Create 0629-k-inverse-pairs-array.kt

a93a · web-flow · commit 95f5f7407aac · 2024-01-27T13:05:03.000+01:00
diff --git a/kotlin/0629-k-inverse-pairs-array.kt b/kotlin/0629-k-inverse-pairs-array.kt
@@ -0,0 +1,64 @@
+// Bottom-up DP, Time O(n^2 * k) and Space O(n * k)
+class Solution {
+    fun kInversePairs(n: Int, k: Int): Int {
+        val mod = 1_000_000_007
+        val dp = Array (n + 1) { LongArray (k + 1) }
+
+        dp[0][0] = 1
+        for (i in 1..n) {
+            for (j in 0..k) {
+                for (p in 0 until i) {
+                    if (j - p >= 0)
+                        dp[i][j] = (dp[i][j] + dp[i - 1][j - p]) % mod
+                }
+            }
+        }
+
+        return dp[n][k].toInt()
+    }
+}
+
+// Space optimized Bottom-up DP, Time O(n^2 * k) and Space O(k)
+class Solution {
+    fun kInversePairs(n: Int, k: Int): Int {
+        val mod = 1_000_000_007
+        var dp = LongArray (k + 1)
+
+        dp[0] = 1
+        for (i in 1..n) {
+            val newDp = LongArray (k + 1)
+            for (j in 0..k) {
+                for (p in 0 until i) {
+                    if (j - p >= 0)
+                        newDp[j] = (newDp[j] + dp[j - p]) % mod
+                }
+            }
+            dp = newDp
+        }
+
+        return dp[k].toInt()
+    }
+}
+
+// Space optimized DP + Sliding window Time O(n * k) and Space O(k)
+class Solution {
+    fun kInversePairs(n: Int, k: Int): Int {
+        val mod = 1_000_000_007
+        var prev = LongArray (k + 1)
+
+        prev[0] = 1
+        for (i in 1..n) {
+            val cur = LongArray (k + 1)
+            var total = 0L
+            for (j in 0..k) {
+                if (j >= i)
+                    total -= prev[j - i]
+                total = (total + prev[j] + mod) % mod
+                cur[j] = total
+            }
+            prev = cur
+        }
+
+        return prev[k].toInt()
+    }
+}
