Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit fc7f5c0

Browse files
a
1 parent cf12b63 commit fc7f5c0

File tree

1 file changed

+147
-0
lines changed

1 file changed

+147
-0
lines changed
Lines changed: 147 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,147 @@
1+
import java.util.ArrayList;
2+
import java.util.HashMap;
3+
import java.util.List;
4+
import java.util.Map;
5+
6+
public class KnightProbabilityInChessboard {
7+
static class Position {
8+
private final int n;
9+
private int row;
10+
private int column;
11+
12+
Position(int row, int column, int n) {
13+
this.n = n;
14+
this.row = row;
15+
this.column = column;
16+
17+
}
18+
19+
private void normalize() {
20+
row = normalize(row);
21+
column = normalize(column);
22+
if (row > column) {
23+
int temp = row;
24+
row = column;
25+
column = temp;
26+
}
27+
}
28+
29+
private int normalize(int index) {
30+
if (index >= (n + 1) / 2) {
31+
return n - index;
32+
}
33+
return index;
34+
}
35+
36+
private Position apply(Movement movement) {
37+
return switch (movement) {
38+
case TOP_LEFT -> new Position(row - 2, column - 1, n);
39+
case TOP_RIGHT -> new Position(row - 2, column + 1, n);
40+
case RIGHT_TOP -> new Position(row - 1, column + 2, n);
41+
case RIGHT_BOTTOM -> new Position(row + 1, column + 2, n);
42+
case BOTTOM_RIGHT -> new Position(row + 2, column + 1, n);
43+
case BOTTOM_LEFT -> new Position(row + 2, column - 1, n);
44+
case LEFT_BOTTOM -> new Position(row + 1, column - 2, n);
45+
case LEFT_TOP -> new Position(row - 1, column - 2, n);
46+
};
47+
}
48+
49+
private boolean isValid() {
50+
return row >= 0
51+
&& row < n
52+
&& column >= 0
53+
&& column < n;
54+
}
55+
56+
@Override
57+
public boolean equals(Object o) {
58+
if (this == o) return true;
59+
Position other = (Position) o;
60+
if (row != other.row) return false;
61+
return column == other.column;
62+
}
63+
64+
@Override
65+
public int hashCode() {
66+
return 31 * row + column;
67+
}
68+
}
69+
70+
private record State(int n, int k, Position position) { }
71+
72+
private enum Movement {
73+
TOP_LEFT,
74+
TOP_RIGHT,
75+
RIGHT_TOP,
76+
RIGHT_BOTTOM,
77+
BOTTOM_RIGHT,
78+
BOTTOM_LEFT,
79+
LEFT_TOP,
80+
LEFT_BOTTOM
81+
}
82+
83+
private final Map<Position, List<Movement>> allowedMovements = new HashMap<>();
84+
private final Map<State, Double> results = new HashMap<>();
85+
86+
public double knightProbability(int n, int k, int row, int column) {
87+
computeValidMovements(n);
88+
return getKnightProbability(n, k, new Position(row, column, n));
89+
}
90+
91+
private double getKnightProbability(int n, int k, Position position) {
92+
if (!position.isValid()) return 0;
93+
if (k == 0) return 1;
94+
95+
position.normalize();
96+
State state = new State(n, k, position);
97+
if (results.containsKey(state)) return results.get(state);
98+
99+
if (k == 1) {
100+
double answer = ((double) validMoves(position)) / 8;
101+
results.put(state, answer);
102+
return answer;
103+
}
104+
105+
int sumOfProbabilities = 0;
106+
for (Movement movement : allowedMovements.get(position)) {
107+
Position newPosition = position.apply(movement);
108+
sumOfProbabilities += getKnightProbability(n, k - 1, newPosition);
109+
}
110+
double answer = ((double) sumOfProbabilities) / 8;
111+
results.put(state, answer);
112+
return answer;
113+
}
114+
115+
private void computeValidMovements(int n) {
116+
for (int row = 0 ; row < (n + 1) / 2 ; row++) {
117+
for (int column = row ; column < (n + 1) / 2 ; column++) {
118+
Position position = new Position(row, column, n);
119+
allowedMovements.put(position, knightMovementsAt(position));
120+
}
121+
}
122+
}
123+
124+
private List<Movement> knightMovementsAt(Position position) {
125+
final List<Movement> movements = new ArrayList<>();
126+
if (isValidIndices(position.row - 2, position.column - 1, position.n)) movements.add(Movement.TOP_LEFT);
127+
if (isValidIndices(position.row - 2, position.column + 1, position.n)) movements.add(Movement.TOP_RIGHT);
128+
if (isValidIndices(position.row - 1, position.column + 2, position.n)) movements.add(Movement.RIGHT_TOP);
129+
if (isValidIndices(position.row + 1, position.column + 2, position.n)) movements.add(Movement.RIGHT_BOTTOM);
130+
if (isValidIndices(position.row + 2, position.column + 1, position.n)) movements.add(Movement.BOTTOM_RIGHT);
131+
if (isValidIndices(position.row + 2, position.column - 1, position.n)) movements.add(Movement.BOTTOM_LEFT);
132+
if (isValidIndices(position.row + 1, position.column - 2, position.n)) movements.add(Movement.LEFT_BOTTOM);
133+
if (isValidIndices(position.row - 1, position.column - 2, position.n)) movements.add(Movement.LEFT_TOP);
134+
return movements;
135+
}
136+
137+
private boolean isValidIndices(int row, int column, int n) {
138+
return row >= 0
139+
&& row < n
140+
&& column >= 0
141+
&& column < n;
142+
}
143+
144+
private int validMoves(Position position) {
145+
return allowedMovements.get(position).size();
146+
}
147+
}

0 commit comments

Comments
(0)

AltStyle γ«γ‚ˆγ£γ¦ε€‰ζ›γ•γ‚ŒγŸγƒšγƒΌγ‚Έ (->γ‚ͺγƒͺγ‚ΈγƒŠγƒ«) /