feat: add solutions to lc problem: No.0801 (#4081)

No.0801.Minimum Swaps To Make Sequences Increasing

Author: yanglbme

solution/0800-0899/0801.Minimum Swaps To Make Sequences Increasing/README.md

@@ -172,6 +172,29 @@ func minSwap(nums1 []int, nums2 []int) int {
 }
 ```
 
+#### TypeScript
+
+```ts
+function minSwap(nums1: number[], nums2: number[]): number {
+    let [a, b] = [0, 1];
+    for (let i = 1; i < nums1.length; ++i) {
+        let x = a,
+            y = b;
+        if (nums1[i - 1] >= nums1[i] || nums2[i - 1] >= nums2[i]) {
+            a = y;
+            b = x + 1;
+        } else {
+            b = y + 1;
+            if (nums1[i - 1] < nums2[i] && nums2[i - 1] < nums1[i]) {
+                a = Math.min(a, y);
+                b = Math.min(b, x + 1);
+            }
+        }
+    }
+    return Math.min(a, b);
+}
+```
+
 <!-- tabs:end -->
 
 <!-- solution:end -->

solution/0800-0899/0801.Minimum Swaps To Make Sequences Increasing/README_EN.md

@@ -33,7 +33,7 @@ tags:
 <pre>
 <strong>Input:</strong> nums1 = [1,3,5,4], nums2 = [1,2,3,7]
 <strong>Output:</strong> 1
-<strong>Explanation:</strong> 
+<strong>Explanation:</strong>
 Swap nums1[3] and nums2[3]. Then the sequences are:
 nums1 = [1, 3, 5, 7] and nums2 = [1, 2, 3, 4]
 which are both strictly increasing.
@@ -61,7 +61,21 @@ which are both strictly increasing.
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Dynamic Programming
+
+Define $a$ and $b$ to represent the minimum number of swaps needed to make the element sequences strictly increasing up to index $[0..i]$, with the $i$-th element not swapped and swapped, respectively. The index starts from $0$.
+
+When $i=0$, we have $a = 0$ and $b = 1$.
+
+When $i \gt 0$, we first save the previous values of $a$ and $b$ in $x$ and $y$, and then discuss the following cases:
+
+If $nums1[i - 1] \ge nums1[i]$ or $nums2[i - 1] \ge nums2[i]$, to make both sequences strictly increasing, the relative positions of the elements at indices $i-1$ and $i$ must change. That is, if the previous position was swapped, then the current position should not be swapped, so $a = y$; if the previous position was not swapped, then the current position must be swapped, so $b = x + 1$.
+
+Otherwise, the relative positions of the elements at indices $i-1$ and $i$ do not need to change, so $b = y + 1$. Additionally, if $nums1[i - 1] \lt nums2[i]$ and $nums2[i - 1] \lt nums1[i]$, the relative positions of the elements at indices $i-1$ and $i$ can change, so $a$ and $b$ can take the smaller values, thus $a = \min(a, y)$ and $b = \min(b, x + 1)$.
+
+Finally, return the smaller value between $a$ and $b$.
+
+The time complexity is $O(n)$, and the space complexity is $O(1)$.
 
 <!-- tabs:start -->
 
@@ -151,6 +165,29 @@ func minSwap(nums1 []int, nums2 []int) int {
 }
 ```
 
+#### TypeScript
+
+```ts
+function minSwap(nums1: number[], nums2: number[]): number {
+    let [a, b] = [0, 1];
+    for (let i = 1; i < nums1.length; ++i) {
+        let x = a,
+            y = b;
+        if (nums1[i - 1] >= nums1[i] || nums2[i - 1] >= nums2[i]) {
+            a = y;
+            b = x + 1;
+        } else {
+            b = y + 1;
+            if (nums1[i - 1] < nums2[i] && nums2[i - 1] < nums1[i]) {
+                a = Math.min(a, y);
+                b = Math.min(b, x + 1);
+            }
+        }
+    }
+    return Math.min(a, b);
+}
+```
+
 <!-- tabs:end -->
 
 <!-- solution:end -->

solution/0800-0899/0801.Minimum Swaps To Make Sequences Increasing/Solution.ts

@@ -0,0 +1,18 @@
+function minSwap(nums1: number[], nums2: number[]): number {
+    let [a, b] = [0, 1];
+    for (let i = 1; i < nums1.length; ++i) {
+        let x = a,
+            y = b;
+        if (nums1[i - 1] >= nums1[i] || nums2[i - 1] >= nums2[i]) {
+            a = y;
+            b = x + 1;
+        } else {
+            b = y + 1;
+            if (nums1[i - 1] < nums2[i] && nums2[i - 1] < nums1[i]) {
+                a = Math.min(a, y);
+                b = Math.min(b, x + 1);
+            }
+        }
+    }
+    return Math.min(a, b);
+}