A solution added for a math problem

src/main/java/org/algo/puzzle/EqualSumGrid.java

@@ -0,0 +1,188 @@
+package org.algo.puzzle;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+/***
+ * Question:
+ * Fill the nine squares with the numbers (e.g. 1 to 9), so that the sum of the numbers in each row, column, and
+ * diagonal is equal.
+ * - - -
+ * |X X X|
+ * |X X X|
+ * |X X X|
+ * - - -
+ */
+public class EqualSumGrid {
+ public static void main(String[] args) {
+
+ EqualSumGrid grid = new EqualSumGrid();
+ grid.place(new int[]{1, 2, 3, 4, 5, 6, 7, 8, 9});
+ }
+
+ public void place(int[] candidates) {
+ for (int i = 0; i < candidates.length; i++) {
+ candidates[i] = i + 1;
+ }
+
+ int[][] grid = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
+ int avg = Arrays.stream(candidates).sum() / grid.length;
+ resolvePuzzle(grid, 0, new boolean[9], candidates, avg);
+
+ printResults();
+ }
+
+ private void resolvePuzzle(int[][] arr, int pos, boolean[] used, int[] candidates, int avg) {
+
+ int rowCnt = arr.length;
+ int colCnt = arr[0].length;
+
+ if (pos >= used.length) {
+ int index = 0;
+ int[] res = new int[used.length];
+ for (int i = 0; i < rowCnt; i++) {
+ for (int j = 0; j < colCnt; j++) {
+ res[index++] = arr[i][j];
+ }
+ }
+ list.add(res);
+ return;
+ }
+
+ int row = pos / colCnt;
+ int col = pos % colCnt;
+
+
+ for (int k = 0; k < candidates.length; k++) {
+ if (!used[k] && arr[row][col] == 0) {
+ arr[row][col] = candidates[k];
+ used[k] = true;
+
+ if (isValid(arr, used, candidates, avg)) {
+ resolvePuzzle(arr, pos + 1, used, candidates, avg);
+ }
+
+ used[k] = false;
+ arr[row][col] = 0;
+ }
+ }
+ }
+
+ public void printResults() {
+ System.out.printf(">>><<< %d result(s) found: \n", list.size());
+ for (int[] res : list) {
+ int i = 0;
+
+ System.out.printf("\n[\n");
+ for (int j = 0; j < res.length; j++) {
+ System.out.printf("%d ", res[i++]);
+ if (j + 1 >= 3 && (j + 1) % 3 == 0) {
+ System.out.printf("\n");
+ }
+ }
+ System.out.printf("]\n");
+ }
+ }
+
+ private final List<int[]> list = new ArrayList<>();
+
+ private boolean isValid(int[][] arr, boolean[] used, int[] candidates, int avg) {
+ if (!hasValidRows(arr, avg)) return false;
+
+ if (!hasValidColumns(arr, avg)) return false;
+
+ if (!hasValidDiagonalLines(arr, avg)) return false;
+
+ return true;
+ }
+
+ private static boolean hasValidDiagonalLines(int[][] arr, int avg) {
+ int sum = 0;
+ int cnt = 0;
+ if (arr[0][0] != 0) {
+ sum += arr[0][0];
+ cnt++;
+ }
+ if (arr[1][1] != 0) {
+ sum += arr[1][1];
+ cnt++;
+ }
+ if (arr[2][2] != 0) {
+ sum += arr[2][2];
+ cnt++;
+ }
+ if (cnt == 2 && sum >= avg) return false;
+ if (cnt == 3 && sum != avg) return false;
+
+
+ sum = cnt = 0;
+ if (arr[0][2] != 0) {
+ sum += arr[0][2];
+ cnt++;
+ }
+ if (arr[1][1] != 0) {
+ sum += arr[1][1];
+ cnt++;
+ }
+ if (arr[2][0] != 0) {
+ sum += arr[2][0];
+ cnt++;
+ }
+ if (cnt == 2 && sum >= avg) return false;
+ if (cnt == 3 && sum != avg) return false;
+
+ return true;
+ }
+
+ private static boolean hasValidColumns(int[][] arr, int avg) {
+ for (int i = 0; i < 3; i++) {
+ // columns
+ int sum = 0;
+ int cnt = 0;
+ if (arr[0][i] != 0) {
+ cnt++;
+ sum += arr[0][i];
+ }
+ if (arr[1][(i + 3) % 3] != 0) {
+ cnt++;
+ sum += arr[1][(i + 3) % 3];
+ }
+ if (arr[2][(i + 6) % 3] != 0) {
+ cnt++;
+ sum += arr[2][(i + 6) % 3];
+ }
+ if (cnt == 2 && sum >= avg) return false;
+ if (cnt == 3 && sum != avg) return false;
+ }
+ return true;
+ }
+
+ private static boolean hasValidRows(int[][] arr, int avg) {
+ for (int i = 0; i < 3; i++) {
+ int sum = 0;
+ int cnt = 0;
+
+ // rows
+ if (arr[i][0] != 0) {
+ cnt++;
+ sum += arr[i][0];
+ }
+ if (arr[i][1] != 0) {
+ cnt++;
+ sum += arr[i][1];
+ }
+
+ if (arr[i][2] != 0) {
+ cnt++;
+ sum += arr[i][2];
+ }
+
+ if (cnt == 2 && sum >= avg) return false;
+ if (cnt == 3 && sum != avg) return false;
+ }
+ return true;
+ }
+
+
+}