优先推理，无法确定的情况下找分支最少的一个去猜，并把当前状态保存，以备将来回溯。
#include <cstdio>#include <cstring>#include <cassert>#include <vector>#include <algorithm>using namespace std;struct Node
{
char str[9][10]; char used[27][10]; int rest; int lastx, lasty; int dup; Node():dup(0)
{
} struct Place { Place(int _x, int _y):x(_x), y(_y){} int x, y; bool operator < (const Place &o) const { return x + y * 3 < o.x + o.y * 3; } }; vector< Place > validplace[27][9]; bool operator < (const Node &o) const { if (rest == o.rest) return dup < o.dup; return rest < o.rest; } struct Index { Index(int _i, int _k, int _size):i(_i), k(_k), size(_size){} int i, k, size; vector<Node> ns; bool operator < (const Index &o) const { return size < o.size; } void sortnode() { sort(ns.begin(), ns.end()); } }; void buildinfo() { int i, j; memset(used, 0, sizeof(used)); rest = 0; for (i = 0; i < 9; i++) { for (j = 0; j < 9; j++) { if (str[i][j] == '0') rest++, str[i][j] = 0; else { str[i][j] -= '0'; assert(used[i][str[i][j]] == 0 && used[j + 9][str[i][j]] == 0 && used[i/3 + j/3*3 + 18][str[i][j]] == 0); used[i][str[i][j]] = 1; used[j + 9][str[i][j]] = 1; used[i/3 + j/3*3 + 18][str[i][j]] = 1; } } } lastx = lasty = -1; } void guess(int i, int j, int k) { assert(str[i][j] == 0); str[i][j] = k; lastx = i; lasty = j; assert(used[i][k] == 0 && used[j + 9][k] == 0 && used[i/3 + j/3*3 + 18][k] == 0); used[i][k] = 1; used[j + 9][k] = 1; used[i/3 + j/3*3 + 18][k] = 1; rest--; } void discursion() { int i, j, k; bool change; // 先进行充分的严格推理 do { change = false; for (i = 0; i < 27; i++) { for (j = 0; j < 9; j++) validplace[i][j].clear(); } for (i = 0; i < 9; i++) { for (j = 0; j < 9; j++) { if (str[i][j]) continue; for (k = 1; k <= 9; k++) { if (used[i][k] || used[j+9][k] || used[i/3 + j/3*3 + 18][k]) continue; validplace[i][k-1].push_back(Place(i, j)); validplace[j+9][k-1].push_back(Place(i, j)); validplace[i/3 + j/3*3 + 18][k-1].push_back(Place(i, j)); } } } for (i = 0; i < 27; i++) { for (k = 1; k <= 9; k++) { if (validplace[i][k - 1].size() != 1) continue; const Place &p = validplace[i][k - 1].front(); guess(p.x, p.y, k); change = true;#ifdef _DEBUG //show();#endif goto End; } } End: ; }while(change && rest); } void solve() { discursion(); if (rest == 0) return; int i, k; //选择分支最少的情况优先进行猜测 vector<Index> best; vector<Node> nextNodes; for (i = 0; i < 27; i++) { for (k = 1; k <= 9; k++) { if (!validplace[i][k - 1].empty()) { //Index idx(i, k, validplace[i][k - 1].size()); for (int t = 0; t < validplace[i][k - 1].size(); t++) { const Place &p = validplace[i][k - 1][t]; Node o2(*this); o2.guess(p.x, p.y, k); o2.discursion(); //idx.ns.push_back(o2); o2.dup = validplace[i][k - 1].size(); nextNodes.push_back(o2); //idx.rest += o2.rest; } //idx.sortnode(); //best.push_back(idx); } } } //sort(best.begin(), best.end()); sort(nextNodes.begin(), nextNodes.end()); //for (vector<Index>::iterator id = best.begin(); id != best.end(); ++id) for (vector<Node>::iterator nd = nextNodes.begin(); nd != nextNodes.end(); ++nd) { //for (int i = 0; i < id->size; i++) { //Node &o2 = id->ns[i]; Node &o2 = *nd; o2.solve(); if (o2.rest == 0) { *this = o2; return; } } } } void show() const { int i, j; printf("rest %d\n", rest); for (i = 0; i < 9; i++) { for (j = 0; j < 9; j++) { if (str[i][j]) { if (i == lastx && j == lasty) printf("-%d-", str[i][j]); else printf(" %d ", str[i][j]); } else printf(" "); } printf("\n"); } //system("pause"); }
};int main(){ Node n; int i, j;#if 0 for (i = 0; i < 9; i++) { scanf("%s", n.str[i]); assert(strlen(n.str[i]) == 9); for (j = 0; j < 9; j++) { assert(n.str[i][j] >= '0' && n.str[i][j] <= '9'); } } n.buildinfo(); n.show(); n.discursion(); if (n.rest == 0) n.show();#else char buf[9*9+1]; while(scanf("%s", buf) == 1 && buf[0] != 'e') { for (i = 0; i < 9; i++) { for (j = 0; j < 9; j++) { n.str[i][j] = buf[i*9+j]; if (n.str[i][j] == '.') n.str[i][j] = '0'; } } n.buildinfo(); //n.show(); n.solve(); //n.show(); for (i = 0; i < 9; i++) { for (j = 0; j < 9; j++) { buf[i*9+j] = n.str[i][j] + '0'; } } buf[81] = 0; printf("%s\n", buf); }#endif return 0;}