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67 lines
1.2 KiB
67 lines
1.2 KiB
package class39;
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public class Code04_DifferentBTNum {
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// k(0) = 1, k(1) = 1
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//
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// k(n) = k(0) * k(n - 1) + k(1) * k(n - 2) + ... + k(n - 2) * k(1) + k(n - 1) * k(0)
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// 或者
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// k(n) = c(2n, n) / (n + 1)
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// 或者
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// k(n) = c(2n, n) - c(2n, n-1)
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public static long num1(int N) {
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if (N < 0) {
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return 0;
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}
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if (N < 2) {
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return 1;
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}
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long[] dp = new long[N + 1];
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dp[0] = 1;
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dp[1] = 1;
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for (int i = 2; i <= N; i++) {
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for (int leftSize = 0; leftSize < i; leftSize++) {
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dp[i] += dp[leftSize] * dp[i - 1 - leftSize];
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}
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}
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return dp[N];
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}
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public static long num2(int N) {
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if (N < 0) {
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return 0;
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}
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if (N < 2) {
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return 1;
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}
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long a = 1;
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long b = 1;
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for (int i = 1, j = N + 1; i <= N; i++, j++) {
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a *= i;
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b *= j;
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long gcd = gcd(a, b);
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a /= gcd;
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b /= gcd;
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}
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return (b / a) / (N + 1);
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}
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public static long gcd(long m, long n) {
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return n == 0 ? m : gcd(n, m % n);
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}
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public static void main(String[] args) {
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System.out.println("test begin");
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for (int i = 0; i < 15; i++) {
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long ans1 = num1(i);
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long ans2 = num2(i);
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if (ans1 != ans2) {
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System.out.println("Oops!");
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}
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}
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System.out.println("test finish");
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}
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}
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