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廖增祥 [专家分：3930] 发布于 2008-12-18 20:36:00
[b]1、破解某论坛管理员的密码[/b]
题目描述:
将数字1-9填入以下九宫格，要求每行每列及每个小方格(共九个)均为1-9，不能重复出现，
管理员密码的后九位就在第五行。要求编程解出其值。
输入: 无
输出: 标准输出，输出这九个整数，每个数字占一行
[center][img]http://www.hxcxit.com/Lory/1.png[/img][/center]
[b]2、Lagrange’s Four-Square Theorem[/b]
Input: lagrange.txt
The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.
For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 4^2 + 3^2 and 3^2 + 4^2 are the same representation.
For example, let’s check the case of 25. This integer has just three representations 1^2+2^2+2^2+4^2, 3^2 + 4^2, and 5^2. Thus you should report 3 in this case. Be careful not to count 4^2 + 3^2 and 3^2 + 4^2 separately.
[b]Input[/b]
The input is composed of at most 255 lines, each containing a single positive integer less than 2^15, followed by a line containing a single zero. The last line is not a part of the input data.
[b]Output[/b]
The output should be composed of lines, each containing a single integer. No other characters
should appear in the output.
The output integer corresponding to the input integer n is the number of all representations
of n as the sum of at most four positive squares.
[b]Sample Input[/b]
1
25
2003
211
20007
0
[b]Output for the Sample Input[/b]
1
3
48
7
738
[color=800080]开始时间: 2008-12-18 20:30:00
结束时间: 2008-12-26 20:30:00
第二题为选做，是我和同学以前做的 Acm 练习题，希望大家都能参与到其中来。[/color]
题目描述:
将数字1-9填入以下九宫格，要求每行每列及每个小方格(共九个)均为1-9，不能重复出现，
管理员密码的后九位就在第五行。要求编程解出其值。
输入: 无
输出: 标准输出，输出这九个整数，每个数字占一行
[center][img]http://www.hxcxit.com/Lory/1.png[/img][/center]
[b]2、Lagrange’s Four-Square Theorem[/b]
Input: lagrange.txt
The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.
For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 4^2 + 3^2 and 3^2 + 4^2 are the same representation.
For example, let’s check the case of 25. This integer has just three representations 1^2+2^2+2^2+4^2, 3^2 + 4^2, and 5^2. Thus you should report 3 in this case. Be careful not to count 4^2 + 3^2 and 3^2 + 4^2 separately.
[b]Input[/b]
The input is composed of at most 255 lines, each containing a single positive integer less than 2^15, followed by a line containing a single zero. The last line is not a part of the input data.
[b]Output[/b]
The output should be composed of lines, each containing a single integer. No other characters
should appear in the output.
The output integer corresponding to the input integer n is the number of all representations
of n as the sum of at most four positive squares.
[b]Sample Input[/b]
1
25
2003
211
20007
0
[b]Output for the Sample Input[/b]
1
3
48
7
738
[color=800080]开始时间: 2008-12-18 20:30:00
结束时间: 2008-12-26 20:30:00
第二题为选做，是我和同学以前做的 Acm 练习题，希望大家都能参与到其中来。[/color]
