72 lines
1.5 KiB
C++
72 lines
1.5 KiB
C++
// Source : https://oj.leetcode.com/problems/unique-binary-search-trees/
|
|
// Author : Hao Chen
|
|
// Date : 2014-06-25
|
|
|
|
/**********************************************************************************
|
|
*
|
|
* Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
|
|
*
|
|
* For example,
|
|
* Given n = 3, there are a total of 5 unique BST's.
|
|
*
|
|
* 1 3 3 2 1
|
|
* \ / / / \ \
|
|
* 3 2 1 1 3 2
|
|
*
|
|
*
|
|
**********************************************************************************/
|
|
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
|
|
int numTrees1(int n) ;
|
|
int numTrees2(int n) ;
|
|
|
|
int numTrees(int n) {
|
|
return numTrees1(n);
|
|
}
|
|
|
|
int numTrees1(int n) {
|
|
int *cnt = (int*)malloc((n+1)*sizeof(int));
|
|
memset(cnt, 0, (n+1)*sizeof(int));
|
|
cnt[0] = 1;
|
|
cnt[1] = 1;
|
|
|
|
for (int i=2; i<=n; i++){
|
|
for(int j=0; j<i; j++){
|
|
cnt[i] += cnt[j]*cnt[i-j-1];
|
|
}
|
|
}
|
|
int sum = cnt[n];
|
|
free(cnt);
|
|
return sum;
|
|
}
|
|
|
|
|
|
|
|
int numTrees2(int n) {
|
|
if (n<=0) return 0;
|
|
if (n == 1 ) return 1;
|
|
int sum=0;
|
|
for (int i=1; i<=n; i++){
|
|
if (i==1||i==n){
|
|
sum += numTrees(n-1);
|
|
}else{
|
|
sum += (numTrees(i-1) * numTrees(n-i));
|
|
}
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
|
|
int main(int argc, char** argv)
|
|
{
|
|
int n=2;
|
|
if (argc>1){
|
|
n = atoi(argv[1]);
|
|
}
|
|
printf("%d=%d\n", n, numTrees(n));
|
|
return 0;
|
|
}
|