feat: add solution 1977. Number of Ways to Separate Numbers

Author: tzuyi0817

solutions/1977. Number of Ways to Separate Numbers/README.md

@@ -0,0 +1,106 @@
+# [1977. Number of Ways to Separate Numbers](https://leetcode.com/problems/number-of-ways-to-separate-numbers)
+
+## Description
+
+<div class="elfjS" data-track-load="description_content"><p>You wrote down many <strong>positive</strong> integers in a string called <code>num</code>. However, you realized that you forgot to add commas to seperate the different numbers. You remember that the list of integers was <strong>non-decreasing</strong> and that <strong>no</strong> integer had leading zeros.</p>
+
+<p>Return <em>the <strong>number of possible lists of integers</strong> that you could have written down to get the string </em><code>num</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre><strong>Input:</strong> num = "327"
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> You could have written down the numbers:
+3, 27
+327
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre><strong>Input:</strong> num = "094"
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> No numbers can have leading zeros and all numbers must be positive.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre><strong>Input:</strong> num = "0"
+<strong>Output:</strong> 0
+<strong>Explanation:</strong> No numbers can have leading zeros and all numbers must be positive.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= num.length &lt;= 3500</code></li>
+	<li><code>num</code> consists of digits <code>'0'</code> through <code>'9'</code>.</li>
+</ul>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Dynamic Programming`**
+
+- Time complexity: <em>O(n<sup>2</sup>)</em>
+- Space complexity: <em>O(n<sup>2</sup>)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {string} num
+ * @return {number}
+ */
+const numberOfCombinations = function (num) {
+  if (num[0] === '0') return 0;
+
+  const MODULO = BigInt(10 ** 9 + 7);
+  const n = num.length;
+  const dp = Array.from({ length: n }, () => new Array(n + 1).fill(0n));
+  const lcs = Array.from({ length: n + 1 }, () => new Array(n + 1).fill(0));
+
+  for (let a = n - 1; a >= 0; a--) {
+    for (let b = a + 1; b < n; b++) {
+      if (num[a] !== num[b]) continue;
+
+      lcs[a][b] = lcs[a + 1][b + 1] + 1;
+    }
+  }
+
+  for (let index = 0; index < n; index++) {
+    for (let len = 1; len <= index + 1; len++) {
+      const start = index - len + 1;
+
+      dp[index][len] += dp[index][len - 1];
+      dp[index][len] %= MODULO;
+
+      if (num[start] === '0') continue;
+      if (start === 0) {
+        dp[index][len] += 1n;
+        continue;
+      }
+
+      if (start < len) {
+        dp[index][len] += dp[start - 1][start];
+        continue;
+      }
+
+      const lc = lcs[start - len][start];
+
+      if (lc >= len || num[start - len + lc] <= num[start + lc]) {
+        dp[index][len] += dp[start - 1][len];
+      } else {
+        dp[index][len] += dp[start - 1][len - 1];
+      }
+    }
+  }
+
+  return Number(dp[n - 1][n] % MODULO);
+};
+```

solutions/1977. Number of Ways to Separate Numbers/solution.js

@@ -0,0 +1,50 @@
+/**
+ * @param {string} num
+ * @return {number}
+ */
+const numberOfCombinations = function (num) {
+  if (num[0] === '0') return 0;
+
+  const MODULO = BigInt(10 ** 9 + 7);
+  const n = num.length;
+  const dp = Array.from({ length: n }, () => new Array(n + 1).fill(0n));
+  const lcs = Array.from({ length: n + 1 }, () => new Array(n + 1).fill(0));
+
+  for (let a = n - 1; a >= 0; a--) {
+    for (let b = a + 1; b < n; b++) {
+      if (num[a] !== num[b]) continue;
+
+      lcs[a][b] = lcs[a + 1][b + 1] + 1;
+    }
+  }
+
+  for (let index = 0; index < n; index++) {
+    for (let len = 1; len <= index + 1; len++) {
+      const start = index - len + 1;
+
+      dp[index][len] += dp[index][len - 1];
+      dp[index][len] %= MODULO;
+
+      if (num[start] === '0') continue;
+      if (start === 0) {
+        dp[index][len] += 1n;
+        continue;
+      }
+
+      if (start < len) {
+        dp[index][len] += dp[start - 1][start];
+        continue;
+      }
+
+      const lc = lcs[start - len][start];
+
+      if (lc >= len || num[start - len + lc] <= num[start + lc]) {
+        dp[index][len] += dp[start - 1][len];
+      } else {
+        dp[index][len] += dp[start - 1][len - 1];
+      }
+    }
+  }
+
+  return Number(dp[n - 1][n] % MODULO);
+};