+ problem 2571

Author: fruit-in

Problemset/2571-Minimum Operations to Reduce an Integer to 0/README.md

@@ -0,0 +1,67 @@
+# 2571. Minimum Operations to Reduce an Integer to 0
+You are given a positive integer `n`, you can do the following operation **any** number of times:
+* Add or subtract a **power** of `2` from `n`.
+
+Return *the **minimum** number of operations to make* `n` *equal to* `0`.
+
+A number `x` is power of `2` if <code>x == 2<sup>i</sup></code> where `i >= 0`.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> n = 39
+<strong>Output:</strong> 3
+<strong>Explanation:</strong> We can do the following operations:
+- Add 2<sup>0</sup> = 1 to n, so now n = 40.
+- Subtract 2<sup>3</sup> = 8 from n, so now n = 32.
+- Subtract 2<sup>5</sup> = 32 from n, so now n = 0.
+It can be shown that 3 is the minimum number of operations we need to make n equal to 0.
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> n = 54
+<strong>Output:</strong> 3
+<strong>Explanation:</strong> We can do the following operations:
+- Add 2<sup>1</sup> = 2 to n, so now n = 56.
+- Add 2<sup>3</sup> = 8 to n, so now n = 64.
+- Subtract 2<sup>6</sup> = 64 from n, so now n = 0.
+So the minimum number of operations is 3.
+</pre>
+
+#### Constraints:
+* <code>1 <= n <= 10<sup>5</sup></code>
+
+## Solutions (Rust)
+
+### 1. Solution
+```Rust
+use std::collections::VecDeque;
+
+impl Solution {
+    pub fn min_operations(n: i32) -> i32 {
+        let m = n.ilog2() + 1;
+        let mut deque = VecDeque::from([(n as usize, 0)]);
+        let mut visited = vec![false; (1 << m) + 1];
+        visited[n as usize] = true;
+
+        while let Some((x, steps)) = deque.pop_front() {
+            if x == 0 {
+                return steps;
+            }
+
+            for i in 0..=m {
+                if x + (1 << i) < visited.len() && !visited[x + (1 << i)] {
+                    deque.push_back((x + (1 << i), steps + 1));
+                    visited[x + (1 << i)] = true;
+                }
+                if x >= 1 << i && !visited[x - (1 << i)] {
+                    deque.push_back((x - (1 << i), steps + 1));
+                    visited[x - (1 << i)] = true;
+                }
+            }
+        }
+
+        unreachable!()
+    }
+}
+```

Problemset/2571-Minimum Operations to Reduce an Integer to 0/README_CN.md

@@ -0,0 +1,67 @@
+# 2571. 将整数减少到零需要的最少操作数
+给你一个正整数 `n` ，你可以执行下述操作 **任意** 次：
+* `n` 加上或减去 `2` 的某个 **幂**
+
+返回使 `n` 等于 `0` 需要执行的 **最少** 操作数。
+
+如果 <code>x == 2<sup>i</sup></code> 且其中 `i >= 0` ，则数字 `x` 是 `2` 的幂。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> n = 39
+<strong>输出:</strong> 3
+<strong>解释:</strong> 我们可以执行下述操作：
+- n 加上 2<sup>0</sup> = 1 ，得到 n = 40 。
+- n 减去 2<sup>3</sup> = 8 ，得到 n = 32 。
+- n 减去 2<sup>5</sup> = 32 ，得到 n = 0 。
+可以证明使 n 等于 0 需要执行的最少操作数是 3 。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> n = 54
+<strong>输出:</strong> 3
+<strong>解释:</strong> 我们可以执行下述操作：
+- n 加上 2<sup>1</sup> = 2 ，得到 n = 56 。
+- n 加上 2<sup>3</sup> = 8 ，得到 n = 64 。
+- n 减去 2<sup>6</sup> = 64 ，得到 n = 0 。
+使 n 等于 0 需要执行的最少操作数是 3 。
+</pre>
+
+#### 提示:
+* <code>1 <= n <= 10<sup>5</sup></code>
+
+## 题解 (Rust)
+
+### 1. 题解
+```Rust
+use std::collections::VecDeque;
+
+impl Solution {
+    pub fn min_operations(n: i32) -> i32 {
+        let m = n.ilog2() + 1;
+        let mut deque = VecDeque::from([(n as usize, 0)]);
+        let mut visited = vec![false; (1 << m) + 1];
+        visited[n as usize] = true;
+
+        while let Some((x, steps)) = deque.pop_front() {
+            if x == 0 {
+                return steps;
+            }
+
+            for i in 0..=m {
+                if x + (1 << i) < visited.len() && !visited[x + (1 << i)] {
+                    deque.push_back((x + (1 << i), steps + 1));
+                    visited[x + (1 << i)] = true;
+                }
+                if x >= 1 << i && !visited[x - (1 << i)] {
+                    deque.push_back((x - (1 << i), steps + 1));
+                    visited[x - (1 << i)] = true;
+                }
+            }
+        }
+
+        unreachable!()
+    }
+}
+```

Problemset/2571-Minimum Operations to Reduce an Integer to 0/Solution.rs

@@ -0,0 +1,29 @@
+use std::collections::VecDeque;
+
+impl Solution {
+    pub fn min_operations(n: i32) -> i32 {
+        let m = n.ilog2() + 1;
+        let mut deque = VecDeque::from([(n as usize, 0)]);
+        let mut visited = vec![false; (1 << m) + 1];
+        visited[n as usize] = true;
+
+        while let Some((x, steps)) = deque.pop_front() {
+            if x == 0 {
+                return steps;
+            }
+
+            for i in 0..=m {
+                if x + (1 << i) < visited.len() && !visited[x + (1 << i)] {
+                    deque.push_back((x + (1 << i), steps + 1));
+                    visited[x + (1 << i)] = true;
+                }
+                if x >= 1 << i && !visited[x - (1 << i)] {
+                    deque.push_back((x - (1 << i), steps + 1));
+                    visited[x - (1 << i)] = true;
+                }
+            }
+        }
+
+        unreachable!()
+    }
+}

README.md

@@ -1834,6 +1834,7 @@
 [2567][2567l]|[Minimum Score by Changing Two Elements][2567]                                        |![rs]
 [2568][2568l]|[Minimum Impossible OR][2568]                                                         |![rs]
 [2570][2570l]|[Merge Two 2D Arrays by Summing Values][2570]                                         |![rs]
+[2571][2571l]|[Minimum Operations to Reduce an Integer to 0][2571]                                  |![rs]
 [2572][2572l]|[Count the Number of Square-Free Subsets][2572]                                       |![rs]
 [2574][2574l]|[Left and Right Sum Differences][2574]                                                |![rs]
 [2575][2575l]|[Find the Divisibility Array of a String][2575]                                       |![rs]
@@ -3710,6 +3711,7 @@
 [2567]:Problemset/2567-Minimum%20Score%20by%20Changing%20Two%20Elements/README.md#2567-minimum-score-by-changing-two-elements
 [2568]:Problemset/2568-Minimum%20Impossible%20OR/README.md#2568-minimum-impossible-or
 [2570]:Problemset/2570-Merge%20Two%202D%20Arrays%20by%20Summing%20Values/README.md#2570-merge-two-2d-arrays-by-summing-values
+[2571]:Problemset/2571-Minimum%20Operations%20to%20Reduce%20an%20Integer%20to%200/README.md#2571-minimum-operations-to-reduce-an-integer-to-0
 [2572]:Problemset/2572-Count%20the%20Number%20of%20Square-Free%20Subsets/README.md#2572-count-the-number-of-square-free-subsets
 [2574]:Problemset/2574-Left%20and%20Right%20Sum%20Differences/README.md#2574-left-and-right-sum-differences
 [2575]:Problemset/2575-Find%20the%20Divisibility%20Array%20of%20a%20String/README.md#2575-find-the-divisibility-array-of-a-string
@@ -5580,6 +5582,7 @@
 [2567l]:https://leetcode.com/problems/minimum-score-by-changing-two-elements/
 [2568l]:https://leetcode.com/problems/minimum-impossible-or/
 [2570l]:https://leetcode.com/problems/merge-two-2d-arrays-by-summing-values/
+[2571l]:https://leetcode.com/problems/minimum-operations-to-reduce-an-integer-to-0/
 [2572l]:https://leetcode.com/problems/count-the-number-of-square-free-subsets/
 [2574l]:https://leetcode.com/problems/left-and-right-sum-differences/
 [2575l]:https://leetcode.com/problems/find-the-divisibility-array-of-a-string/

README_CN.md

@@ -1834,6 +1834,7 @@
 [2567][2567l]|[修改两个元素的最小分数][2567]                            |![rs]
 [2568][2568l]|[最小无法得到的或值][2568]                                |![rs]
 [2570][2570l]|[合并两个二维数组 - 求和法][2570]                         |![rs]
+[2571][2571l]|[将整数减少到零需要的最少操作数][2571]                    |![rs]
 [2572][2572l]|[无平方子集计数][2572]                                    |![rs]
 [2574][2574l]|[左右元素和的差值][2574]                                  |![rs]
 [2575][2575l]|[找出字符串的可整除数组][2575]                            |![rs]
@@ -3710,6 +3711,7 @@
 [2567]:Problemset/2567-Minimum%20Score%20by%20Changing%20Two%20Elements/README_CN.md#2567-修改两个元素的最小分数
 [2568]:Problemset/2568-Minimum%20Impossible%20OR/README_CN.md#2568-最小无法得到的或值
 [2570]:Problemset/2570-Merge%20Two%202D%20Arrays%20by%20Summing%20Values/README_CN.md#2570-合并两个二维数组---求和法
+[2571]:Problemset/2571-Minimum%20Operations%20to%20Reduce%20an%20Integer%20to%200/README_CN.md#2571-将整数减少到零需要的最少操作数
 [2572]:Problemset/2572-Count%20the%20Number%20of%20Square-Free%20Subsets/README_CN.md#2572-无平方子集计数
 [2574]:Problemset/2574-Left%20and%20Right%20Sum%20Differences/README_CN.md#2574-左右元素和的差值
 [2575]:Problemset/2575-Find%20the%20Divisibility%20Array%20of%20a%20String/README_CN.md#2575-找出字符串的可整除数组
@@ -5580,6 +5582,7 @@
 [2567l]:https://leetcode.cn/problems/minimum-score-by-changing-two-elements/
 [2568l]:https://leetcode.cn/problems/minimum-impossible-or/
 [2570l]:https://leetcode.cn/problems/merge-two-2d-arrays-by-summing-values/
+[2571l]:https://leetcode.cn/problems/minimum-operations-to-reduce-an-integer-to-0/
 [2572l]:https://leetcode.cn/problems/count-the-number-of-square-free-subsets/
 [2574l]:https://leetcode.cn/problems/left-and-right-sum-differences/
 [2575l]:https://leetcode.cn/problems/find-the-divisibility-array-of-a-string/