Created nqueensproblem.c

nqueensproblem.c

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+// The n queens puzzle.
+#include <stdio.h>
+#include <string.h>
+#include <stdbool.h>
+#include <stdlib.h>
+
+// Store the puzzle (problem) size and the number of valid solutions.
+typedef struct {
+    int size;
+    int solutions;
+} NQueens;
+
+// Show the queens positions on the board in compressed form,
+// each number represent the occupied column position in the corresponding row.
+void show_short_board(NQueens *nqueens, int *positions) {
+    for(int i = 0; i < nqueens->size; ++i) {
+        printf("%d ", positions[i]);
+    }
+    printf("\n");
+}
+
+// Show the full NxN board
+void show_full_board(NQueens *nqueens, int *positions) {
+    for(int row = 0; row < nqueens->size; ++row) {
+        for(int column = 0; column < nqueens->size; ++column) {
+            if(positions[row] == column) {
+                printf("Q ");
+            } else {
+                printf(". ");
+            }
+        }
+        printf("\n");
+    }
+    printf("\n");
+}
+
+// Check if a given position is under attack from any of
+// the previously placed queens (check column and diagonal positions)
+bool check_place(int *positions, int ocuppied_rows, int column) {
+    for(int i = 0; i < ocuppied_rows; ++i) {
+        if(positions[i] == column || positions[i] - i == column - ocuppied_rows || positions[i] + i == column + ocuppied_rows) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// Try to place a queen on target_row by checking all N possible cases.
+// If a valid place is found the function calls itself trying to place a queen
+// on the next row until all N queens are placed on the NxN board.
+void put_queen(NQueens *nqueens, int *positions, int target_row) {
+    // Base (stop) case - all N rows are occupied
+    if(target_row == nqueens->size) {
+        // show_short_board(nqueens, positions);
+        show_full_board(nqueens, positions);
+        nqueens->solutions++;
+    } else {
+        // For all N columns positions try to place a queen
+        for(int column = 0; column < nqueens->size; ++column) {
+            // Reject all invalid positions
+            if(check_place(positions, target_row, column)) {
+                positions[target_row] = column;
+                put_queen(nqueens, positions, target_row + 1);
+            }
+        }
+    }
+}
+
+// Solve the n queens puzzle and print the number of solutions
+void solve(NQueens *nqueens) {
+    int *positions = malloc(nqueens->size * sizeof(int));
+    memset(positions, ~0, nqueens->size * sizeof(int));
+    put_queen(nqueens, positions, 0);
+    printf("Found %d solutions\n", nqueens->solutions);
+    free(positions);
+}
+
+int main(void) {
+    NQueens nqueens = {.size = 8};
+    solve(&nqueens);
+    return 0;
+}