873. Length of Longest Fibonacci Subsequence 

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class Solution {
    public int lenLongestFibSubseq(int[] arr) {
        int n = arr.length;
        int maxLength = 0;

        // 定义 dp[j][k] 为以 arr[j], arr[k] 结尾的最长的斐波那契式子序列长度
        int[][] dp = new int[n][n];

        Map<Integer, Integer> numToIndexMap = new HashMap<>();
        for (int i = 0; i < arr.length; i++) {
            numToIndexMap.put(arr[i], i);
        }

        for (int j = 1; j < n - 1; j++) {
            for (int k = j + 1; k < n && j + 2 > maxLength; k++) {
                int target = arr[k] - arr[j];
                if (target >= arr[j]) {
                    // 剪枝
                    break;
                }

                Integer targetIndex = numToIndexMap.get(target);
                if (targetIndex == null) {
                    continue;
                }

                dp[j][k] = Math.max(3, dp[targetIndex][j] + 1);
                maxLength = Math.max(maxLength, dp[j][k]);
            }
        }

        return maxLength;
    }
}

References

873. Length of Longest Fibonacci Subsequence
剑指 Offer II 093. 最长斐波那契数列