Zoj 3656 bit magic (2-Sat judgment)

[Question link]

Http://acm.zju.edu.cn/onlinejudge/showProblem.do? Problemcode = 3656.

[Topic]

Assume that an array a [n] is known, use the following function to generate a matrix B:

void calculate(int a[N], int b[N][N]) {for (int i = 0; i < N; ++i) {for (int j = 0; j < N; ++j) {if (i == j) b[i][j] = 0;else if (i % 2 == 1 && j % 2 == 1) b[i][j] = a[i] | a[j];else if (i % 2 == 0 && j % 2 == 0) b[i][j] = a[i] & a[j];else b[i][j] = a[i] ^ a[j];}}}

If a matrix B is known, can array a be converted to matrix B?

[Analysis]

This is actually an enhanced version of poj 3678 Katu puzzle.

Poj3678 each number can only be 0 or 1, equivalent to a binary integer with only one digit.

The range of each number in this question is 0 ≤ B [I] [J] ≤ 2 ^ 31-1, which is equivalent to a 31-bit integer in the binary system, perform a 2-Sat judgment on each binary!

[Code]

# Include <iostream> # include <cstdio> # include <cstring> using namespace STD; typedef long int64; const int maxn = 610; const int VN = maxn * 62; const int en = 2000010; int N; int mat [maxn] [maxn]; struct graph {int size; int head [VN]; struct edge {int V, next ;} E [En]; void Init () {size = 0; memset (Head,-1, sizeof (head);} void addedge (int u, int V) {e [size]. V = V; E [size]. next = head [u]; head [u] = size ++ ;}} G; Class two_sat {public: bool check (const graph & G, const int N) {SCC (G, n); For (INT I = 0; I <n; ++ I) if (belong [I * 2] = belong [I * 2 + 1]) return false; return true;} PRIVATE: void Tarjan (const graph & G, const int U) {int V; dfn [u] = low [u] = ++ idx; STA [top ++] = u; instack [u] = true; For (int e = G. head [u]; e! =-1; E = G. E [e]. next) {v = G. E [e]. v; If (dfn [v] =-1) {Tarjan (G, V); low [u] = min (low [u], low [v]);} else if (instack [v]) {LOW [u] = min (low [u], dfn [v]);} if (low [u] = dfn [u]) {++ bcnt; do {v = sta [-- top]; instack [v] = false; belong [v] = bcnt;} while (u! = V) ;}} void SCC (const graph & G, const int N) {Top = idx = bcnt = 0; memset (dfn,-1, sizeof (dfn )); memset (instack, 0, sizeof (instack); For (INT I = 0; I <2 * n; ++ I) if (dfn [I] =-1) tarjan (G, I);} PRIVATE: int top, idx, bcnt; int dfn [VN]; int low [VN]; int sta [VN]; int belong [VN]; bool instack [VN];} sat; bool OK () {for (INT I = 0; I <n; ++ I) {If (MAT [I] [I]! = 0) return false; For (Int J = I + 1; j <n; ++ J) if (MAT [I] [J]! = Mat [J] [I]) return false;} return true;} bool judge () {// enumerated binary bits for (int K = 0; k <31; ++ K) {G. init (); For (INT I = 0; I <n; ++ I) {for (Int J = I + 1; j <n; ++ J) {int u = I, V = J, W = (MAT [I] [J]> K) & 1; if (I % 2 = 0 & J % 2 = 0) {If (w) {G. addedge (u * 2, V * 2 + 1), G. addedge (V * 2, u * 2 + 1); // 0, 0g. addedge (u * 2, V * 2), G. addedge (V * 2 + 1, u * 2 + 1); // 0, 1g. addedge (u * 2 + 1, V * 2 + 1), G. addedge (V * 2, u * 2); // 1, 0} else {G. addedge (u * 2 + 1, V * 2), G. addedge (V * 2 + 1, u * 2); // 1, 1} else if (I % 2 = 1 & J % 2 = 1) {If (w) {G. addedge (u * 2, V * 2 + 1), G. addedge (V * 2, u * 2 + 1); // 0, 0} else {G. addedge (u * 2, V * 2), G. addedge (V * 2 + 1, u * 2 + 1); // 0, 1g. addedge (u * 2 + 1, V * 2 + 1), G. addedge (V * 2, u * 2); // 1, 0g. addedge (u * 2 + 1, V * 2), G. addedge (V * 2 + 1, u * 2); // 1, 1} else {// XOR if (w) {G. addedge (u * 2, V * 2 + 1), G. addedge (V * 2, u * 2 + 1); // 0, 0g. addedge (u * 2 + 1, V * 2), G. added Ge (V * 2 + 1, u * 2); // 1, 1} else {G. addedge (u * 2, V * 2), G. addedge (V * 2 + 1, u * 2 + 1); // 0, 1g. addedge (u * 2 + 1, V * 2 + 1), G. addedge (V * 2, u * 2); // 1, 0 }}} if (! Sat. Check (G, n) return false;} return true;} int main () {While (~ Scanf ("% d", & N) {G. init (); bool flag = true; For (INT I = 0; I <n; ++ I) for (Int J = 0; j <n; ++ J) scanf ("% d", & mat [I] [J]); If (! OK () {puts ("no"); continue;} If (Judge () puts ("yes"); else puts ("no ");} return 0 ;}