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def uniqueArrangements( input1, input2, input3): n = input1 k = input2 arr = input3 unique_patterns = set() for i in range(n - k + 1): new_pattern = tuple(arr[:i] + arr[i + k:]) unique_patterns.add(new_pattern) return len(unique_patterns) //The Robot Transmission Filter✅

def find_equal_biomass_cut(input1, input2, input3): n = input1 biomass = input2 edges = input3 graph = [[] for _ in range(n)] for u, v in edges: graph[u].append(v) graph[v].append(u) total = sum(biomass) if total % 2 != 0: return [-1, -1] target = total // 2 valid_cuts = [] visited = [False] * n def dfs(node): visited[node] = True subtotal = biomass[node] for nei in graph[node]: if not visited[nei]: sub = dfs(nei) subtotal += sub if sub == target: valid_cuts.append(sorted([node, nei])) return subtotal dfs(0) if not valid_cuts: return [-1, -1] valid_cuts.sort() return valid_cuts[0] //Equal Biomass Partition✅✅

def longest_decay_path(cls, input1, input2, input3, input4, input5): N, M = input1, input2 grid = input3 start_x, start_y = input4, input5 directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] dp = [[-1] * M for _ in range(N)] def dfs(x, y): if dp[x][y] != -1: return dp[x][y] max_len = 1 for dx, dy in directions: nx, ny = x + dx, y + dy if 0 <= nx < N and 0 <= ny < M and grid[nx][ny] < grid[x][y]: max_len = max(max_len, 1 + dfs(nx, ny)) dp[x][y] = max_len return dp[x][y] return dfs(start_x, start_y) //Decay Trail Optimization✅ VIRTUSA✅✅

def transform_to_smallest_prime(cls, input1, input2): from collections import deque N, K = str(input1), input2 n = len(N) def is_prime(x): if x < 2: return False if x % 2 == 0 and x != 2: return False d = 3 while d * d <= x: if x % d == 0: return False d += 2 return True q = deque([(N, 0)]) seen = {N: 0} best_prime = None while q: cur, steps = q.popleft() if steps <= K: val = int(cur) if cur[0] != '0' and is_prime(val): if best_prime is None or val < best_prime: best_prime = val if steps < K: for i in range(n): d = int(cur[i]) for nd in [d - 1, d + 1]: if 0 <= nd <= 9: nxt = cur[:i] + str(nd) + cur[i+1:] if nxt not in seen or seen[nxt] > steps + 1: seen[nxt] = steps + 1 q.append((nxt, steps + 1)) return best_prime if best_prime is not None else -1 //prime transformation✅✅ VIRTUSA✅

def maximizeQuality(cls, input1, input2, input3): n = input1 R = input2 P = input3 X = [] for b in range(32): mask = 1 << b contrib = 0 for val in P: contrib += (val & mask) X.append((contrib, b)) X.sort(key=lambda x: (-x[0], x[1])) chosen = sorted([b for _, b in X[:R]]) result = 0 for b in chosen: result |= (1 << b) return result //MAXIMIZE THE QUALITY✅ VIRTUSA✅

from collections import deque def minMovesToHospital(cls, input1, input2, input3): N = input1 E = input2 K = input3 - 1 if E[K] == 0: return 0 visited = [False] * N q = deque([(K, 0)]) visited[K] = True while q: idx, moves = q.popleft() for nxt in [idx + E[idx], idx - E[idx]]: if 0 <= nxt < N and not visited[nxt]: if E[nxt] == 0: return moves + 1 visited[nxt] = True q.append((nxt, moves + 1)) return -1 //MINIMUM MOVES✅ VIRTUSA✅

def maxSumOfNonAdjacentNodes(cls, input1, input2): a = input2 n = len(a) if n == 0: return 0 eff = [0]*n for i in range(n): penalty = a[i-1] if i > 0 and a[i-1] < 0 else 0 eff[i] = a[i] + penalty def nz(x): return x if x > 0 else 0 if n == 1: return nz(eff[0]) if n == 2: return max(nz(eff[0]), nz(eff[1])) prev2 = nz(eff[0]) prev1 = max(prev2, nz(eff[1])) for i in range(2, n): take = prev2 + nz(eff[i]) skip = prev1 cur = take if take > skip else skip prev2, prev1 = prev1, cur return prev1 //MAX REWARD POINTS✅ VIRTUSA✅

def legoString(input1, input2, input3): wall = input1 n = input2 blocks = input3 if not wall or not blocks: return [-1] word_len = len(blocks[0]) if len(wall) < word_len: return [-1] from collections import Counter block_count = Counter(blocks) result = [] for i in range(len(wall) - word_len + 1): for used in range(2, n+1): length = used * word_len if i + length > len(wall): break substring = wall[i:i+length] words = [substring[j:j+word_len] for j in range(0, length, word_len)] count_words = Counter(words) if all(count_words[w] <= block_count[w] for w in count_words) and sum(count_words.values()) == used: result.append(i) return sorted(set(result)) if result else [-1] //Legato strings✅✅ VIRTUSA✅

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