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DP13.java
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DP13.java
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import java.util.Arrays;
public class DP13 {
//RECURSION
public static int Catalan(int n) {
if (n == 0 || n == 1) {
return 1;
}
int ans = 0;
for (int i = 0; i < n; i++) {
ans += (Catalan(i) * Catalan(n - i - 1));
}
return ans;
}
//MEMOISATION
public static int CatalanMemo(int n, int dp[]) {
if (n == 0 || n == 1) {
return 1;
}
if (dp[n] != -1) {
return dp[n];
}
int ans = 0;
for (int i = 0; i < n; i++) {
ans += (CatalanMemo(i, dp) * CatalanMemo(n - i - 1, dp));
}
return dp[n] = ans;
}
// TABULATION
public static int CatalanTab(int n) {
int dp[] = new int[n + 1];
dp[0] = 1;
dp[1] = 1;
for (int i = 2; i <= n; i++) {
for (int j = 0; j <= i - 1; j++) {
dp[i] += (dp[j] * dp[i - j - 1]);
}
}
return dp[n];
}
public static void main(String[] args) {
// CATALAN NUMBER
int n = 4;
//RECURSION
System.out.println("C4 is: " + Catalan(n));
//RECURSION
int dp[] = new int[n + 1];
Arrays.fill(dp, -1);
System.out.println("C4 is: " + CatalanMemo(n, dp));
// TABULATION
System.out.println("C4 is :" + CatalanTab(n));
}
}