DLX數獨建圖:一共9*9*9 = 729行,9*9*4 = 324列。第i行表示數獨的i/81行i/9%9列放置數字i%9。324列分成4個部分,每個部分81列,分別限制每個格子只能放一個數字、每行只能放一種數字、每列只能放一種數字、每個3*3的格子只能放一種數字。
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <algorithm>
#include <iostream>
#include <sstream>
using namespace std;
const int maxn = 3241;
const int inf = 1000000000;
char mtx[729][324];
char sudoku[82];
int N, M, head, idx; // 分別是行數, 列數, 列頭結點鏈表的頭結點, 結點計數器
int L[maxn], R[maxn], U[maxn], D[maxn];
int RH[maxn], CH[maxn], S[maxn]; // RH爲結點的行編號, CH結點的列編號, S爲每列結點數
void InitMtx() {
int i, j, k, t;
memset(mtx, 0, sizeof(mtx));
for (i = 0; i < 9; i++) {
for (j = 0; j < 9; j++) {
t = i * 9 + j;
if (sudoku[t] == '.') {
for (k = 0; k < 9; k++) {
mtx[t*9+k][t] = 1; // (行,列)
mtx[t*9+k][81+i*9+k] = 1; // (行,數)
mtx[t*9+k][162+j*9+k] = 1; // (列,數)
mtx[t*9+k][243+(i/3*3+j/3)*9+k] = 1; // (格,數)
}
} else {
k = sudoku[t] - '1';
mtx[t*9+k][t] = 1; // (行,列)
mtx[t*9+k][81+i*9+k] = 1; // (行,數)
mtx[t*9+k][162+j*9+k] = 1; // (列,數)
mtx[t*9+k][243+(i/3*3+j/3)*9+k] = 1; // (格,數)
}
}
}
}
int Node(int up, int down, int left, int right) {
U[idx] = up; D[idx] = down;
L[idx] = left; R[idx] = right;
D[up] = U[down] = R[left] = L[right] = idx;
return idx++;
}
void Build() {
int i, j, k;
idx = maxn - 1;
head = Node(idx, idx, idx, idx); // 初始化列頭結點鏈表的頭結點
idx = 0;
for (j = 0; j < M; j++) { // 申請M個結點爲每列的頭結點
Node(idx, idx, L[head], head);
CH[j] = j; S[j] = 0;
}
for (i = 0; i < N; i++) {
k = -1;
for (j = 0; j < M; j++) {
if (!mtx[i][j]) continue;
if (k == -1) {
k = Node(U[CH[j]], CH[j], idx, idx);
RH[k] = i; CH[k] = j; S[j]++;
} else {
k = Node(U[CH[j]], CH[j], k, R[k]);
RH[k] = i; CH[k] = j; S[j]++;
}
}
}
}
void Remove(int c) {
int i, j;
L[R[c]] = L[c];
R[L[c]] = R[c];
for (i = D[c]; i != c; i = D[i]) {
for (j = R[i]; j != i; j = R[j]) {
U[D[j]] = U[j];
D[U[j]] = D[j];
S[CH[j]]--;
}
}
}
void Resume(int c) {
int i, j;
R[L[c]] = c;
L[R[c]] = c;
for (i = U[c]; i != c; i = U[i]) {
for (j = L[i]; j != i; j = L[j]) {
S[CH[j]]++;
D[U[j]] = j;
U[D[j]] = j;
}
}
}
int dfs() {
if (R[head] == head)
return 1;
int i, j, k, c, min = inf;
for (j = R[head]; j != head; j = R[j]) {
if (S[j] < min) {
min = S[j];
c = j;
}
}
Remove(c);
for (i = D[c]; i != c; i = D[i]) {
k = RH[i];
sudoku[k/9] = '1' + k % 9;
for (j = R[i]; j != i; j = R[j])
Remove(CH[j]);
if (dfs()) return 1;
for (j = L[i]; j != i; j = L[j])
Resume(CH[j]);
}
Resume(c);
return 0;
}
int main() {
N = 729, M = 324;
while (gets(sudoku), strcmp(sudoku, "end")) {
InitMtx();
Build();
dfs();
printf("%s\n", sudoku);
}
return 0;
}