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困难 |
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给定一个长度为4的整数数组 cards 。你有 4 张卡片，每张卡片上都包含一个范围在 [1,9] 的数字。您应该使用运算符 ['+', '-', '*', '/'] 和括号 '(' 和 ')' 将这些卡片上的数字排列成数学表达式，以获得值24。
你须遵守以下规则:
- 除法运算符
'/'表示实数除法，而不是整数除法。<ul> <li>例如， <code>4 /(1 - 2 / 3)= 4 /(1 / 3)= 12</code> 。</li> </ul> </li> <li>每个运算都在两个数字之间。特别是，不能使用 <code>“-”</code> 作为一元运算符。 <ul> <li>例如，如果 <code>cards =[1,1,1,1]</code> ，则表达式 <code>“-1 -1 -1 -1”</code> 是 <strong>不允许</strong> 的。</li> </ul> </li> <li>你不能把数字串在一起 <ul> <li>例如，如果 <code>cards =[1,2,1,2]</code> ，则表达式 <code>“12 + 12”</code> 无效。</li> </ul> </li>
如果可以得到这样的表达式，其计算结果为 24 ，则返回 true ，否则返回 false 。
示例 1:
输入: cards = [4, 1, 8, 7] 输出: true 解释: (8-4) * (7-1) = 24
示例 2:
输入: cards = [1, 2, 1, 2] 输出: false
提示:
cards.length == 41 <= cards[i] <= 9
我们设计一个函数
如果
否则，我们可以枚举
如果枚举完所有的情况都没有返回
class Solution:
def judgePoint24(self, cards: List[int]) -> bool:
def dfs(nums: List[float]):
n = len(nums)
if n == 1:
if abs(nums[0] - 24) < 1e-6:
return True
return False
ok = False
for i in range(n):
for j in range(n):
if i != j:
nxt = [nums[k] for k in range(n) if k != i and k != j]
for op in ops:
match op:
case "/":
if nums[j] == 0:
continue
ok |= dfs(nxt + [nums[i] / nums[j]])
case "*":
ok |= dfs(nxt + [nums[i] * nums[j]])
case "+":
ok |= dfs(nxt + [nums[i] + nums[j]])
case "-":
ok |= dfs(nxt + [nums[i] - nums[j]])
if ok:
return True
return ok
ops = ("+", "-", "*", "/")
nums = [float(x) for x in cards]
return dfs(nums)class Solution {
private final char[] ops = {'+', '-', '*', '/'};
public boolean judgePoint24(int[] cards) {
List<Double> nums = new ArrayList<>();
for (int num : cards) {
nums.add((double) num);
}
return dfs(nums);
}
private boolean dfs(List<Double> nums) {
int n = nums.size();
if (n == 1) {
return Math.abs(nums.get(0) - 24) < 1e-6;
}
boolean ok = false;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (i != j) {
List<Double> nxt = new ArrayList<>();
for (int k = 0; k < n; ++k) {
if (k != i && k != j) {
nxt.add(nums.get(k));
}
}
for (char op : ops) {
switch (op) {
case '/' -> {
if (nums.get(j) == 0) {
continue;
}
nxt.add(nums.get(i) / nums.get(j));
}
case '*' -> {
nxt.add(nums.get(i) * nums.get(j));
}
case '+' -> {
nxt.add(nums.get(i) + nums.get(j));
}
case '-' -> {
nxt.add(nums.get(i) - nums.get(j));
}
}
ok |= dfs(nxt);
if (ok) {
return true;
}
nxt.remove(nxt.size() - 1);
}
}
}
}
return ok;
}
}class Solution {
public:
bool judgePoint24(vector<int>& cards) {
vector<double> nums;
for (int num : cards) {
nums.push_back(static_cast<double>(num));
}
return dfs(nums);
}
private:
const char ops[4] = {'+', '-', '*', '/'};
bool dfs(vector<double>& nums) {
int n = nums.size();
if (n == 1) {
return abs(nums[0] - 24) < 1e-6;
}
bool ok = false;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (i != j) {
vector<double> nxt;
for (int k = 0; k < n; ++k) {
if (k != i && k != j) {
nxt.push_back(nums[k]);
}
}
for (char op : ops) {
switch (op) {
case '/':
if (nums[j] == 0) {
continue;
}
nxt.push_back(nums[i] / nums[j]);
break;
case '*':
nxt.push_back(nums[i] * nums[j]);
break;
case '+':
nxt.push_back(nums[i] + nums[j]);
break;
case '-':
nxt.push_back(nums[i] - nums[j]);
break;
}
ok |= dfs(nxt);
if (ok) {
return true;
}
nxt.pop_back();
}
}
}
}
return ok;
}
};func judgePoint24(cards []int) bool {
ops := [4]rune{'+', '-', '*', '/'}
nums := make([]float64, len(cards))
for i, num := range cards {
nums[i] = float64(num)
}
var dfs func([]float64) bool
dfs = func(nums []float64) bool {
n := len(nums)
if n == 1 {
return math.Abs(nums[0]-24) < 1e-6
}
ok := false
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if i != j {
var nxt []float64
for k := 0; k < n; k++ {
if k != i && k != j {
nxt = append(nxt, nums[k])
}
}
for _, op := range ops {
switch op {
case '/':
if nums[j] == 0 {
continue
}
nxt = append(nxt, nums[i]/nums[j])
case '*':
nxt = append(nxt, nums[i]*nums[j])
case '+':
nxt = append(nxt, nums[i]+nums[j])
case '-':
nxt = append(nxt, nums[i]-nums[j])
}
ok = ok || dfs(nxt)
if ok {
return true
}
nxt = nxt[:len(nxt)-1]
}
}
}
}
return ok
}
return dfs(nums)
}function judgePoint24(cards: number[]): boolean {
const ops: string[] = ['+', '-', '*', '/'];
const dfs = (nums: number[]): boolean => {
const n: number = nums.length;
if (n === 1) {
return Math.abs(nums[0] - 24) < 1e-6;
}
let ok: boolean = false;
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
if (i !== j) {
const nxt: number[] = [];
for (let k = 0; k < n; k++) {
if (k !== i && k !== j) {
nxt.push(nums[k]);
}
}
for (const op of ops) {
switch (op) {
case '/':
if (nums[j] === 0) {
continue;
}
nxt.push(nums[i] / nums[j]);
break;
case '*':
nxt.push(nums[i] * nums[j]);
break;
case '+':
nxt.push(nums[i] + nums[j]);
break;
case '-':
nxt.push(nums[i] - nums[j]);
break;
}
ok = ok || dfs(nxt);
if (ok) {
return true;
}
nxt.pop();
}
}
}
}
return ok;
};
return dfs(cards);
}