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// 873. Length of Longest Fibonacci Subsequence
#include "leetcode.h"
/*
* a sequence 'x1, x2, ..., xn' is fibonacci like if 'n >= 3' and 'x_i + x_i + 1
* == x_i + 2' for all 'i + 2 <= n'. given a strictly increasing 'arr' of
* positive integers forming a sequence, return the length of the longest
* fibonacci like subsequence of 'arr'. if one does not exist, return 0. a
* subsequence is derived from another sequence 'arr' by deleting any number of
* elements (including none) from 'arr', without changing the order of the
* remaining elements.
*/
static int a_max;
int helper(int *arr, int *map, int i, int j, int sum) {
int cnt = 0;
while (sum <= a_max) {
if (!map[sum])
break;
cnt++;
i = j;
j = map[sum] - 1;
sum = arr[i] + arr[j];
}
return cnt;
}
int lenLongestFibSubseq(int *arr, int arrSize) {
a_max = arr[arrSize - 1];
int map_size = a_max + 1;
int *map = (int *)calloc(map_size, sizeof(int));
int cnt = 0, i, j, sum, tmp;
for (int i = 0; i < arrSize; i++)
map[arr[i]] = i + 1;
for (int i = 0; i < arrSize; i++) {
for (int j = i + 1; j < arrSize; j++) {
sum = arr[i] + arr[j];
if (sum > a_max)
break;
if (!map[sum])
continue;
tmp = helper(arr, map, i, j, sum);
cnt = fmax(cnt, tmp);
}
}
cnt += 2;
free(map);
return cnt > 2 ? cnt : 0;
}
int main() {
int a1[] = {1, 2, 3, 4, 5, 6, 7, 8}, a2[] = {1, 3, 7, 11, 12, 14, 18};
printf("%d\n", lenLongestFibSubseq(a1, ARRAY_SIZE(a1))); // expect: 5
printf("%d\n", lenLongestFibSubseq(a2, ARRAY_SIZE(a2))); // expect: 3
}
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