Minimum number of increasing subsequences
Given an array of integers of size N, you have to divide it into the minimum number of “strictly increasing subsequences” For example: let the sequence be {1, 3, 2, 4}, then the answer would be 2. In this case, the first increasing sequence would be {1, 3, 4} and the second would be {2}.
Examples:
Input : arr[] = {1 3 2 4} Output: 2 There are two increasing subsequences {1, 3, 4} and {2}
Input : arr[] = {4 3 2 1} Output : 4
Input : arr[] = {1 2 3 4} Output : 1
Input : arr[] = {1 6 2 4 3} Output : 3
class Solution {
public int minIncSubsequences(int arr[], int n) {
// Ans -> Max lenth of longest decreasing subsequence
int[] dp = new int[n];
int max = 0;
for (int i = 0; i < n; i++) {
// base case
dp[i] = 1;
for (int j = 0; j < i; j++)
if (arr[j] > arr[i])
dp[i] = Math.max(dp[i], dp[j] + 1);
max = Math.max(max, dp[i]);
}
return max;
}
}
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