50022. Matrix
難度：4.5/5
backtracking的技術還要再改進，寫了100多行，之後看Morris的code來改進。
Second Try: 3.5/5 Used Time: 20:24 (used 79 lines)1
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109#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
int m, n;
int max_num;
int r[16], c[16];
int board[16][16];
int used_cnt;
bool used[17] = {false};
bool check_row(int row_num){
int sum = 0;
for(int i = 0; i < n; i++){
sum += board[row_num][i];
}
return sum == r[row_num];
}
bool check_col(int col_num){
int sum = 0;
for(int i = 0; i < m; i++){
sum += board[i][col_num];
}
return sum == c[col_num];
}
bool board_filled(){
for(int i = 0; i < m; i++) for(int j = 0; j < n; j++){
if(board[i][j] == 0) return false;
}
return true;
}
bool board_is_valid(){
for(int i = 0; i < m; i++){
if(check_row(i) == false) return false;
}
for(int i = 0; i < n; i++){
if(check_col(i) == false) return false;
}
return true;
}
int find_next_cell(){
for(int i = 0; i < m; i++) for(int j = 0; j < n; j++){
if(board[i][j] == 0) return i * n + j;
}
return -1;
}
void print_line(int row_num){
printf("%d", board[row_num][0]);
for(int i = 1; i < n; i++) printf(" %d", board[row_num][i]);
printf("\n");
}
void print_board(){
for(int i = 0; i < m; i++) print_line(i);
}
bool solve(){
if(board_filled() == true){
if(board_is_valid() == true) return true;
else return false;
}
else{
int tmp = find_next_cell();
int next_cell_x = tmp / n, next_cell_y = tmp % n;
// pruning
if(next_cell_x == m - 1 && next_cell_y != 0){
if(check_col(next_cell_y - 1) == false) return false;
}
else if(next_cell_x > 0 && next_cell_y == 0){
if(check_row(next_cell_x - 1) == false) return false;
}
for(int i = 1; i <= max_num; i++){
if(used[i] == true) continue;
board[next_cell_x][next_cell_y] = i;
used[i] = true;
if(solve() == true) return true;
board[next_cell_x][next_cell_y] = 0;
used[i] = false;
}
board[next_cell_x][next_cell_y] = 0;
return false;
}
}
int main(){
while(scanf("%d %d", &m, &n) != EOF){
max_num = m * n;
for(int i = 0; i < m; i++) scanf("%d", &r[i]);
for(int i = 0; i < n; i++) scanf("%d", &c[i]);
used_cnt = 0;
for(int i = 1; i <= max_num; i++) used[i] = false;
for(int i = 0; i < m; i++) for(int j = 0; j < n; j++) board[i][j] = 0;
if(solve()){
print_board();
}
else{
printf("no solution\n");
}
}
}