diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README.md b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README.md index 24e22b57c188f..ac0a450546314 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README.md +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README.md @@ -65,13 +65,15 @@ tags: ### 方法一：差分数组 -我们可以使用差分数组的思想，对于每个区间 $[l, r]$，我们将 $diff[l]$ 加 $1$，将 $diff[r + 1]$ 减 $1$。 +我们可以使用差分数组的思想，创建一个长度为 $52$ 的差分数组 $\textit{diff}$。 -最后遍历差分数组，累加每个位置的值，记为 $cur$，如果 $left \le i \le right$ 且 $cur = 0$，则说明 $i$ 没有被任何区间覆盖，返回 `false`。 +接下来，我们遍历数组 $\textit{ranges}$，对于每个区间 $[l, r]$，我们令 $\textit{diff}[l]$ 自增 $1$，而 $\textit{diff}[r + 1]$ 自减 $1$。 -否则遍历结束后，返回 `true`。 +接着，我们遍历差分数组 $\textit{diff}$，维护一个前缀和 $s$，对于每个位置 $i$，我们令 $s$ 自增 $\textit{diff}[i]$，如果 $s \le 0$ 且 $left \le i \le right$，则说明区间 $[left, right]$ 中有一个整数 $i$ 没有被覆盖，返回 $\textit{false}$。 -时间复杂度 $O(n + M)$，空间复杂度 $O(M)$。其中 $n$ 和 $M$ 分别为区间的数量和区间的范围。 +如果遍历完差分数组 $\textit{diff}$ 后都没有返回 $\textit{false}$，则说明区间 $[left, right]$ 中的每个整数都被 $\textit{ranges}$ 中至少一个区间覆盖，返回 $\textit{true}$。 + +时间复杂度 $O(n + M)$，空间复杂度 $O(M)$。其中 $n$ 是数组 $\textit{ranges}$ 的长度，而 $M$ 是区间的最大值，本题中 $M \le 50$。 @@ -84,10 +86,10 @@ class Solution: for l, r in ranges: diff[l] += 1 diff[r + 1] -= 1 - cur = 0 + s = 0 for i, x in enumerate(diff): - cur += x - if left <= i <= right and cur == 0: + s += x + if s <= 0 and left <= i <= right: return False return True ``` @@ -103,10 +105,10 @@ class Solution { ++diff[l]; --diff[r + 1]; } - int cur = 0; + int s = 0; for (int i = 0; i < diff.length; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur == 0) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -121,16 +123,16 @@ class Solution { class Solution { public: bool isCovered(vector>& ranges, int left, int right) { - int diff[52]{}; + vector diff(52); for (auto& range : ranges) { int l = range[0], r = range[1]; ++diff[l]; --diff[r + 1]; } - int cur = 0; - for (int i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + int s = 0; + for (int i = 0; i < diff.size(); ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -144,15 +146,15 @@ public: ```go func isCovered(ranges [][]int, left int, right int) bool { diff := [52]int{} - for _, rg := range ranges { - l, r := rg[0], rg[1] + for _, e := range ranges { + l, r := e[0], e[1] diff[l]++ diff[r+1]-- } - cur := 0 + s := 0 for i, x := range diff { - cur += x - if i >= left && i <= right && cur <= 0 { + s += x + if s <= 0 && left <= i && i <= right { return false } } @@ -164,15 +166,15 @@ func isCovered(ranges [][]int, left int, right int) bool { ```ts function isCovered(ranges: number[][], left: number, right: number): boolean { - const diff = new Array(52).fill(0); + const diff: number[] = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -190,15 +192,15 @@ function isCovered(ranges: number[][], left: number, right: number): boolean { * @return {boolean} */ var isCovered = function (ranges, left, right) { - const diff = new Array(52).fill(0); + const diff = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README_EN.md b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README_EN.md index 0952f79b6a358..0c03b5abdeca4 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README_EN.md +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/README_EN.md @@ -61,7 +61,17 @@ tags: -### Solution 1 +### Solution 1: Difference Array + +We can use the idea of a difference array to create a difference array $\textit{diff}$ of length $52$. + +Next, we iterate through the array $\textit{ranges}$. For each interval $[l, r]$, we increment $\textit{diff}[l]$ by $1$ and decrement $\textit{diff}[r + 1]$ by $1$. + +Then, we iterate through the difference array $\textit{diff}$, maintaining a prefix sum $s$. For each position $i$, we increment $s$ by $\textit{diff}[i]$. If $s \le 0$ and $left \le i \le right$, it indicates that an integer $i$ within the interval $[left, right]$ is not covered, and we return $\textit{false}$. + +If we finish iterating through the difference array $\textit{diff}$ without returning $\textit{false}$, it means that every integer within the interval $[left, right]$ is covered by at least one interval in $\textit{ranges}$, and we return $\textit{true}$. + +The time complexity is $O(n + M)$, and the space complexity is $O(M)$. Here, $n$ is the length of the array $\textit{ranges}$, and $M$ is the maximum value of the interval, which in this case is $M \le 50$. @@ -74,10 +84,10 @@ class Solution: for l, r in ranges: diff[l] += 1 diff[r + 1] -= 1 - cur = 0 + s = 0 for i, x in enumerate(diff): - cur += x - if left <= i <= right and cur == 0: + s += x + if s <= 0 and left <= i <= right: return False return True ``` @@ -93,10 +103,10 @@ class Solution { ++diff[l]; --diff[r + 1]; } - int cur = 0; + int s = 0; for (int i = 0; i < diff.length; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur == 0) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -111,16 +121,16 @@ class Solution { class Solution { public: bool isCovered(vector>& ranges, int left, int right) { - int diff[52]{}; + vector diff(52); for (auto& range : ranges) { int l = range[0], r = range[1]; ++diff[l]; --diff[r + 1]; } - int cur = 0; - for (int i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + int s = 0; + for (int i = 0; i < diff.size(); ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -134,15 +144,15 @@ public: ```go func isCovered(ranges [][]int, left int, right int) bool { diff := [52]int{} - for _, rg := range ranges { - l, r := rg[0], rg[1] + for _, e := range ranges { + l, r := e[0], e[1] diff[l]++ diff[r+1]-- } - cur := 0 + s := 0 for i, x := range diff { - cur += x - if i >= left && i <= right && cur <= 0 { + s += x + if s <= 0 && left <= i && i <= right { return false } } @@ -154,15 +164,15 @@ func isCovered(ranges [][]int, left int, right int) bool { ```ts function isCovered(ranges: number[][], left: number, right: number): boolean { - const diff = new Array(52).fill(0); + const diff: number[] = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } @@ -180,15 +190,15 @@ function isCovered(ranges: number[][], left: number, right: number): boolean { * @return {boolean} */ var isCovered = function (ranges, left, right) { - const diff = new Array(52).fill(0); + const diff = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.cpp b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.cpp index 0da3e6350bb99..821bbf7d0c091 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.cpp +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.cpp @@ -1,16 +1,16 @@ class Solution { public: bool isCovered(vector>& ranges, int left, int right) { - int diff[52]{}; + vector diff(52); for (auto& range : ranges) { int l = range[0], r = range[1]; ++diff[l]; --diff[r + 1]; } - int cur = 0; - for (int i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + int s = 0; + for (int i = 0; i < diff.size(); ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.go b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.go index 74599b41f40d3..2f71488f305bd 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.go +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.go @@ -1,14 +1,14 @@ func isCovered(ranges [][]int, left int, right int) bool { diff := [52]int{} - for _, rg := range ranges { - l, r := rg[0], rg[1] + for _, e := range ranges { + l, r := e[0], e[1] diff[l]++ diff[r+1]-- } - cur := 0 + s := 0 for i, x := range diff { - cur += x - if i >= left && i <= right && cur <= 0 { + s += x + if s <= 0 && left <= i && i <= right { return false } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.java b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.java index cbda82e1469fc..f587208213b4f 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.java +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.java @@ -6,10 +6,10 @@ public boolean isCovered(int[][] ranges, int left, int right) { ++diff[l]; --diff[r + 1]; } - int cur = 0; + int s = 0; for (int i = 0; i < diff.length; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur == 0) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.js b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.js index e28bea7e11ba6..530c2368bbeae 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.js +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.js @@ -5,15 +5,15 @@ * @return {boolean} */ var isCovered = function (ranges, left, right) { - const diff = new Array(52).fill(0); + const diff = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.py b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.py index 2e231f185a62a..f28b947d0e0fb 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.py +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.py @@ -4,9 +4,9 @@ def isCovered(self, ranges: List[List[int]], left: int, right: int) -> bool: for l, r in ranges: diff[l] += 1 diff[r + 1] -= 1 - cur = 0 + s = 0 for i, x in enumerate(diff): - cur += x - if left <= i <= right and cur == 0: + s += x + if s <= 0 and left <= i <= right: return False return True diff --git a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.ts b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.ts index 97e03b7bee50e..fe11ff60392db 100644 --- a/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.ts +++ b/solution/1800-1899/1893.Check if All the Integers in a Range Are Covered/Solution.ts @@ -1,13 +1,13 @@ function isCovered(ranges: number[][], left: number, right: number): boolean { - const diff = new Array(52).fill(0); + const diff: number[] = Array(52).fill(0); for (const [l, r] of ranges) { ++diff[l]; --diff[r + 1]; } - let cur = 0; - for (let i = 0; i < 52; ++i) { - cur += diff[i]; - if (i >= left && i <= right && cur <= 0) { + let s = 0; + for (let i = 0; i < diff.length; ++i) { + s += diff[i]; + if (s <= 0 && left <= i && i <= right) { return false; } } diff --git a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README.md b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README.md index 6f3b6008fa4c4..52b60e46aace6 100644 --- a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README.md +++ b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README.md @@ -161,10 +161,7 @@ func chalkReplacer(chalk []int, k int) int { ```ts function chalkReplacer(chalk: number[], k: number): number { - let s = 0; - for (const x of chalk) { - s += x; - } + const s = chalk.reduce((acc, cur) => acc + cur, 0); k %= s; for (let i = 0; ; ++i) { if (k < chalk[i]) { diff --git a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README_EN.md b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README_EN.md index 56f3439def7e9..bc6288fca1cc6 100644 --- a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README_EN.md +++ b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/README_EN.md @@ -159,10 +159,7 @@ func chalkReplacer(chalk []int, k int) int { ```ts function chalkReplacer(chalk: number[], k: number): number { - let s = 0; - for (const x of chalk) { - s += x; - } + const s = chalk.reduce((acc, cur) => acc + cur, 0); k %= s; for (let i = 0; ; ++i) { if (k < chalk[i]) { diff --git a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/Solution.ts b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/Solution.ts index 4c4e55915d353..39859d65a9bf7 100644 --- a/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/Solution.ts +++ b/solution/1800-1899/1894.Find the Student that Will Replace the Chalk/Solution.ts @@ -1,8 +1,5 @@ function chalkReplacer(chalk: number[], k: number): number { - let s = 0; - for (const x of chalk) { - s += x; - } + const s = chalk.reduce((acc, cur) => acc + cur, 0); k %= s; for (let i = 0; ; ++i) { if (k < chalk[i]) { diff --git a/solution/3200-3299/3213.Construct String with Minimum Cost/README.md b/solution/3200-3299/3213.Construct String with Minimum Cost/README.md index 5a2d06667d114..c2b9f03bdfdfc 100644 --- a/solution/3200-3299/3213.Construct String with Minimum Cost/README.md +++ b/solution/3200-3299/3213.Construct String with Minimum Cost/README.md @@ -92,7 +92,7 @@ $$ f[i] = \min(f[i], f[i - j] + \textit{cost}[k]) $$ -其中 $textit{cost}[k]$ 表示长度为 $j$ 的单词且哈希值与 $\textit{target}[i - j + 1, i]$ 相同的单词的最小代价。 +其中 $\textit{cost}[k]$ 表示长度为 $j$ 的单词且哈希值与 $\textit{target}[i - j + 1, i]$ 相同的单词的最小代价。 时间复杂度 $O(n \times \sqrt{L})$，空间复杂度 $O(n)$。其中 $n$ 是 $\textit{target}$ 的长度，而 $L$ 是数组 $\textit{words}$ 中所有单词的长度之和。