diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README.md b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README.md index bd2dd4900b382..930ca16644b71 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README.md +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README.md @@ -57,46 +57,44 @@ ## 解法 -### 方法一 +### 方法一：滑动窗口 + +我们先统计数组中 $1$ 的个数，记为 $k$，那么题目实际上就是求一个长度为 $k$ 的环形子数组，使得子数组中 $1$ 的个数最多，那么最少交换次数就是 $k$ 减去子数组中 $1$ 的个数最多的那个子数组中 $1$ 的个数。 + +我们可以使用滑动窗口来解决这个问题，首先统计数组中前 $k$ 个元素中 $1$ 的个数，记为 $cnt$，然后我们维护一个长度为 $k$ 的滑动窗口，每次向右移动一个位置，更新 $cnt$，同时更新最大的 $cnt$ 值，即 $mx = \max(mx, cnt)$，最后答案就是 $k - mx$。 + +时间复杂度 $O(n)$，其中 $n$ 是数组 $nums$ 的长度。空间复杂度 $O(1)$。 ```python class Solution: def minSwaps(self, nums: List[int]) -> int: - cnt = nums.count(1) + k = nums.count(1) + mx = cnt = sum(nums[:k]) n = len(nums) - s = [0] * ((n << 1) + 1) - for i in range(n << 1): - s[i + 1] = s[i] + nums[i % n] - mx = 0 - for i in range(n << 1): - j = i + cnt - 1 - if j < (n << 1): - mx = max(mx, s[j + 1] - s[i]) - return cnt - mx + for i in range(k, n + k): + cnt += nums[i % n] + cnt -= nums[(i - k + n) % n] + mx = max(mx, cnt) + return k - mx ``` ```java class Solution { public int minSwaps(int[] nums) { - int cnt = 0; - for (int v : nums) { - cnt += v; - } + int k = Arrays.stream(nums).sum(); int n = nums.length; - int[] s = new int[(n << 1) + 1]; - for (int i = 0; i < (n << 1); ++i) { - s[i + 1] = s[i] + nums[i % n]; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; } - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) { - mx = Math.max(mx, s[j + 1] - s[i]); - } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); } - return cnt - mx; + return k - mx; } } ``` @@ -105,56 +103,90 @@ class Solution { class Solution { public: int minSwaps(vector& nums) { - int cnt = 0; - for (int& v : nums) cnt += v; + int k = accumulate(nums.begin(), nums.end(), 0); int n = nums.size(); - vector s((n << 1) + 1); - for (int i = 0; i < (n << 1); ++i) s[i + 1] = s[i] + nums[i % n]; - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) mx = max(mx, s[j + 1] - s[i]); + int cnt = accumulate(nums.begin(), nums.begin() + k, 0); + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = max(mx, cnt); } - return cnt - mx; + return k - mx; } }; ``` ```go func minSwaps(nums []int) int { + k := 0 + for _, x := range nums { + k += x + } cnt := 0 - for _, v := range nums { - cnt += v + for i := 0; i < k; i++ { + cnt += nums[i] } + mx := cnt n := len(nums) - s := make([]int, (n<<1)+1) - for i := 0; i < (n << 1); i++ { - s[i+1] = s[i] + nums[i%n] - } - mx := 0 - for i := 0; i < (n << 1); i++ { - j := i + cnt - 1 - if j < (n << 1) { - mx = max(mx, s[j+1]-s[i]) - } + for i := k; i < n+k; i++ { + cnt += nums[i%n] - nums[(i-k+n)%n] + mx = max(mx, cnt) } - return cnt - mx + return k - mx } ``` ```ts function minSwaps(nums: number[]): number { + const k = nums.reduce((a, b) => a + b, 0); + let cnt = nums.slice(0, k).reduce((a, b) => a + b, 0); + let mx = cnt; const n = nums.length; - const m = nums.reduce((a, c) => a + c, 0); - let cnt = nums.reduce((a, c, i) => a + (i < m ? c : 0), 0); - let ans = cnt; - for (let i = m; i < m + n; i++) { - let prev = nums[i - m]; - let post = nums[i % n]; - cnt += post - prev; - ans = Math.max(cnt, ans); + for (let i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); + } + return k - mx; +} +``` + +```rust +impl Solution { + pub fn min_swaps(nums: Vec) -> i32 { + let k: i32 = nums.iter().sum(); + let n: usize = nums.len(); + let mut cnt: i32 = 0; + for i in 0..k { + cnt += nums[i as usize]; + } + let mut mx: i32 = cnt; + for i in k..(n as i32) + k { + cnt += + nums[(i % (n as i32)) as usize] - + nums[((i - k + (n as i32)) % (n as i32)) as usize]; + mx = mx.max(cnt); + } + return k - mx; + } +} +``` + +```cs +public class Solution { + public int MinSwaps(int[] nums) { + int k = nums.Sum(); + int n = nums.Length; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; + } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.Max(mx, cnt); + } + return k - mx; } - return m - ans; } ``` diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README_EN.md b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README_EN.md index 99dfbc16de6d4..150f1530cce00 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README_EN.md +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/README_EN.md @@ -57,46 +57,44 @@ Thus, the minimum number of swaps required is 0. ## Solutions -### Solution 1 +### Solution 1: Sliding Window + +First, we count the number of $1$s in the array, denoted as $k$. The problem is actually asking for a circular subarray of length $k$ that contains the maximum number of $1$s. Therefore, the minimum number of swaps is $k$ minus the maximum number of $1$s in that subarray. + +We can solve this problem using a sliding window. First, we count the number of $1$s in the first $k$ elements of the array, denoted as $cnt$. Then, we maintain a sliding window of length $k$. Each time we move the window one position to the right, we update $cnt$ and simultaneously update the maximum $cnt$ value, i.e., $mx = \max(mx, cnt)$. Finally, the answer is $k - mx$. + +The time complexity is $O(n)$, where $n$ is the length of the array $nums$. The space complexity is $O(1)$. ```python class Solution: def minSwaps(self, nums: List[int]) -> int: - cnt = nums.count(1) + k = nums.count(1) + mx = cnt = sum(nums[:k]) n = len(nums) - s = [0] * ((n << 1) + 1) - for i in range(n << 1): - s[i + 1] = s[i] + nums[i % n] - mx = 0 - for i in range(n << 1): - j = i + cnt - 1 - if j < (n << 1): - mx = max(mx, s[j + 1] - s[i]) - return cnt - mx + for i in range(k, n + k): + cnt += nums[i % n] + cnt -= nums[(i - k + n) % n] + mx = max(mx, cnt) + return k - mx ``` ```java class Solution { public int minSwaps(int[] nums) { - int cnt = 0; - for (int v : nums) { - cnt += v; - } + int k = Arrays.stream(nums).sum(); int n = nums.length; - int[] s = new int[(n << 1) + 1]; - for (int i = 0; i < (n << 1); ++i) { - s[i + 1] = s[i] + nums[i % n]; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; } - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) { - mx = Math.max(mx, s[j + 1] - s[i]); - } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); } - return cnt - mx; + return k - mx; } } ``` @@ -105,56 +103,90 @@ class Solution { class Solution { public: int minSwaps(vector& nums) { - int cnt = 0; - for (int& v : nums) cnt += v; + int k = accumulate(nums.begin(), nums.end(), 0); int n = nums.size(); - vector s((n << 1) + 1); - for (int i = 0; i < (n << 1); ++i) s[i + 1] = s[i] + nums[i % n]; - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) mx = max(mx, s[j + 1] - s[i]); + int cnt = accumulate(nums.begin(), nums.begin() + k, 0); + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = max(mx, cnt); } - return cnt - mx; + return k - mx; } }; ``` ```go func minSwaps(nums []int) int { + k := 0 + for _, x := range nums { + k += x + } cnt := 0 - for _, v := range nums { - cnt += v + for i := 0; i < k; i++ { + cnt += nums[i] } + mx := cnt n := len(nums) - s := make([]int, (n<<1)+1) - for i := 0; i < (n << 1); i++ { - s[i+1] = s[i] + nums[i%n] - } - mx := 0 - for i := 0; i < (n << 1); i++ { - j := i + cnt - 1 - if j < (n << 1) { - mx = max(mx, s[j+1]-s[i]) - } + for i := k; i < n+k; i++ { + cnt += nums[i%n] - nums[(i-k+n)%n] + mx = max(mx, cnt) } - return cnt - mx + return k - mx } ``` ```ts function minSwaps(nums: number[]): number { + const k = nums.reduce((a, b) => a + b, 0); + let cnt = nums.slice(0, k).reduce((a, b) => a + b, 0); + let mx = cnt; const n = nums.length; - const m = nums.reduce((a, c) => a + c, 0); - let cnt = nums.reduce((a, c, i) => a + (i < m ? c : 0), 0); - let ans = cnt; - for (let i = m; i < m + n; i++) { - let prev = nums[i - m]; - let post = nums[i % n]; - cnt += post - prev; - ans = Math.max(cnt, ans); + for (let i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); + } + return k - mx; +} +``` + +```rust +impl Solution { + pub fn min_swaps(nums: Vec) -> i32 { + let k: i32 = nums.iter().sum(); + let n: usize = nums.len(); + let mut cnt: i32 = 0; + for i in 0..k { + cnt += nums[i as usize]; + } + let mut mx: i32 = cnt; + for i in k..(n as i32) + k { + cnt += + nums[(i % (n as i32)) as usize] - + nums[((i - k + (n as i32)) % (n as i32)) as usize]; + mx = mx.max(cnt); + } + return k - mx; + } +} +``` + +```cs +public class Solution { + public int MinSwaps(int[] nums) { + int k = nums.Sum(); + int n = nums.Length; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; + } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.Max(mx, cnt); + } + return k - mx; } - return m - ans; } ``` diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cpp b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cpp index f0ea2dd571c24..b7b8c0fbaabaa 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cpp +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cpp @@ -1,16 +1,14 @@ class Solution { public: int minSwaps(vector& nums) { - int cnt = 0; - for (int& v : nums) cnt += v; + int k = accumulate(nums.begin(), nums.end(), 0); int n = nums.size(); - vector s((n << 1) + 1); - for (int i = 0; i < (n << 1); ++i) s[i + 1] = s[i] + nums[i % n]; - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) mx = max(mx, s[j + 1] - s[i]); + int cnt = accumulate(nums.begin(), nums.begin() + k, 0); + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = max(mx, cnt); } - return cnt - mx; + return k - mx; } }; \ No newline at end of file diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cs b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cs new file mode 100644 index 0000000000000..bab000ac4200b --- /dev/null +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.cs @@ -0,0 +1,16 @@ +public class Solution { + public int MinSwaps(int[] nums) { + int k = nums.Sum(); + int n = nums.Length; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; + } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.Max(mx, cnt); + } + return k - mx; + } +} \ No newline at end of file diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.go b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.go index fd174b827b0a4..766785d65d453 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.go +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.go @@ -1,19 +1,17 @@ func minSwaps(nums []int) int { + k := 0 + for _, x := range nums { + k += x + } cnt := 0 - for _, v := range nums { - cnt += v + for i := 0; i < k; i++ { + cnt += nums[i] } + mx := cnt n := len(nums) - s := make([]int, (n<<1)+1) - for i := 0; i < (n << 1); i++ { - s[i+1] = s[i] + nums[i%n] - } - mx := 0 - for i := 0; i < (n << 1); i++ { - j := i + cnt - 1 - if j < (n << 1) { - mx = max(mx, s[j+1]-s[i]) - } + for i := k; i < n+k; i++ { + cnt += nums[i%n] - nums[(i-k+n)%n] + mx = max(mx, cnt) } - return cnt - mx + return k - mx } \ No newline at end of file diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.java b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.java index f494573d15a33..645bc5201f7f3 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.java +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.java @@ -1,21 +1,16 @@ class Solution { public int minSwaps(int[] nums) { - int cnt = 0; - for (int v : nums) { - cnt += v; - } + int k = Arrays.stream(nums).sum(); int n = nums.length; - int[] s = new int[(n << 1) + 1]; - for (int i = 0; i < (n << 1); ++i) { - s[i + 1] = s[i] + nums[i % n]; + int cnt = 0; + for (int i = 0; i < k; ++i) { + cnt += nums[i]; } - int mx = 0; - for (int i = 0; i < (n << 1); ++i) { - int j = i + cnt - 1; - if (j < (n << 1)) { - mx = Math.max(mx, s[j + 1] - s[i]); - } + int mx = cnt; + for (int i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); } - return cnt - mx; + return k - mx; } } \ No newline at end of file diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.py b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.py index 287b9d861fb97..a7359dee53edf 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.py +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.py @@ -1,13 +1,10 @@ class Solution: def minSwaps(self, nums: List[int]) -> int: - cnt = nums.count(1) + k = nums.count(1) + mx = cnt = sum(nums[:k]) n = len(nums) - s = [0] * ((n << 1) + 1) - for i in range(n << 1): - s[i + 1] = s[i] + nums[i % n] - mx = 0 - for i in range(n << 1): - j = i + cnt - 1 - if j < (n << 1): - mx = max(mx, s[j + 1] - s[i]) - return cnt - mx + for i in range(k, n + k): + cnt += nums[i % n] + cnt -= nums[(i - k + n) % n] + mx = max(mx, cnt) + return k - mx diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.rs b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.rs new file mode 100644 index 0000000000000..ad29456ae0a9c --- /dev/null +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.rs @@ -0,0 +1,18 @@ +impl Solution { + pub fn min_swaps(nums: Vec) -> i32 { + let k: i32 = nums.iter().sum(); + let n: usize = nums.len(); + let mut cnt: i32 = 0; + for i in 0..k { + cnt += nums[i as usize]; + } + let mut mx: i32 = cnt; + for i in k..(n as i32) + k { + cnt += + nums[(i % (n as i32)) as usize] - + nums[((i - k + (n as i32)) % (n as i32)) as usize]; + mx = mx.max(cnt); + } + return k - mx; + } +} diff --git a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.ts b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.ts index cc6bf5cc92d3b..6c616343055a4 100644 --- a/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.ts +++ b/solution/2100-2199/2134.Minimum Swaps to Group All 1's Together II/Solution.ts @@ -1,13 +1,11 @@ function minSwaps(nums: number[]): number { + const k = nums.reduce((a, b) => a + b, 0); + let cnt = nums.slice(0, k).reduce((a, b) => a + b, 0); + let mx = cnt; const n = nums.length; - const m = nums.reduce((a, c) => a + c, 0); - let cnt = nums.reduce((a, c, i) => a + (i < m ? c : 0), 0); - let ans = cnt; - for (let i = m; i < m + n; i++) { - let prev = nums[i - m]; - let post = nums[i % n]; - cnt += post - prev; - ans = Math.max(cnt, ans); + for (let i = k; i < n + k; ++i) { + cnt += nums[i % n] - nums[(i - k + n) % n]; + mx = Math.max(mx, cnt); } - return m - ans; + return k - mx; }