Add 52 in c language

Author: julienChemillier

c/52-n-queens-ii.c

@@ -0,0 +1,53 @@
+/*
+Given an integer n, return the number of distinct solutions to the n-queens puzzle.
+
+Space: O(n²)
+Time: ?
+*/
+
+int min(int a, int b){
+    return a<b?a:b;
+}
+
+int can_ce_placed(int i, int j, int n, int** board) {
+    for (int k=i-1; k>=0; k--)
+        if (board[k][j])
+            return false;
+    for (int k=j-1; k>=0; k--)
+        if (board[i][k])
+            return false;
+    int m = min(i, j)+1;
+    for (int k=1; k<m; k++)
+        if (board[i-k][j-k])
+            return false;
+    m = min(i+1, n-j);
+    for (int k=1; k<m; k++)
+        if (board[i-k][j+k])
+            return false;
+    return true;
+}
+
+int backtracking(int i, int n, int** board) {
+    if (i==n)
+        return 1;
+    int cpt = 0;
+    for (int k=0; k<n; k++){
+        if (can_ce_placed(i, k, n, board)){
+            board[i][k] = 1;
+            cpt += backtracking(i+1, n, board);
+            board[i][k] = 0;
+        }
+    }
+    return cpt;
+}
+
+int totalNQueens(int n){
+    int** board = malloc(sizeof(int*)*n);
+    for (int i=0; i<n; i++)
+        board[i] = calloc(n, sizeof(int));
+    int ans = backtracking(0, n, board);
+    for (int i=0; i<n; i++)
+        free(board[i]);
+    free(board);
+    return ans;
+}