Longest_increasing_subsequence.cpp

Advanced/CPP/Longest_increasing_subsequence.cpp

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+/*
+Given an integer array 'nums', return the length of the longest strictly increasing subsequence.
+A subsequence is a sequence that can be derived from an array by deleting some or no elements without 
+changing the order of the remaining elements. 
+Example 1:
+	Input: nums[] = [10,9,2,5,3,7,101,18]
+	Output: 4
+	Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
+Example 2:
+	Input: nums[] = [0,1,0,3,2,3]
+	Output: 4
+*/
+
+
+#include<iostream>
+#include<vector>
+#include<climits>
+
+using namespace std;
+
+int f(vector<int>& nums, int i) {
+	// base case
+	if(i == nums.size()-1) {
+		return 1;
+	}
+
+	// recursive case
+	int ans = 0;
+	for(int j=i+1; j<nums.size(); j++) {
+		if(nums[j] > nums[i]) {
+			ans = max(ans, f(nums, j));
+		}
+	}
+
+	return 1 + ans;
+}
+
+int LIS(vector<int>& nums) {
+
+	// nums.insert(nums.begin(), INT_MIN);
+	// return f(nums, 0) - 1;
+
+	int finalAns = 0;
+	for(int i=0; i<nums.size(); i++) {
+		finalAns = max(finalAns, f(nums, i));
+	}
+	return finalAns;
+
+}
+
+int LISBottomUp(vector<int>& nums) {
+	int n = nums.size();
+	vector<int> dp(n);
+
+	dp[n-1] = 1;
+	// int finalAns = 0;
+	for(int i=n-2; i>=0; i--) {
+		int ans = 0;
+		for(int j=i+1; j<n; j++) {
+			if(nums[j] > nums[i]) {
+				ans = max(ans, dp[j]);
+			}
+		}
+		// finalAns = max(ans, finalAns);
+		dp[i] =  1+ans;
+	}
+
+	cout << "dp[] = ";
+	for(int i=0; i<n; i++) {
+		cout << dp[i] << " ";
+	}
+
+	cout << endl;
+
+	int finalAns = 0;
+	int k = -1;
+	for(int i=0; i<n; i++) {
+		if(dp[i] > finalAns) {
+			finalAns = dp[i];
+			k = i;
+		}
+	}
+
+	vector<int> lis = {nums[k]};
+	int len = finalAns - 1;
+	for(int i=k+1; i<n; i++) {
+		if(nums[i] > lis.back() && dp[i] == len) {
+			lis.push_back(nums[i]);
+			len--;
+		}
+	}
+
+	cout << "lis[] = ";
+	for(int i=0; i<lis.size(); i++) {
+		cout << lis[i] << " ";
+	}
+
+	cout << endl;
+
+	return finalAns;
+
+}
+
+int LISBottomUpV2(vector<int>& nums) {
+	nums.insert(nums.begin(), INT_MIN);
+	int n = nums.size();
+	vector<int> dp(n);
+
+	dp[n-1] = 1;
+	for(int i=n-2; i>=0; i--) {
+		int ans = 0;
+		for(int j=i+1; j<n; j++) {
+			if(nums[j] > nums[i]) {
+				ans = max(ans, dp[j]);
+			}
+		}
+
+		dp[i] =  1+ans;
+	}
+
+	return dp[0]-1;
+
+}
+
+int main() {
+
+	vector<int> nums = {10,9,2,5,3,7,101,18};
+	cout << LIS(nums) << endl;
+	cout << LISBottomUp(nums) << endl;
+	cout << LISBottomUpV2(nums) << endl;
+
+	return 0;
+}