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// 96. Unique Binary Search Trees
#include <stdio.h>
/*
* given an integer 'n', return the number of structurally unique BST's which
* has exactly 'n' nodes of unique values from 1 to 'n'
*/
int numTrees(int n) {
int rem[n + 1];
if (!n)
return 1;
if (n == 1 || n == 2)
return n;
rem[0] = 1;
rem[1] = 1;
rem[2] = 2;
for (int i = 3; i <= n; i++) {
rem[i] = 0;
for (int j = 1; j <= i; j++)
rem[i] = rem[i] + rem[i - j] * rem[j - 1];
}
return rem[n];
}
int main() {
printf("%d\n", numTrees(3)); // expect: 5
printf("%d\n", numTrees(1)); // expect: 1
}
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