feat: solve No.2147

Author: BaffinLee

Diff for: 2101-2200/2147. Number of Ways to Divide a Long Corridor.md

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+# 2147. Number of Ways to Divide a Long Corridor
+
+- Difficulty: Hard.
+- Related Topics: Math, String, Dynamic Programming.
+- Similar Questions: Decode Ways II, Minimum Cost to Cut a Stick, Ways to Split Array Into Three Subarrays.
+
+## Problem
+
+Along a long library corridor, there is a line of seats and decorative plants. You are given a **0-indexed** string `corridor` of length `n` consisting of letters `'S'` and `'P'` where each `'S'` represents a seat and each `'P'` represents a plant.
+
+One room divider has **already** been installed to the left of index `0`, and **another** to the right of index `n - 1`. Additional room dividers can be installed. For each position between indices `i - 1` and `i` (`1 <= i <= n - 1`), at most one divider can be installed.
+
+Divide the corridor into non-overlapping sections, where each section has **exactly two seats** with any number of plants. There may be multiple ways to perform the division. Two ways are **different** if there is a position with a room divider installed in the first way but not in the second way.
+
+Return **the number of ways to divide the corridor**. Since the answer may be very large, return it **modulo** `109 + 7`. If there is no way, return `0`.
+
+ 
+Example 1:
+
+![](https://assets.leetcode.com/uploads/2021/12/04/1.png)
+
+```
+Input: corridor = "SSPPSPS"
+Output: 3
+Explanation: There are 3 different ways to divide the corridor.
+The black bars in the above image indicate the two room dividers already installed.
+Note that in each of the ways, each section has exactly two seats.
+```
+
+Example 2:
+
+![](https://assets.leetcode.com/uploads/2021/12/04/2.png)
+
+```
+Input: corridor = "PPSPSP"
+Output: 1
+Explanation: There is only 1 way to divide the corridor, by not installing any additional dividers.
+Installing any would create some section that does not have exactly two seats.
+```
+
+Example 3:
+
+![](https://assets.leetcode.com/uploads/2021/12/12/3.png)
+
+```
+Input: corridor = "S"
+Output: 0
+Explanation: There is no way to divide the corridor because there will always be a section that does not have exactly two seats.
+```
+
+ 
+**Constraints:**
+
+
+	
+- `n == corridor.length`
+	
+- `1 <= n <= 105`
+	
+- `corridor[i]` is either `'S'` or `'P'`.
+
+
+
+## Solution
+
+```javascript
+/**
+ * @param {string} corridor
+ * @return {number}
+ */
+var numberOfWays = function(corridor) {
+    var num = BigInt(1);
+    var mod = BigInt(Math.pow(10, 9) + 7);
+    var seatNum = 0;
+    var plantNum = 0;
+    for (var i = 0; i < corridor.length; i++) {
+        if (corridor[i] === 'S') {
+            if (seatNum === 2) {
+                num *= BigInt(plantNum + 1);
+                num %= mod;
+                seatNum = 1;
+                plantNum = 0;
+            } else {
+                seatNum += 1;
+            }
+        } else {
+            if (seatNum === 2) {
+                plantNum += 1;
+            }
+        }
+    }
+    return seatNum === 2 ? Number(num) : 0;
+};
+```
+
+**Explain:**
+
+nope.
+
+**Complexity:**
+
+* Time complexity : O(n).
+* Space complexity : O(1).