Date : 22 November 2020

Find the common difference of an AP. whose first term is 100 and the sum of whose first six-term is five times the sum of the next six terms. 10 -10 5 -5

Answer: -10 Here a=100

Let difference is d. ⇒a1 +a2 +a3+a4 +a5+a6=5(a7 +a8+a9+a10+a11+a12 )

⇒6( a1 +a6)/2=5×6( a7 +a12 )/2

⇒a1+a6=5(a7 +a12 )

⇒a+a+5d=5(a+6d+a+11d)

⇒2a+5d=10a+85d

⇒80d=−8a

⇒d= -a/10 ⇒ -100/10 ⇒−10

Which algorithm is used to check the negative cycle in the graph? 1. Prim's Algorithm 2. Kruskal Algorithm 3. Bellman Ford Algorithm 4. Floyd Warshall Algorithm

Bellman-Ford Algorithm is used to check negative cycles. Negative cycle is a cycle whose sum of edges result in negative value.

Given a string s, partition s such that every substring of the partition is a palindrome. Return all possible palindrome partitioning of s. Example: Input: "aab" Output: [ ["aa","b"], ["a","a","b"] ]

class Solution {public:vector<vector<string>> partition(string s) {int len = s.length();vector<vector<bool>> dp (len, vector <bool> (len, false));vector<vector<string>> result;vector<string> currentList;dfs(result, s, 0, currentList, dp);return result;}void dfs(vector<vector<string>> &result, string &s, int start, vector<string> ¤tList, vector<vector<bool>> &dp) {if (start >= s.length()) result.push_back(currentList);for (int end = start; end < s.length(); end++) {if (s[start] == s[end] && (end - start <= 2 || dp[start + 1][end - 1])) {dp[start][end] = true;currentList.push_back(s.substr(start, end - start + 1));dfs(result, s, end + 1, currentList, dp);currentList.pop_back();}}}};

A given string s starting at index start and ending at index end is a palindrome if following conditions are satisfied :1. The characters at start and end indexes are equal.2. The substring starting at index start+1 and ending at index end−1 is a palindrome.Let N be the length of the string.To determine if a substring starting at index start and ending at end is a palindrome or not,we use a 2 Dimensional array dp of size N⋅N where,dp[start][end]=true , if the substring beginning at index start and ending at index end is a palindrome.Otherwise dp[start][end] ==false.Also, we must update the dp array, if we find that the current string is a palindrome