Added backtracking solution for N-Queens (LeetCode 51) using just C language

leetcode/src/51.c

@@ -0,0 +1,97 @@
+/**
+ * Return an array of arrays of size *returnSize.
+ * The sizes of the arrays are returned as *returnColumnSizes array.
+ * Note: Both returned array and *columnSizes array must be malloced, assume
+ * caller calls free().
+ */
+bool isSafe(char** board, int row, int col, int n)
+{
+    int r, c;
+
+    // upper-left diagonal
+    r = row;
+    c = col;
+    while (r >= 0 && c >= 0)
+    {
+        if (board[r][c] == 'Q')
+            return false;
+        r--;
+        c--;
+    }
+
+    // left row
+    c = col;
+    while (c >= 0)
+    {
+        if (board[row][c] == 'Q')
+            return false;
+        c--;
+    }
+
+    // lower-left diagonal
+    r = row;
+    c = col;
+    while (r < n && c >= 0)
+    {
+        if (board[r][c] == 'Q')
+            return false;
+        r++;
+        c--;
+    }
+
+    return true;
+}
+
+void solve(int col, char** board, int n, char**** ans, int* ansCount,
+           int** returnColumnSizes)
+{
+    if (col == n)
+    {
+        // save current solution
+        (*ans)[*ansCount] = (char**)malloc(sizeof(char*) * n);
+        for (int i = 0; i < n; i++)
+        {
+            (*ans)[*ansCount][i] = (char*)malloc((n + 1) * sizeof(char));
+            strcpy((*ans)[*ansCount][i], board[i]);
+        }
+        (*returnColumnSizes)[*ansCount] = n;
+        (*ansCount)++;
+        return;
+    }
+
+    for (int row = 0; row < n; row++)
+    {
+        if (isSafe(board, row, col, n))
+        {
+            board[row][col] = 'Q';
+            solve(col + 1, board, n, ans, ansCount, returnColumnSizes);
+            board[row][col] = '.';
+        }
+    }
+}
+
+char*** solveNQueens(int n, int* returnSize, int** returnColumnSizes)
+{
+    int maxSolutions =
+        1000;  // safe upper bound (works since n <= 9 in LeetCode)
+    char*** ans = (char***)malloc(sizeof(char**) * maxSolutions);
+    *returnColumnSizes = (int*)malloc(sizeof(int) * maxSolutions);
+    *returnSize = 0;
+
+    // initialize board
+    char** board = (char**)malloc(sizeof(char*) * n);
+    for (int i = 0; i < n; i++)
+    {
+        board[i] = (char*)malloc((n + 1) * sizeof(char));
+        for (int j = 0; j < n; j++) board[i][j] = '.';
+        board[i][n] = '\0';
+    }
+
+    solve(0, board, n, &ans, returnSize, returnColumnSizes);
+
+    // free temp board
+    for (int i = 0; i < n; i++) free(board[i]);
+    free(board);
+
+    return ans;
+}