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Jul 31, 2024
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feat: update lc problems #3345

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180 changes: 122 additions & 58 deletions lcp/LCP 40. 心算挑战/README.md
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Expand Up @@ -42,13 +42,20 @@ edit_url: https://github.com/doocs/leetcode/edit/main/lcp/LCP%2040.%20%E5%BF%83%

<!-- solution:start -->

### 方法一：排序 + 贪心
### 方法一：贪心 + 排序

排序先取最大的 $cnt$ 个数，如果和为偶数则直接返回答案。
我们注意到，题目选取的是子序列，因此我们可以考虑先对数组进行排序。

否则，找一个已取的最小奇数换成剩余未取的最大偶数，或者找一个已取的最小偶数换成剩下未取的最大奇数，取两者中较大的。
接下来，我们先贪心地选取最大的 $\textit{cnt}$ 个数，如果这些数的和为偶数，则直接返回这个和 $ans$。

时间复杂度 $O(nlogn)$。
否则，我们有两种贪心策略：

1. 在最大的 $\textit{cnt}$ 个数中，找到一个最小的偶数 $mi1$，然后在剩下的 $n - \textit{cnt}$ 个数中，找到一个最大的奇数 $mx1$，将 $mi1$ 替换为 $mx1$，如果存在这样的替换，那么替换后的和 $ans - mi1 + mx1$ 一定是偶数；
1. 在最大的 $\textit{cnt}$ 个数中，找到一个最小的奇数 $mi2$，然后在剩下的 $n - \textit{cnt}$ 个数中，找到一个最大的偶数 $mx2$，将 $mi2$ 替换为 $mx2$，如果存在这样的替换，那么替换后的和 $ans - mi2 + mx2$ 一定是偶数。

我们取最大的偶数和作为答案。如果不存在偶数和，则返回 $0$。

时间复杂度 $O(n \times \log n)$，空间复杂度 $O(\log n)$。其中 $n$ 为数组长度。

<!-- tabs:start -->

Expand All @@ -57,16 +64,25 @@ edit_url: https://github.com/doocs/leetcode/edit/main/lcp/LCP%2040.%20%E5%BF%83%
```python
class Solution:
def maxmiumScore(self, cards: List[int], cnt: int) -> int:
cards.sort(reverse=True)
t = cards[:cnt]
ans = sum(t)
cards.sort()
ans = sum(cards[-cnt:])
if ans % 2 == 0:
return ans
a = min([v for v in t if v & 1], default=inf)
b = min([v for v in t if v % 2 == 0], default=inf)
c = max([v for v in cards[cnt:] if v % 2 == 0], default=-inf)
d = max([v for v in cards[cnt:] if v & 1], default=-inf)
return max(ans - a + c, ans - b + d, 0)
n = len(cards)
mx1 = mx2 = -inf
for x in cards[: n - cnt]:
if x & 1:
mx1 = x
else:
mx2 = x
mi1 = mi2 = inf
for x in cards[-cnt:][::-1]:
if x & 1:
mi2 = x
else:
mi1 = x
ans = max(ans - mi1 + mx1, ans - mi2 + mx2, -1)
return 0 if ans < 0 else ans
```

#### Java
Expand All @@ -83,26 +99,25 @@ class Solution {
if (ans % 2 == 0) {
return ans;
}
int inf = 0x3f3f3f3f;
int a = inf, b = inf;
for (int i = 0; i < cnt; ++i) {
int v = cards[n - i - 1];
if (v % 2 == 1) {
a = Math.min(a, v);
final int inf = 1 << 29;
int mx1 = -inf, mx2 = -inf;
for (int i = 0; i < n - cnt; ++i) {
if (cards[i] % 2 == 1) {
mx1 = cards[i];
} else {
b = Math.min(b, v);
mx2 = cards[i];
}
}
int c = -inf, d = -inf;
for (int i = cnt; i < n; ++i) {
int v = cards[n - i - 1];
if (v % 2 == 0) {
c = Math.max(c, v);
int mi1 = inf, mi2 = inf;
for (int i = n - 1; i >= n - cnt; --i) {
if (cards[i] % 2 == 1) {
mi2 = cards[i];
} else {
d = Math.max(d, v);
mi1 = cards[i];
}
}
return Math.max(0, Math.max(ans - a + c, ans - b + d));
ans = Math.max(ans - mi1 + mx1, ans - mi2 + mx2);
return ans < 0 ? 0 : ans;
}
}
```
Expand All @@ -114,27 +129,33 @@ class Solution {
public:
int maxmiumScore(vector<int>& cards, int cnt) {
sort(cards.begin(), cards.end());
reverse(cards.begin(), cards.end());
int ans = 0, n = cards.size();
for (int i = 0; i < cnt; ++i) ans += cards[i];
if (ans % 2 == 0) return ans;
int inf = 0x3f3f3f3f;
int a = inf, b = inf, c = -inf, d = -inf;
int ans = 0;
int n = cards.size();
for (int i = 0; i < cnt; ++i) {
int v = cards[i];
if (v % 2 == 1)
a = min(a, v);
else
b = min(b, v);
ans += cards[n - i - 1];
}
for (int i = cnt; i < n; ++i) {
int v = cards[i];
if (v % 2 == 0)
c = max(c, v);
else
d = max(d, v);
if (ans % 2 == 0) {
return ans;
}
const int inf = 1 << 29;
int mx1 = -inf, mx2 = -inf;
for (int i = 0; i < n - cnt; ++i) {
if (cards[i] % 2) {
mx1 = cards[i];
} else {
mx2 = cards[i];
}
}
return max(0, max(ans - a + c, ans - b + d));
int mi1 = inf, mi2 = inf;
for (int i = n - 1; i >= n - cnt; --i) {
if (cards[i] % 2) {
mi2 = cards[i];
} else {
mi1 = cards[i];
}
}
ans = max(ans - mi1 + mx1, ans - mi2 + mx2);
return ans < 0 ? 0 : ans;
}
};
```
Expand All @@ -143,31 +164,74 @@ public:

```go
func maxmiumScore(cards []int, cnt int) int {
sort.Ints(cards)
ans := 0
sort.Slice(cards, func(i, j int) bool { return cards[i] > cards[j] })
for _, v := range cards[:cnt] {
ans += v
n := len(cards)
for i := 0; i < cnt; i++ {
ans += cards[n-1-i]
}
if ans%2 == 0 {
return ans
}
inf := 0x3f3f3f3f
a, b, c, d := inf, inf, -inf, -inf
for _, v := range cards[:cnt] {
if v%2 == 1 {
a = min(a, v)
const inf = 1 << 29
mx1, mx2 := -inf, -inf
for _, x := range cards[:n-cnt] {
if x%2 == 1 {
mx1 = x
} else {
b = min(b, v)
mx2 = x
}
}
for _, v := range cards[cnt:] {
if v%2 == 0 {
c = max(c, v)
mi1, mi2 := inf, inf
for i := n - 1; i >= n-cnt; i-- {
if cards[i]%2 == 1 {
mi2 = cards[i]
} else {
d = max(d, v)
mi1 = cards[i]
}
}
return max(0, max(ans-a+c, ans-b+d))
ans = max(-1, max(ans-mi1+mx1, ans-mi2+mx2))
if ans < 0 {
return 0
}
return ans
}
```

#### TypeScript

```ts
function maxmiumScore(cards: number[], cnt: number): number {
cards.sort((a, b) => a - b);
let ans = 0;
const n = cards.length;
for (let i = 0; i < cnt; ++i) {
ans += cards[n - i - 1];
}
if (ans % 2 === 0) {
return ans;
}
const inf = 1 << 29;
let mx1 = -inf,
mx2 = -inf;
for (let i = 0; i < n - cnt; ++i) {
if (cards[i] % 2 === 1) {
mx1 = cards[i];
} else {
mx2 = cards[i];
}
}
let mi1 = inf,
mi2 = inf;
for (let i = n - 1; i >= n - cnt; --i) {
if (cards[i] % 2 === 1) {
mi2 = cards[i];
} else {
mi1 = cards[i];
}
}
ans = Math.max(ans - mi1 + mx1, ans - mi2 + mx2);
return ans < 0 ? 0 : ans;
}
```

Expand Down
44 changes: 25 additions & 19 deletions lcp/LCP 40. 心算挑战/Solution.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -2,26 +2,32 @@ class Solution {
public:
int maxmiumScore(vector<int>& cards, int cnt) {
sort(cards.begin(), cards.end());
reverse(cards.begin(), cards.end());
int ans = 0, n = cards.size();
for (int i = 0; i < cnt; ++i) ans += cards[i];
if (ans % 2 == 0) return ans;
int inf = 0x3f3f3f3f;
int a = inf, b = inf, c = -inf, d = -inf;
int ans = 0;
int n = cards.size();
for (int i = 0; i < cnt; ++i) {
int v = cards[i];
if (v % 2 == 1)
a = min(a, v);
else
b = min(b, v);
ans += cards[n - i - 1];
}
for (int i = cnt; i < n; ++i) {
int v = cards[i];
if (v % 2 == 0)
c = max(c, v);
else
d = max(d, v);
if (ans % 2 == 0) {
return ans;
}
return max(0, max(ans - a + c, ans - b + d));
const int inf = 1 << 29;
int mx1 = -inf, mx2 = -inf;
for (int i = 0; i < n - cnt; ++i) {
if (cards[i] % 2) {
mx1 = cards[i];
} else {
mx2 = cards[i];
}
}
int mi1 = inf, mi2 = inf;
for (int i = n - 1; i >= n - cnt; --i) {
if (cards[i] % 2) {
mi2 = cards[i];
} else {
mi1 = cards[i];
}
}
ans = max(ans - mi1 + mx1, ans - mi2 + mx2);
return ans < 0 ? 0 : ans;
}
};
};
36 changes: 21 additions & 15 deletions lcp/LCP 40. 心算挑战/Solution.go
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Original file line number Diff line number Diff line change
@@ -1,27 +1,33 @@
func maxmiumScore(cards []int, cnt int) int {
sort.Ints(cards)
ans := 0
sort.Slice(cards, func(i, j int) bool { return cards[i] > cards[j] })
for _, v := range cards[:cnt] {
ans += v
n := len(cards)
for i := 0; i < cnt; i++ {
ans += cards[n-1-i]
}
if ans%2 == 0 {
return ans
}
inf := 0x3f3f3f3f
a, b, c, d := inf, inf, -inf, -inf
for _, v := range cards[:cnt] {
if v%2 == 1 {
a = min(a, v)
const inf = 1 << 29
mx1, mx2 := -inf, -inf
for _, x := range cards[:n-cnt] {
if x%2 == 1 {
mx1 = x
} else {
b = min(b, v)
mx2 = x
}
}
for _, v := range cards[cnt:] {
if v%2 == 0 {
c = max(c, v)
mi1, mi2 := inf, inf
for i := n - 1; i >= n-cnt; i-- {
if cards[i]%2 == 1 {
mi2 = cards[i]
} else {
d = max(d, v)
mi1 = cards[i]
}
}
return max(0, max(ans-a+c, ans-b+d))
}
ans = max(-1, max(ans-mi1+mx1, ans-mi2+mx2))
if ans < 0 {
return 0
}
return ans
}
29 changes: 14 additions & 15 deletions lcp/LCP 40. 心算挑战/Solution.java
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Original file line number Diff line number Diff line change
Expand Up @@ -9,25 +9,24 @@ public int maxmiumScore(int[] cards, int cnt) {
if (ans % 2 == 0) {
return ans;
}
int inf = 0x3f3f3f3f;
int a = inf, b = inf;
for (int i = 0; i < cnt; ++i) {
int v = cards[n - i - 1];
if (v % 2 == 1) {
a = Math.min(a, v);
final int inf = 1 << 29;
int mx1 = -inf, mx2 = -inf;
for (int i = 0; i < n - cnt; ++i) {
if (cards[i] % 2 == 1) {
mx1 = cards[i];
} else {
b = Math.min(b, v);
mx2 = cards[i];
}
}
int c = -inf, d = -inf;
for (int i = cnt; i < n; ++i) {
int v = cards[n - i - 1];
if (v % 2 == 0) {
c = Math.max(c, v);
int mi1 = inf, mi2 = inf;
for (int i = n - 1; i >= n - cnt; --i) {
if (cards[i] % 2 == 1) {
mi2 = cards[i];
} else {
d = Math.max(d, v);
mi1 = cards[i];
}
}
return Math.max(0, Math.max(ans - a + c, ans - b + d));
ans = Math.max(ans - mi1 + mx1, ans - mi2 + mx2);
return ans < 0 ? 0 : ans;
}
}
}
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