From 84883feb9262627b59e9b6e658be37de394ed1aa Mon Sep 17 00:00:00 2001
From: Xu Shaohua <shaohua@biofan.org>
Date: Mon, 29 Jul 2024 11:10:07 +0800
Subject: [PATCH] leetcode: Add index to 2485

---
 src/SUMMARY.md                                |  2 +
 .../2485.find-the-pivot-integer/Cargo.toml    |  2 +-
 .../2485.find-the-pivot-integer/index.md      | 53 ++++++++++++++++++-
 .../2485.find-the-pivot-integer/src/main.rs   |  7 ++-
 src/leetcode/by-id/2401-2500.md               |  1 +
 src/leetcode/tags/prefix-sum.md               |  7 +--
 6 files changed, 64 insertions(+), 8 deletions(-)
 create mode 100644 src/leetcode/by-id/2401-2500.md

diff --git a/src/SUMMARY.md b/src/SUMMARY.md
index cc8680bbd..031917a38 100644
--- a/src/SUMMARY.md
+++ b/src/SUMMARY.md
@@ -300,6 +300,8 @@
     - [2101-2200](leetcode/by-id/2101-2200.md)
         - [2108. 找出数组中的第一个回文字符串 Find First Palindromic String in the Array](leetcode/2108.find-first-palindromic-string-in-the-array/index.md)
         - [2119. 反转两次的数字 A Number After a Double Reversal](leetcode/2119.a-number-after-a-double-reversal/index.md)
+    - [2401-2500](leetcode/by-id/2401-2500.md)
+        - [2485. 找出中枢整数 Find the Pivot Integer](leetcode/2485.find-the-pivot-integer/index.md)
     - [2501-2600](leetcode/by-id/2501-2600.md)
         - [2574. 左右元素和的差值 Left and Right Sum Differences](leetcode/2574.left-and-right-sum-differences/index.md)
     - [2801-2900](leetcode/by-id/2801-2900.md)
diff --git a/src/leetcode/2485.find-the-pivot-integer/Cargo.toml b/src/leetcode/2485.find-the-pivot-integer/Cargo.toml
index 06d239521..4a9f56f94 100644
--- a/src/leetcode/2485.find-the-pivot-integer/Cargo.toml
+++ b/src/leetcode/2485.find-the-pivot-integer/Cargo.toml
@@ -1,5 +1,5 @@
 [package]
-name = "lc-0000-name"
+name = "lc-2485-find-the-pivot-integer"
 version = "0.1.0"
 edition = "2021"
 publish = false
diff --git a/src/leetcode/2485.find-the-pivot-integer/index.md b/src/leetcode/2485.find-the-pivot-integer/index.md
index 845f89887..2b581b518 100644
--- a/src/leetcode/2485.find-the-pivot-integer/index.md
+++ b/src/leetcode/2485.find-the-pivot-integer/index.md
@@ -1,4 +1,53 @@
+# 2485. 找出中枢整数 Find the Pivot Integer
 
-# 
+[问题描述](https://leetcode.com/problems/find-the-pivot-integer)
 
-[问题描述](https://leetcode.com/problems/)
+这个问题的解法就比较多了.
+
+## 前缀和 Prefix Sum
+
+根据问题中的描述, 可以直接想到的方法就是前缀和.
+
+处理步骤如下:
+
+1. 构造 `[1..=n]` 的前缀和数组
+2. 遍历前缀和数组, 如果左侧部分等于右侧部分, 就返回, `prefix * 2 == total_sum + i as i32`
+3. 否则没有找到, 就返回 -1
+
+代码实现如下:
+
+```rust
+{{#include src/main.rs:5:28}}
+```
+
+该算法的时间复杂度是 `O(n)`, 空间复杂度是 `O(n)`.
+
+## 双指针法
+
+步骤如下:
+
+1. 构造两个指针, 分别代表左侧之和与右侧之和
+    1. 左侧之和初始化为0
+    2. 右侧之和被初始化为 `n * (n + 1) /2`
+2. 遍历 `1..=n`, 然后判断左侧之和与右侧之和的关系
+    1. 如果 `left_sum + i == right_sum`, 说明找到了该位置, 直接返回
+    2. 否则更新左侧之和与右侧之和
+    3. 如果 `left_sum > right_sum`, 说明没有找到合适的位置, 直接返回 -1
+
+该算法的实现如下:
+
+```rust
+{{#include src/main.rs:30:44}}
+```
+
+该算法的时间复杂度是 `O(n)`, 空间复杂度是 `O(1)`.
+
+## 平方根法
+
+这个方法的原理还不太清楚, 先计录一下.
+
+```rust
+{{#include src/main.rs:49:58}}
+```
+
+该算法的时间复杂度是 `O(1)`, 空间复杂度是 `O(1)`.
diff --git a/src/leetcode/2485.find-the-pivot-integer/src/main.rs b/src/leetcode/2485.find-the-pivot-integer/src/main.rs
index 23f32d109..6ca4b3d44 100644
--- a/src/leetcode/2485.find-the-pivot-integer/src/main.rs
+++ b/src/leetcode/2485.find-the-pivot-integer/src/main.rs
@@ -17,9 +17,9 @@ pub fn pivot_integer1(n: i32) -> i32 {
     let total_sum = prefix_sum[len - 1];
 
     // 遍历前缀和数组
-    for i in 0..len {
+    for (i, prefix) in prefix_sum.into_iter().enumerate() {
         // 满足左侧之和等于右侧之后
-        if prefix_sum[i] * 2 == total_sum + i as i32 {
+        if prefix * 2 == total_sum + i as i32 {
             return i as i32;
         }
     }
@@ -39,6 +39,9 @@ pub fn pivot_integer2(n: i32) -> i32 {
         }
         left_sum += i;
         right_sum -= i;
+        if left_sum > right_sum {
+            break;
+        }
     }
     -1
 }
diff --git a/src/leetcode/by-id/2401-2500.md b/src/leetcode/by-id/2401-2500.md
new file mode 100644
index 000000000..4775cf06f
--- /dev/null
+++ b/src/leetcode/by-id/2401-2500.md
@@ -0,0 +1 @@
+# 2401-2500
\ No newline at end of file
diff --git a/src/leetcode/tags/prefix-sum.md b/src/leetcode/tags/prefix-sum.md
index 3f8238867..e55469868 100644
--- a/src/leetcode/tags/prefix-sum.md
+++ b/src/leetcode/tags/prefix-sum.md
@@ -8,9 +8,10 @@
 4. [1480. 一维数组的动态和 Running Sum of 1d Array](../1480.running-sum-of-1d-array/index.md)
 5. [1732. 找到最高海拔 Find the Highest Altitude](../1732.find-the-highest-altitude/index.md)
 6. [1991. 找到数组的中间位置 Find the Middle Index in Array](../1991.find-the-middle-index-in-array/index.md)
-7. [2574. 左右元素和的差值 Left and Right Sum Differences](../2574.left-and-right-sum-differences/index.md)
-8. [2848. 与车相交的点 Points That Intersect With Cars](../2848.points-that-intersect-with-cars/index.md)
-9. [3028. 边界上的蚂蚁 Ant on the Boundary](../3028.ant-on-the-boundary/index.md)
+7. [2485. 找出中枢整数 Find the Pivot Integer](../2485.find-the-pivot-integer/index.md)
+8. [2574. 左右元素和的差值 Left and Right Sum Differences](../2574.left-and-right-sum-differences/index.md)
+9. [2848. 与车相交的点 Points That Intersect With Cars](../2848.points-that-intersect-with-cars/index.md)
+10. [3028. 边界上的蚂蚁 Ant on the Boundary](../3028.ant-on-the-boundary/index.md)
 
 ## 中等