Poj 2115 C looooops (solving model linear equation)

Link: poj 2115

C-language cyclic statements for (I = A; I! = B; I + = C ),

Q: How many times does it end in a K-bit storage system.

If it ends within a limited period of time, the number of loops is output; otherwise, the endless loop is output.

Note: The data features of the K-bit storage system are used for loop (overflow)

For example, if the int type is 16 bits, the int type can store 2 ^ 16 data records,

That is, the maximum number is 65535 (the default value is unsigned ),

When the loop causes I to exceed 65535, I will return 0 and start counting again.

If I = 65534, When I + = 3, I = 1 that is, I = (65534 + 3) % (2 ^ 16) = 1

Analysis: if a group of data needs to be cyclically completed X times, the following equation is available:

X = [(B-A + 2 ^ K) % 2 ^ K]/C

That is, Cx = (B-A) (mod 2 ^ K) This equation is a model linear equation, This is the value of X.

That is, modulus linear equation.Ax = B mod n. Where a = C, B = B-A, n = 2 ^ K.

The sufficient and required conditions for the equation to be resolved are gcd (A, n) | B, that is, B % gcd (A, n) = 0.

So that D = gcd (A, n) has the smallest integer of this equation and returns X0 = x (mod n/D)

X is an arbitrary solution, and x0 is the smallest integer solution.

# Include <stdio. h >__ int64 exgcd (_ int64 A ,__ int64 B ,__ int64 & X ,__ int64 & Y) // Extended Euclidean {_ int64 T, D; if (B = 0) {x = 1; y = 0; return a;} d = exgcd (B, A % B, x, y); t = X; X = y; y = T-A/B * Y; return D;} int main () {_ int64 A, B, C, K, A, B, n, d, X, Y; while (scanf ("% i64d % i64d % i64d % i64d", & A, & B, & C, & K )! = EOF) {if (a = 0 & B = 0 & C = 0 & K = 0) break; A = C; B = B-A; N = (_ int64) 1 <K; // 1 to convert to 64-bit D = exgcd (A, n, x, y); If (B % d) {// If the equation has no solution, printf ("Forever \ n"); continue;} X = x * (B/d) % N; X = (X % (n/D) + (n/D) % (n/d); // returns the smallest positive solution printf ("% i64d \ n ", x);} return 0 ;}

Poj 2115 C looooops (solving model linear equation)