0679. 24 Game
https://leetcode.com/problems/24-game
Description
You are given an integer array cards
of length 4
. You have four cards, each containing a number in the range [1, 9]
. You should arrange the numbers on these cards in a mathematical expression using the operators ['+', '-', '*', '/']
and the parentheses '('
and ')'
to get the value 24.
You are restricted with the following rules:
The division operator
'/'
represents real division, not integer division.For example,
4 / (1 - 2 / 3) = 4 / (1 / 3) = 12
.
Every operation done is between two numbers. In particular, we cannot use
'-'
as a unary operator.For example, if
cards = [1, 1, 1, 1]
, the expression"-1 - 1 - 1 - 1"
is not allowed.
You cannot concatenate numbers together
For example, if
cards = [1, 2, 1, 2]
, the expression"12 + 12"
is not valid.
Return true
if you can get such expression that evaluates to 24
, and false
otherwise.
Example 1:
**Input:** cards = [4,1,8,7]
**Output:** true
**Explanation:** (8-4) * (7-1) = 24
Example 2:
**Input:** cards = [1,2,1,2]
**Output:** false
Constraints:
cards.length == 4
1 <= cards[i] <= 9
ac
class Solution {
public boolean judgePoint24(int[] nums) {
// edge cases
List<Double> list = new ArrayList<>();
for (int n : nums) list.add((double) n);
return dfs(list);
}
private boolean dfs(List<Double> list) {
int n = list.size();
if (n == 1) return Math.abs(list.get(0) - 24.0) < 0.0001;
// pick 2 numbers, calculate a new number
for (int i = 0; i < n-1; i++) {
for (int j = i + 1; j < n; j++) {
List<Double> newVal = cal(list.get(i), list.get(j));
// new list, pick remaining number from old list
List<Double> newList = new ArrayList<>();
for (int k = 0; k < n; k++) {
if (k != i && k != j) newList.add(list.get(k));
}
// backtracking, try new values
int lastIdx = newList.size();
for (double d : newVal) {
newList.add(d);
if (dfs(newList)) return true;
newList.remove(lastIdx);
}
}
}
return false;
}
private List<Double> cal(double n1, double n2) {
List<Double> res = new ArrayList<>();
res.add(n1 + n2);
res.add(n1 - n2);
res.add(n1 * n2);
res.add(n1 / n2);
res.add(n2 - n1);
res.add(n2 / n1);
return res;
}
}
/*
1) pick 2 numbers, calculate a new number put back to array. 2) repeat, until only one number in array, check if it's 24.
*/
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