Poj1006 Chinese Residue Theorem

China Remainder Theorem
Example 1: What is the minimum value of A number divided by 3 to 1, 4 to 2, and 5 to 4?
The numbers 3, 4, and 5 are mutually qualitative. Then [4, 5] = 20; [3, 5] = 15; [3, 4] = 12; [3, 4, 5] = 60. In order to divide 20 by 3 to 1, 20 × 2 = 40; so that 15 is divided by 4 to 1, 15 × 3 = 45; so that 12 is divided by 5 to 1, use 12 × 3 = 36. Then, 40 × 1 + 45 × 2 + 36 × 4 = 274, because, 274> 60, so, 274-60 × 4 = 34, is the number of requests.

Example 2: What is the minimum value of A number divided by 3, 2, 7, 4, and 8? The numbers 3, 7, and 8 are mutually qualitative. Then [168] = 56; [] = 24; [] = 21; [, 8] =. In order to divide 56 into 3 and 1, 56 × 2 = 112; make 24 to 7 and 24 × 5 = 120. So that 21 is divided by 8 and 1, 21 × 5 = 105; then, 112 × 2 + 120 × 4 + 105 × 5 = 1229, because, 1229> 168, so, 1229-168x7 = 53, which is the number of requests.

Example 3: divide a number by 5 plus 4, divide by 8 plus 3, and divide by 11 plus 2 to obtain the minimum natural number that meets the conditions. The numbers 5, 8, and 11 are mutually qualitative.
Then [8, 11] = 88; [5, 11] = 55; [5, 8] = 40; [5, 8, 11] = 440. In order to make 88 be divided by 5 and 1, 88 × 2 = 176 is used;
So that 55 is divided by 8 to 1, with 55 × 7 = 385; so that 40 is divided by 11 to 1, with 40 × 8 = 320. Then, 176 × 4 + 385 × 3 + 320 × 2 = 2499. Because, 2499> 440, 2499-440 × 5 = 299 is the desired number.

Example 4: A grade student has five more people in a row per 9 people, one more person in a row per 7 people, and two more people in a row per 5 people, how many people are there in this grade?
(Questions asked by happy 123 teachers) The numbers 9, 7, and 5 are of mutual quality. Then [7, 5] = 35; [9, 5] = 45; [9, 7] = 63;
(9, 7, 5) = 315. In order to divide 35 by 9 to allow 1, 35x8 = 280; 45 is divided by 7 to allow 1, 45x5 = 225; 63 is divided by 5 to allow 1,
Use 63 × 2 = 126. Then, 280 × 5 + 225 × 1 + 126 × 2 = 1877, because, 1877> 315, so, 1877-315 × 5 = 302, is the desired number.

Example 5: There is a grade student. There are 6 more people in each 9-person row. There are 2 more people in each 7-person row, and 3 more people in each 5-person row, how many people are there in this grade?
The numbers 9, 7, and 5 are mutually qualitative. Then [7, 5] = 35; [9, 5] = 45; [9, 7] = 63; [9, 7, 5] = 315. In order to divide 35 by 9 to allow 1, 35x8 = 280; 45 is divided by 7 to allow 1, 45x5 = 225; 63 is divided by 5 to allow 1, use 63 × 2 = 126. Then, 280 × 6 + 225 × 2 + 126 × 3 = 2508, because, 2508> 315, therefore, 2508-315 × 7 = 303 is the desired number. (In Example 5 and in example 4, the divisor is the same, and the remainder is the same. The difference is the last two steps .)

# Include <iostream>
Using namespace STD;
Int main ()
{
Int P, E, I, D, Count = 0;

While (CIN> P> E> I> D, P! =-1)
{
Int day = 21252;
Count ++;
Int A, B, C, x, y, z;

A = P #;
B = E (;
C = I3;

For (Int J = 1; j ++)
{
If (924 * J # = 1)
{
X = 924 * J;
Break;
}
}
For (Int J = 1; j ++)
{
If (759 * j (= 1)
{
Y = 759 * J;
Break;
}
}
For (Int J = 1; j ++)
{
If (644 * J3 = 1)
{
Z = 644 * J;
Break;
}
}
Int S;
S = x * A + y * B + z * C;
Day = s! 252-d;
If (day <= 0)
Day ++ = 21252;
Cout <"case" <count <": The next Triple peak occurs in" <day <"days." <Endl;
}

System ("pause ");
Return 0;
}