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import java.io.*; import java.util.*; class FI12HW02 { private static HashSet<SearchNode> nodes; // Configuration nodes set // Main method public static void main(String[] args) throws Exception { System.out.println(solve()); } // Solving method (main), builds the structure and calls auxiliary method. Time: Unknown public static int solve() throws IOException { BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); String line = br.readLine(); StringTokenizer st = new StringTokenizer(line); String nextToken = st.nextToken(); int[][] puzzle = new int[4][4]; for(int i = 0; i < 4; i++) // Building the initial matrix { for(int j = 0; j < 4; j++) { puzzle[i][j] = Integer.parseInt(nextToken); if(st.hasMoreTokens()) nextToken = st.nextToken(); } line = br.readLine(); if(line != null) st = new StringTokenizer(line); if(st.hasMoreTokens()) nextToken = st.nextToken(); } SearchNode first = new SearchNode(puzzle, 0, null); // Initializes first node in sequence to initial configuration nodes = new HashSet<SearchNode>(20, 0.5f); return minDistance(first); // Calculates the minimum number of moves necessary } // Calculates minimum moves. Time: Unknown private static int minDistance(SearchNode n) { if(n.isFinal()) return n.moves; int[][] up = moveUp(n.config); int[][] down = moveDown(n.config); int[][] left = moveLeft(n.config); int[][] right = moveRight(n.config); if((n.previous == null || !n.previous.notMoved(up)) && !n.notMoved(up)) nodes.add(new SearchNode(up, n.moves + 1, n)); if((n.previous == null || !n.previous.notMoved(down)) && !n.notMoved(down)) nodes.add(new SearchNode(down, n.moves + 1, n)); if((n.previous == null || !n.previous.notMoved(left)) && !n.notMoved(left)) nodes.add(new SearchNode(left, n.moves + 1, n)); if((n.previous == null || !n.previous.notMoved(right)) && !n.notMoved(right)) nodes.add(new SearchNode(right, n.moves + 1, n)); SearchNode next = removeMin(); return minDistance(next); } // Takes an input configuration and returns the node containing the following configuration, moving up the first free square. Time: O(n^2) private static int[][] moveUp(int[][] m) { int[][] out = new int[4][4]; boolean substituted = false; int switchedRow = -1; int switchedColumn = -1; for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { if(m[i][j] == 0 && !substituted && i < 3) { out[i][j] = m[i + 1][j]; out[i + 1][j] = 0; substituted = true; switchedRow = i + 1; switchedColumn = j; } else { if(i != switchedRow || j != switchedColumn) out[i][j] = m[i][j]; } } } return out; } // Takes an input configuration and returns the node containing the following configuration, moving down the first free square. Time: O(n^2) private static int[][] moveDown(int[][] m) { int[][] out = new int[4][4]; boolean substituted = false; int switchedRow = -1; int switchedColumn = -1; for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { if(m[i][j] == 0 && !substituted && i > 0) { out[i][j] = m[i - 1][j]; out[i - 1][j] = 0; substituted = true; switchedRow = i - 1; switchedColumn = j; } else { if(i != switchedRow || j != switchedColumn) out[i][j] = m[i][j]; } } } return out; } // Takes an input configuration and returns the node containing the following configuration, moving left the first free square. Time: O(n^2) private static int[][] moveLeft(int[][] m) { int[][] out = new int[4][4]; boolean substituted = false; int switchedRow = -1; int switchedColumn = -1; for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { if(m[i][j] == 0 && !substituted && j < 3) { out[i][j] = m[i][j + 1]; out[i][j + 1] = 0; substituted = true; switchedRow = i; switchedColumn = j + 1; } else { if(i != switchedRow || j != switchedColumn) out[i][j] = m[i][j]; } } } return out; } // Takes an input configuration and returns the node containing the following configuration, moving right the first free square. Time: O(n^2) private static int[][] moveRight(int[][] m) { int[][] out = new int[4][4]; boolean substituted = false; int switchedRow = -1; int switchedColumn = -1; for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { if(m[i][j] == 0 && !substituted && j > 0) { out[i][j] = m[i][j - 1]; out[i][j - 1] = 0; substituted = true; switchedRow = i; switchedColumn = j - 1; } else { if(i != switchedRow || j != switchedColumn) out[i][j] = m[i][j]; } } } return out; } // Removes and returns the minimum distance node in the list. Time: O(n) private static SearchNode removeMin() { SearchNode out = null; int manhMin = Integer.MAX_VALUE; Iterator<SearchNode> it = nodes.iterator(); while(it.hasNext()) { SearchNode n = (SearchNode)it.next(); if(n.manhattan + n.moves < manhMin) { out = n; manhMin = n.manhattan + n.moves; } } nodes.remove(out); return out; } // SearchNode class static class SearchNode { int[][] config; int moves; SearchNode previous; int manhattan; SearchNode(int[][] config, int moves, SearchNode previous) { this.config = config; this.moves = moves; this.previous = previous; manhattan = manhattanDistance(); } // Checks if the given configuration is final. Time: O(1) boolean isFinal() { return (config[0][0] == 1 && config[0][1] == 2 && config[0][2] == 3 && config[0][3] == 4 && config[1][0] == 5 && config[1][1] == 6 && config[1][2] == 7 && config[1][3] == 8 && config[2][0] == 9 && config[2][1] == 10 && config[2][2] == 11 && config[2][3] == 12 && config[3][0] == 13 && config[3][1] == 14 && config[3][2] == 15 && config[3][3] == 0); } // Checks if the given node has the same configuration as the current node. Time: O(1) boolean notMoved(int[][] m) { return (config[0][0] == m[0][0] && config[0][1] == m[0][1] && config[0][2] == m[0][2] && config[0][3] == m[0][3] && config[1][0] == m[1][0] && config[1][1] == m[1][1] && config[1][2] == m[1][2] && config[1][3] == m[1][3] && config[2][0] == m[2][0] && config[2][1] == m[2][1] && config[2][2] == m[2][2] && config[2][3] == m[2][3] && config[3][0] == m[3][0] && config[3][1] == m[3][1] && config[3][2] == m[3][2] && config[3][3] == m[3][3]); } // Calculates the current node's Manhattan distance. Time: O(n^2) int manhattanDistance() { int manh = 0; for(int i = 0; i < 4; i++) { for(int j = 0; j < 4; j++) { if(config[i][j] == 1) manh = manh + Math.abs(i) + Math.abs(j); else if(config[i][j] == 2) manh = manh + Math.abs(i) + Math.abs(j - 1); else if(config[i][j] == 3) manh = manh + Math.abs(i) + Math.abs(j - 2); else if(config[i][j] == 4) manh = manh + Math.abs(i) + Math.abs(j - 3); else if(config[i][j] == 5) manh = manh + Math.abs(i - 1) + Math.abs(j); else if(config[i][j] == 6) manh = manh + Math.abs(i - 1) + Math.abs(j - 1); else if(config[i][j] == 7) manh = manh + Math.abs(i - 1) + Math.abs(j - 2); else if(config[i][j] == 8) manh = manh + Math.abs(i - 1) + Math.abs(j - 3); else if(config[i][j] == 9) manh = manh + Math.abs(i - 2) + Math.abs(j); else if(config[i][j] == 10) manh = manh + Math.abs(i - 2) + Math.abs(j - 1); else if(config[i][j] == 11) manh = manh + Math.abs(i - 2) + Math.abs(j - 2); else if(config[i][j] == 12) manh = manh + Math.abs(i - 2) + Math.abs(j - 3); else if(config[i][j] == 13) manh = manh + Math.abs(i - 3) + Math.abs(j); else if(config[i][j] == 14) manh = manh + Math.abs(i - 3) + Math.abs(j - 1); else if(config[i][j] == 15) manh = manh + Math.abs(i - 3) + Math.abs(j - 2); else; } } return manh; } } }
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