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Program to find length of longest bitonic subsequence in C++
Suppose we have a list of numbers. We have to find length of longest bitonic subsequence. As we knot a sequence is said to be bitonic if it's strictly increasing and then strictly decreasing. A strictly increasing sequence is bitonic. Or a strictly decreasing sequence is bitonic also.
So, if the input is like nums = [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15], size of sequence 16., then the output will be 7.
To solve this, we will follow these steps −
increasingSubSeq := new array of given array size, and fill with 1
for initialize i := 1, when i < size, update (increase i by 1), do −
for initialize j := 0, when j < i, update (increase j by 1), do −
if arr[i] > arr[j] and increasingSubSeq[i] < increasingSubSeq[j] + 1, then −
increasingSubSeq[i] := increasingSubSeq[j] + 1
*decreasingSubSeq := new array of given array size, and fill with 1
for initialize i := size - 2, when i >= 0, update (decrease i by 1), do −
for initialize j := size - 1, when j > i, update (decrease j by 1), do −
if arr[i] > arr[j] and decreasingSubSeq[i] < decreasingSubSeq[j] + 1, then −
decreasingSubSeq[i] := decreasingSubSeq[j] + 1
max := increasingSubSeq[0] + decreasingSubSeq[0] - 1
for initialize i := 1, when i < size, update (increase i by 1), do −
if increasingSubSeq[i] + decreasingSubSeq[i] - 1 > max, then:
max := increasingSubSeq[i] + decreasingSubSeq[i] - 1
return max
Let us see the following implementation to get better understanding −
Example
#include<iostream>
using namespace std;
int longBitonicSub( int arr[], int size ) {
int *increasingSubSeq = new int[size];
for (int i = 0; i < size; i++)
increasingSubSeq[i] = 1;
for (int i = 1; i < size; i++)
for (int j = 0; j < i; j++)
if (arr[i] > arr[j] && increasingSubSeq[i] <
increasingSubSeq[j] + 1)
increasingSubSeq[i] = increasingSubSeq[j] + 1;
int *decreasingSubSeq = new int [size];
for (int i = 0; i < size; i++)
decreasingSubSeq[i] = 1;
for (int i = size-2; i >= 0; i--)
for (int j = size-1; j > i; j--)
if (arr[i] > arr[j] && decreasingSubSeq[i] < decreasingSubSeq[j] + 1)
decreasingSubSeq[i] = decreasingSubSeq[j] + 1;
int max = increasingSubSeq[0] + decreasingSubSeq[0] - 1;
for (int i = 1; i < size; i++)
if (increasingSubSeq[i] + decreasingSubSeq[i] - 1 > max)
max = increasingSubSeq[i] + decreasingSubSeq[i] - 1;
return max;
}
int main() {
int arr[] = {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15};
int n = 16;
cout << longBitonicSub(arr, n);
}Input
[0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15], 16
Output
7
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