Create number-of-ways-to-rearrange-sticks-with-k-sticks-visible.cpp

Author: kamyu104

C++/number-of-ways-to-rearrange-sticks-with-k-sticks-visible.cpp

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+// Time:  O(n * k)
+// Space: O(k)
+
+class Solution {
+public:
+    int rearrangeSticks(int n, int k) {
+        static const int MOD = 1e9 + 7;
+        vector<vector<int>> dp(2, vector<int>(k + 1));
+        dp[1][1] = 1;
+        for (int i = 2; i <= n; ++i) {
+            for (int j = 1; j <= min(i, k); ++j) {
+                // choose the tallest as the last one which would be visible:    dp[i-1][j-1]
+                // choose the non-tallest as the last one which would be hidden: (i-1) * dp[i-1][j]
+                dp[i % 2][j] = (dp[(i - 1) % 2][j - 1] + int64_t(i - 1) * dp[(i - 1) % 2][j]) % MOD;
+            }
+        }
+        return dp[n % 2][k];
+    }
+};