diff --git a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README.md b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README.md index a94e4baeba78e..68e8a16fb7729 100644 --- a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README.md +++ b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README.md @@ -61,7 +61,7 @@ tags: 输出：1 解释： 第 0 分钟开始时，怪物的距离是 [3,2,4]，你消灭了第一个怪物。 -第 1 分钟开始时，怪物的距离是 [X,0,2]，你输掉了游戏。 +第 1 分钟开始时，怪物的距离是 [X,0,2]，你输掉了游戏。 你只能消灭 1 个怪物。 @@ -83,13 +83,13 @@ tags: ### 方法一：排序 + 贪心 -我们用 $times$ 数组记录每个怪物最晚可被消灭的时间。对于第 $i$ 个怪物，最晚可被消灭的时间满足： +我们用 $\textit{times}$ 数组记录每个怪物最晚可被消灭的时间。对于第 $i$ 个怪物，最晚可被消灭的时间满足： -$$times[i] = \lfloor \frac{dist[i]-1}{speed[i]} \rfloor$$ +$$\textit{times}[i] = \left\lfloor \frac{\textit{dist}[i]-1}{\textit{speed}[i]} \right\rfloor$$ -接下来，我们对 $times$ 数组升序排列。 +接下来，我们对 $\textit{times}$ 数组升序排列。 -然后遍历 $times$ 数组，对于第 $i$ 个怪物，如果 $times[i] \geq i$，说明第 $i$ 个怪物可以被消灭，否则说明第 $i$ 个怪物无法被消灭，直接返回 $i$ 即可。 +然后遍历 $\textit{times}$ 数组，对于第 $i$ 个怪物，如果 $\textit{times}[i] \geq i$，说明第 $i$ 个怪物可以被消灭，否则说明第 $i$ 个怪物无法被消灭，直接返回 $i$ 即可。 若所有怪物都可以被消灭，则返回 $n$。 @@ -176,7 +176,7 @@ func eliminateMaximum(dist []int, speed []int) int { ```ts function eliminateMaximum(dist: number[], speed: number[]): number { const n = dist.length; - const times = new Array(n).fill(0); + const times: number[] = Array(n).fill(0); for (let i = 0; i < n; ++i) { times[i] = Math.floor((dist[i] - 1) / speed[i]); } @@ -199,17 +199,18 @@ function eliminateMaximum(dist: number[], speed: number[]): number { * @return {number} */ var eliminateMaximum = function (dist, speed) { - let arr = []; - for (let i = 0; i < dist.length; i++) { - arr[i] = dist[i] / speed[i]; + const n = dist.length; + const times = Array(n).fill(0); + for (let i = 0; i < n; ++i) { + times[i] = Math.floor((dist[i] - 1) / speed[i]); } - arr.sort((a, b) => a - b); - let ans = 0; - while (arr[0] > ans) { - arr.shift(); - ++ans; + times.sort((a, b) => a - b); + for (let i = 0; i < n; ++i) { + if (times[i] < i) { + return i; + } } - return ans; + return n; }; ``` diff --git a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README_EN.md b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README_EN.md index d4bb1dc74e0e8..34cca9242ad0b 100644 --- a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README_EN.md +++ b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/README_EN.md @@ -79,7 +79,19 @@ You can only eliminate 1 monster. -### Solution 1 +### Solution 1: Sorting + Greedy + +We use the $\textit{times}$ array to record the latest time each monster can be eliminated. For the $i$-th monster, the latest time it can be eliminated is: + +$$\textit{times}[i] = \left\lfloor \frac{\textit{dist}[i]-1}{\textit{speed}[i]} \right\rfloor$$ + +Next, we sort the $\textit{times}$ array in ascending order. + +Then, we traverse the $\textit{times}$ array. For the $i$-th monster, if $\textit{times}[i] \geq i$, it means the $i$-th monster can be eliminated. Otherwise, it means the $i$-th monster cannot be eliminated, and we return $i$ immediately. + +If all monsters can be eliminated, we return $n$. + +The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array. @@ -162,7 +174,7 @@ func eliminateMaximum(dist []int, speed []int) int { ```ts function eliminateMaximum(dist: number[], speed: number[]): number { const n = dist.length; - const times = new Array(n).fill(0); + const times: number[] = Array(n).fill(0); for (let i = 0; i < n; ++i) { times[i] = Math.floor((dist[i] - 1) / speed[i]); } @@ -185,21 +197,22 @@ function eliminateMaximum(dist: number[], speed: number[]): number { * @return {number} */ var eliminateMaximum = function (dist, speed) { - let arr = []; - for (let i = 0; i < dist.length; i++) { - arr[i] = dist[i] / speed[i]; + const n = dist.length; + const times = Array(n).fill(0); + for (let i = 0; i < n; ++i) { + times[i] = Math.floor((dist[i] - 1) / speed[i]); } - arr.sort((a, b) => a - b); - let ans = 0; - while (arr[0] > ans) { - arr.shift(); - ++ans; + times.sort((a, b) => a - b); + for (let i = 0; i < n; ++i) { + if (times[i] < i) { + return i; + } } - return ans; + return n; }; ``` -#### C# +#### C ```cs public class Solution { diff --git a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.js b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.js index d3a74bb0d7f43..e20224d448d3e 100644 --- a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.js +++ b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.js @@ -4,15 +4,16 @@ * @return {number} */ var eliminateMaximum = function (dist, speed) { - let arr = []; - for (let i = 0; i < dist.length; i++) { - arr[i] = dist[i] / speed[i]; + const n = dist.length; + const times = Array(n).fill(0); + for (let i = 0; i < n; ++i) { + times[i] = Math.floor((dist[i] - 1) / speed[i]); } - arr.sort((a, b) => a - b); - let ans = 0; - while (arr[0] > ans) { - arr.shift(); - ++ans; + times.sort((a, b) => a - b); + for (let i = 0; i < n; ++i) { + if (times[i] < i) { + return i; + } } - return ans; + return n; }; diff --git a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.ts b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.ts index 67ff723647b76..26e8b390ee441 100644 --- a/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.ts +++ b/solution/1900-1999/1921.Eliminate Maximum Number of Monsters/Solution.ts @@ -1,6 +1,6 @@ function eliminateMaximum(dist: number[], speed: number[]): number { const n = dist.length; - const times = new Array(n).fill(0); + const times: number[] = Array(n).fill(0); for (let i = 0; i < n; ++i) { times[i] = Math.floor((dist[i] - 1) / speed[i]); } diff --git a/solution/1900-1999/1922.Count Good Numbers/README.md b/solution/1900-1999/1922.Count Good Numbers/README.md index e7054911b43c7..d21de809345f0 100644 --- a/solution/1900-1999/1922.Count Good Numbers/README.md +++ b/solution/1900-1999/1922.Count Good Numbers/README.md @@ -77,17 +77,7 @@ tags: class Solution: def countGoodNumbers(self, n: int) -> int: mod = 10**9 + 7 - - def myPow(x, n): - res = 1 - while n: - if (n & 1) == 1: - res = res * x % mod - x = x * x % mod - n >>= 1 - return res - - return myPow(5, (n + 1) >> 1) * myPow(4, n >> 1) % mod + return pow(5, (n + 1) >> 1, mod) * pow(4, n >> 1, mod) % mod ``` #### Java diff --git a/solution/1900-1999/1922.Count Good Numbers/README_EN.md b/solution/1900-1999/1922.Count Good Numbers/README_EN.md index b69c7c28f34a5..31c5d830c607c 100644 --- a/solution/1900-1999/1922.Count Good Numbers/README_EN.md +++ b/solution/1900-1999/1922.Count Good Numbers/README_EN.md @@ -75,17 +75,7 @@ tags: class Solution: def countGoodNumbers(self, n: int) -> int: mod = 10**9 + 7 - - def myPow(x, n): - res = 1 - while n: - if (n & 1) == 1: - res = res * x % mod - x = x * x % mod - n >>= 1 - return res - - return myPow(5, (n + 1) >> 1) * myPow(4, n >> 1) % mod + return pow(5, (n + 1) >> 1, mod) * pow(4, n >> 1, mod) % mod ``` #### Java diff --git a/solution/1900-1999/1922.Count Good Numbers/Solution.py b/solution/1900-1999/1922.Count Good Numbers/Solution.py index 0fcdb625ecbc6..8383d6a0e41df 100644 --- a/solution/1900-1999/1922.Count Good Numbers/Solution.py +++ b/solution/1900-1999/1922.Count Good Numbers/Solution.py @@ -1,14 +1,4 @@ class Solution: def countGoodNumbers(self, n: int) -> int: mod = 10**9 + 7 - - def myPow(x, n): - res = 1 - while n: - if (n & 1) == 1: - res = res * x % mod - x = x * x % mod - n >>= 1 - return res - - return myPow(5, (n + 1) >> 1) * myPow(4, n >> 1) % mod + return pow(5, (n + 1) >> 1, mod) * pow(4, n >> 1, mod) % mod