___________________ _______ ___________________________________________ _____________________________________________ _______________________________________ _______ ____________________________________________________ ___ _______________________________________ _______ ______________________________________________ ____________________________________________ 72 ____________________________________ 73 ____________________ __________ ___________________________________________ _________ _______________________________________ 74 ______________________ __________________________________________ __________ ____________________________________________ 75 ____________________________________ 76 ___________ ________________________________________ _______ _________________________________________ _____________________________________________________ __________ ___________________________________________________ _ ________________________________________ _______ _________________________________________ _______________________________________ 77 __________ ________________________________________________________ _ ________________________________________ _______ _________________________________________ _______________________________________ 78 _____________________________________ 79 _____________________________________ 80 _____________________________________ 81 ____________________ _______________ __________________________________________ ____________________ _ ______________________________________ ____________________ __ ____________________________________________ 82 ____________________________________ 83 ____________________ __________ ___________________________________________ _____________________________________________ _______________________________________ 84 ______________________ __________________________________________ __ ____________________________________________ 85 ____________________________________ 86 _______________________ __________________________________________ __ __________________________________________________ _____________________________________________ ____________________________________________ 87 __________ ___________________________________________ __________ ________________________________________________ _ _________________________________________________ ____________ _______________________________________ 88 _ ___________________________________________ _ ________________________________________________ _ _________________________________________________ ____________ _______________________________________ 89 __ ______________________________________________________ _____________________________________________ _______________________________________ 90 _____________________________________ 91 ________________________ __________ _________________________________________________ ____________ _______________________________________ 92 _____________________________________ 93 ___________________ _________________________ __________________________________________ ____________________________________________ 94 ____________________________________ 95 __________________________ __________________________________________ ___________________________ ______________________________________ ____________________________ ______________________________________ _____________________________ ____________________________________________ _______________________________________ 96 __________________________ __________________________________________ ______________________________ ______________________________________ _______________________________ ______________________________________ ________________________________ ____________________________________________ _______________________________________ 97 _________________________________ __________________________________________ ___________________________________ ______________________________________ __________________________________________________ _________ ____________________________________________ _______________________________________ 98 ______ __________________________________________ ____________________________________________ _______________________________________ 99 ______________ __________________________________________ ____________________________________________ _______________________________________100 _____________________ __________________________________________ ___________________ _______ ___________________________________________ _____________________________________________ _______________________________________ _______ ____________________________________________________ ___ _______________________________________ _______ ______________________________________________ ____________________________________________101 _____ ___________________________________________ __________________________________________ _____ ________________________________________________ _______________ __________________________________________ _ ________________________________________ _______ _________________________________________ ______________________________________ ___________ ________________________________________ _______ _________________________________________ ___________________________________________________ _______________________________________________ ________________________________________________ _______________________________________________ ____________________________________________ _________________________________________________ ____________ ____________________________________________ _________________________________________________ ____________ _______________________________________102 __________________________________ __________________________________________ ___________________________________ ______________________________________ _____ ____________________________________________ _______________________________________103 ________________________ _________________________________________________________ _______________________________________104 _____________________________________
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6.28数论测试
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