8-Puzzle - Amazon Top Interview Questions
Problem Statement :
You are given a 3x3 board of unique integers from 0 to 8, representing the state of a puzzle. In this puzzle, you can swap the 0 with one of its 4 neighbours (if it exists), and you are trying to solve it by obtaining the following configuration:
[[0, 1, 2],
[3, 4, 5],
[6, 7, 8]]
Return the minimum number of swaps required to solve the puzzle, or return -1 if it's not possible.
Constraints
n = 3 where n is the number of rows and columns in board
0 ≤ board[r][c] ≤ 8
Example 1
Input
board = [
[1, 0, 2],
[3, 4, 5],
[6, 7, 8]
]
Output
1
Explanation
We can swap the 0 and the 1 to solve the puzzle.
Solution :
Solution in C++ :
static unordered_map<string, int64_t> cost;
/* Precompute Utility */
inline void precompute() {
string initial_node = "012345678";
queue<string> q;
q.push(initial_node);
cost[initial_node] = 0;
while (!q.empty()) {
auto current_node = q.front();
q.pop();
int z = find(current_node.begin(), current_node.end(), '0') - current_node.begin();
assert(z >= 0 && z < 9);
int curr = cost[current_node];
int lo = z / 3 * 3;
int hi = (z / 3 + 1) * 3;
for (auto i : {-3, 3, -1, 1}) {
if (abs(i) == 3 && z + i < (int)current_node.size() && z + i >= 0 ||
abs(i) == 1 && z + i >= lo && z + i < hi) {
swap(current_node[z + i], current_node[z]);
if (!cost.count(current_node)) {
cost[current_node] = curr + 1;
q.push(current_node);
} else if (cost[current_node] > curr + 1) {
cost[current_node] = curr + 1;
q.push(current_node);
}
swap(current_node[z + i], current_node[z]);
}
}
}
}
/* Calling Precompute */
struct S {
S() {
precompute();
}
} _;
int solve(vector<vector<int>>& board) {
string target;
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) target += (board[i][j] + '0');
return cost.count(target) ? cost[target] : -1;
}
Solution in Java :
import java.util.*;
class Solution {
public int solve(int[][] board) {
StringBuilder sb = new StringBuilder();
int rows = board.length, cols = board[0].length;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
sb.append(String.valueOf(board[i][j]));
}
}
Map<Integer, List<Integer>> map = new HashMap<>();
map.put(0, Arrays.asList(1, 3));
map.put(1, Arrays.asList(0, 2, 4));
map.put(2, Arrays.asList(1, 5));
map.put(3, Arrays.asList(0, 4, 6));
map.put(4, Arrays.asList(1, 3, 5, 7));
map.put(5, Arrays.asList(2, 4, 8));
map.put(6, Arrays.asList(3, 7));
map.put(7, Arrays.asList(4, 6, 8));
map.put(8, Arrays.asList(5, 7));
String source = sb.toString(), target = "012345678";
if (source.equals(target)) {
return 0;
}
Queue<String> q = new LinkedList<>();
Set<String> visited = new HashSet<>();
q.add(source);
visited.add(source);
int count = 0;
while (!q.isEmpty()) {
for (int b = q.size(); b > 0; b--) {
String cur = q.poll();
int zeroIdx = cur.indexOf("0");
char[] arr = cur.toCharArray();
for (int nextIdx : map.get(zeroIdx)) {
swap(arr, zeroIdx, nextIdx);
String nextStr = new String(arr);
if (!visited.contains(nextStr)) {
if (nextStr.equals(target)) {
return count + 1;
}
visited.add(nextStr);
q.add(nextStr);
}
swap(arr, zeroIdx, nextIdx);
}
}
++count;
}
return -1;
}
private void swap(char[] arr, int i, int j) {
char temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
Solution in Python :
class Solution:
def solve(self, board):
def get_neighbours(state):
state = list(state) # make mutable
idx = state.index(0) # find index
neighbors = []
for move in [-3, 3]: # vertical switch
switch = idx + move
if 0 <= switch < 9: # check if out of bounds
state[idx], state[switch] = state[switch], state[idx]
neighbors.append(tuple(state))
state[idx], state[switch] = state[switch], state[idx]
for move in [-1, 1]: # horizontal switch
switch = idx + move
if idx // 3 == switch // 3: # check if row is not changed
state[idx], state[switch] = state[switch], state[idx]
neighbors.append(tuple(state))
state[idx], state[switch] = state[switch], state[idx]
return neighbors
board = sum(board, []) # flatten the board
board = tuple(board) # make tuple
target = tuple(range(9))
visited = set(tuple(board))
queue = deque([(board, 0)])
while queue:
cur, cnt = queue.popleft()
if cur == target:
return cnt
for nex in get_neighbours(cur):
if nex in visited:
continue
queue.append((nex, cnt + 1))
visited.add(nex)
return -1
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