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Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: sums = {0:-1} prefix = 0 dp = [math.inf for _ in range(len(arr)+1)] ans = math.inf for idx, num in enumerate(arr): prefix += num dp[idx+1] = min(dp[idx+1], dp[idx]) if prefix-target in sums: ans = min(ans, idx-sums[prefix-target] + dp[sums[prefix-target]+1]) dp[idx+1] = min(dp[idx+1], idx-sums[prefix-target]) sums[prefix] = idx return ans if ans != math.inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # h[key] stores list of indices, let ind = h[key][-1] # Here, run[ind] == key (INCLUDING arr[ind - 1]) run = [0, arr[0]] h = {0: 0, arr[0]: 1} prefix = [len(arr)] for i in range(1, len(arr)): if run[i] - target in h: prefix.append(min(prefix[-1], i - h[run[i] - target])) else: prefix.append(prefix[-1]) run.append(run[-1] + arr[i]) h[run[-1]] = i + 1 suffix = [len(arr) for i in range(len(arr))] if arr[-1] == target: suffix[-1] = 1 for i in range(len(arr) - 2, -1, -1): if run[i] + target in h: suffix[i] = min(suffix[i + 1], h[run[i] + target] - i) else: suffix[i] = suffix[i + 1] res = len(arr) + 1 for i in range(len(arr)): if not (prefix[i] == len(arr) or suffix[i] == len(arr)): res = min(res, prefix[i] + suffix[i]) if res == len(arr) + 1: return -1 return res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from collections import defaultdict class Solution: def getSubArray(self, array, target): dic = defaultdict(int) minSub = [float('inf')] * len(array) currentSum = 0 for i, num in enumerate(array): currentSum += num if currentSum == target: minSub[i] = min(minSub[i - 1], i - 0 + 1) elif currentSum - target in dic: minSub[i] = min(minSub[i - 1], i - dic[currentSum - target]) else: minSub[i] = min(minSub[i - 1], minSub[i]) dic[currentSum] = i return minSub def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) result = float('inf') leftMinSub = self.getSubArray(arr, target) rightMinSub = self.getSubArray(arr[::-1], target)[::-1] for i in range(1, n): result = min(result, leftMinSub[i-1] + rightMinSub[i]) if result == float('inf'): return -1 else: return result
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from collections import defaultdict class Solution: def getSubArray(self, array, target): dic = defaultdict(int) minSub = [float('inf')] * len(array) currentSum = 0 for i, num in enumerate(array): currentSum += num if currentSum == target: minSub[i] = i - 0 + 1 elif currentSum - target in dic: minSub[i] = i - dic[currentSum - target] + 1 minSub[i] = min(minSub[i - 1], minSub[i] ) dic[currentSum] = i + 1 return minSub def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) result = float('inf') leftMinSub = self.getSubArray(arr, target) rightMinSub = self.getSubArray(arr[::-1], target)[::-1] for i in range(1, n): result = min(result, leftMinSub[i-1] + rightMinSub[i]) if result == float('inf'): return -1 else: return result
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: INF = len(arr) + 1 best_idx = [INF]*len(arr) best = INF csum = 0 left = 0 for right in range(len(arr)): csum += arr[right] while csum > target and left<=right: csum -= arr[left] left +=1 if csum == target: best = min(best, best_idx[left-1] + right - left + 1 ) best_idx[right] = min(best_idx[right-1], right - left + 1) else: best_idx[right] = best_idx[right-1] if INF == best: return -1 return best ''' class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: INF = len(arr) + 1 best_at_i = [INF]*len(arr) # the ith index represents the smallest length subarray we've found ending <= i that sums to target best = INF # output curr_sum = 0 # current sum between left and right left = 0 for right in range(len(arr)): # update the running sum curr_sum += arr[right] # arr is strictly positive, so shrink window until we're not above target while curr_sum > target and left <= right: curr_sum -= arr[left] left += 1 if curr_sum == target: # we have a new shortest candidate to consider best = min(best, best_at_i[left-1] + right - left + 1) best_at_i[right] = min(best_at_i[right-1], right - left + 1) else: # best we've seen is the previous best (overlaps to end if right == 0) best_at_i[right] = best_at_i[right-1] if best == INF: return -1 return best'''
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: N = len(arr) prefix = [N+1] * N suffix = [N+1] * N presum = dict() total = 0 presum[0] = -1 for i in range(N): total += arr[i] presum[total] = i prefix[0] = N+1 total = 0 for i in range(0, N): total += arr[i] t = N+1 xx = total - target if xx in presum: # 找到一个target t = i - presum[xx] prefix[i] = min(prefix[i-1], t) sufsum = dict() total = 0 sufsum[0] = N for i in range(N-1, -1, -1): total += arr[i] sufsum[total] = i total = 0 if arr[-1] == target: suffix[-1] = 1 total = arr[-1] for i in range(N-2, -1, -1): total += arr[i] t = N+1 xx = total - target if xx in sufsum: # 找到一个target t = sufsum[xx] - i suffix[i] = min(suffix[i+1], t) # print(prefix) # print(suffix) rtv = N+1 for i in range(N-1): cur = prefix[i] + suffix[i+1] rtv = min(rtv, cur) if rtv > N: return -1 return rtv
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
import collections class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: def get_sub_arrays( arr ): lookup = collections.defaultdict(int) running_sum = 0 dp = [float('inf')] * len(arr) for i, num in enumerate(arr): running_sum += num if running_sum == target: dp[i] = i - 0 + 1 elif running_sum - target in lookup: dp[i] = i - lookup[running_sum - target] + 1 lookup[running_sum] = i+1 dp[i] = min( dp[i-1], dp[i] ) return dp dp_left = get_sub_arrays( arr ) # from front dp_right = get_sub_arrays( arr[::-1] )[::-1] # from backwards ans = float('inf') for i in range( 1, len(arr) ): ans = min( ans, dp_left[i-1] + dp_right[i] ) return ans if( ans != float('inf') ) else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: # 864 ms def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i = window = count = 0 # preMin: store previous shortest length preMin = deque([(-1, inf)]) # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 while len(preMin) >= 2 and preMin[1][0] <= i-1: preMin.popleft() if window == target: # curr: current length curr = j - i + 1 # find first minimal length n before window start i n = preMin[0][1] # update result if less if result > curr + n: result = curr + n # update shortest length if less if curr < preMin[-1][-1]: preMin.append((j, curr)) # early stopping if found two single targets if curr == 1: count += 1 if count == 2: return 2 return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i = window = 0 premin = [inf] * len(arr) # i: window start, j: window end for j in range(len(arr)): window += arr[j] while window > target: window -= arr[i] i += 1 if window == target: # curr: length curr = j - i + 1 if result > curr + premin[i - 1]: result = curr + premin[i - 1] premin[j] = curr if curr < premin[j - 1] else premin[j - 1] else: premin[j] = premin[j - 1] return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) def get_min(arr): min_left = [float('inf')] * n window = 0 l = 0 for r in range(n): window += arr[r] while window > target: window -= arr[l] l += 1 if window == target: min_left[r] = r - l + 1 if r > 0: min_left[r] = min(min_left[r], min_left[r - 1]) return min_left def get_min_right(): min_right = [float('inf') for _ in range(n)] window = 0 r = n - 1 for l in range(n - 1, -1, -1): window += arr[l] while window > target: window -= arr[r] r -= 1 if window == target: min_right[l] = r - l + 1 if l < n - 1: min_right[l] = min(min_right[l], min_right[l - 1]) return min_right min_left = get_min(arr) min_right = get_min_right() # get_min(arr[::-1])[::-1] print((min_right[::-1])) best = float('inf') for i in range(1, n): best = min(best, min_left[i - 1] + min_right[i]) return best if best < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: result = float('inf') # prefix shortest length read from left to right leftmin = self.getMinLen(arr, target, True) # suffix shortest length read from right to left rightmin = self.getMinLen(arr, target, False) for i in range(0, len(arr)-1): result = min(result, leftmin[i] + rightmin[i+1]) return result if result != float('inf') else -1 def getMinLen(self, arr, target, l2r): # if it's reading from right to left, then reverse input array if not l2r: arr = arr[::-1] memo = {0: 0} result = [float('inf')] * len(arr) curSum = 0 for i, num in enumerate(arr): if i > 0: result[i] = result[i-1] curSum += num if curSum - target in memo: curLen = i - memo[curSum - target] + 1 result[i] = min(result[i], curLen) memo[curSum] = i + 1 if not l2r: result = result[::-1] return result
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) prefix = [float('INF')] * (n+1) suffix = [float('INF')] * (n+1) tmp = 0 start = 0 for i in range(n): if arr[i] == target: prefix[i+1] = 1 elif tmp + arr[i] < target: tmp += arr[i] else: # tmp + arr[i] > target tmp += arr[i] while tmp > target and start < i: tmp -= arr[start] start += 1 if tmp == target: prefix[i+1] = i - start + 1 prefix[i+1] = min(prefix[i+1], prefix[i]) tmp = 0 start = -1 for i in range(-1,-n-1,-1): if arr[i] == target: suffix[i] = 1 elif tmp + arr[i] < target: tmp += arr[i] else: # tmp + arr[i] > target tmp += arr[i] while tmp > target and start > i: tmp -= arr[start] start -= 1 if tmp == target: suffix[i] = start -i + 1 suffix[i] = min(suffix[i], suffix[i+1]) # print(prefix) # print(suffix) min_val = float('INF') for i in range(n): min_val = min(min_val, prefix[i] + suffix[i+1]) return min_val if min_val != float('INF') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) acc = dict() acc[-1] = 0 for i in range(0, n): acc[i] = acc[i-1] + arr[i] best_to = [n + 1 for _ in range(n)] best_from = dict() min_total = n + 1 # Naturally impossible length. Will be updated if any possible case exist. Will tell when no possible case min_left = n + 1 sum_left = 0 s_left = 0 for i in range(n): sum_left = acc[i] - acc[s_left-1] # if i == 3: # print(s_left) # print(sum_left) if sum_left == target: best_to[i] = i - s_left + 1 best_from[s_left] = i - s_left + 1 elif sum_left > target: while s_left < i: s_left += 1 if acc[i] - acc[s_left-1] < target: break if acc[i] - acc[s_left-1] == target: best_to[i] = i - s_left + 1 best_from[s_left] = i - s_left + 1 break for i in range(1, n): best_to[i] = min(best_to[i], best_to[i-1]) # print(best_to) # print(best_from) for i in range(n - 1): if best_to[i] > n: continue if i + 1 in best_from: min_total = min(min_total, best_to[i] + best_from[i + 1]) if min_total > n: return -1 return min_total
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: dp = [len(arr) + 1] * len(arr) # min valid subarray length for arr[:i + 1] table = {0: -1} # key: prefix sum, value: latest index s = 0 min_sum = len(arr) + 1 for i in range(len(arr)): s += arr[i] if i > 0: dp[i] = dp[i - 1] if s - target in table: length = i - table[s - target] dp[i] = min(dp[i], length) if length <= i: min_sum = min(min_sum, length + dp[i - length]) table[s] = i if min_sum == len(arr) + 1: return -1 else: return min_sum
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix={0:-1} current=0 queue=[] for i in range(len(arr)): current+=arr[i] prefix[current]=i if not prefix.get(current-target) is None: if len(queue)==0 or prefix[current-target]+1>queue[-1][0]: queue.append((prefix[current-target]+1,i)) if len(queue)<2: return -1 min_q=[] current=len(arr) for i in range(len(queue)-1,-1,-1): current=min(current,queue[i][1]-queue[i][0]+1) min_q.append(current) min_q=min_q[::-1] pointer1=0 pointer2=1 res=-1 #print(queue,min_q) while(pointer2<len(queue)): if queue[pointer2][0]<=queue[pointer1][1]: pointer2+=1 continue #print(pointer1,pointer2,res) if res<0: res=queue[pointer1][1]-queue[pointer1][0]+1+min_q[pointer2] else: res=min(res,queue[pointer1][1]-queue[pointer1][0]+1+min_q[pointer2]) pointer1+=1 return res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: l = r = 0 s = arr[l] res = [] while r < len(arr): if s == target: ln = r - l + 1 res.append((ln, l, r)) if s <= target: r += 1 if r < len(arr): s += arr[r] else: l += 1 s -= arr[l-1] if l > r: r += 1 if r < len(arr): s += arr[r] msl = [math.inf] * len(arr) #minimum interval length so far from left msr = [math.inf] * len(arr) # minimum interval length so far fromm right mi = math.inf resi = -1 for i in range(len(arr)): if resi + 1 < len(res) and res[resi+1][2] == i: resi += 1 mi = min(mi,res[resi][0]) msl[i] = mi mi = math.inf resi = len(res) for i in range(len(arr) - 1, -1 , -1): if resi-1 >= 0 and res[resi-1][1] == i: resi -= 1 mi = min(mi,res[resi][0]) msr[i] = mi mn = math.inf for i in range(len(arr) - 1): mn = min(mn, msl[i] + msr[i+1]) if mn == math.inf: return -1 return mn
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: # 864 ms def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i = window = count = 0 # preMin: store previous shortest length preMin = [(-1, inf)] # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: current length curr = j - i + 1 n = 0 # find first minimal length before window start i for index, length in preMin[::-1]: if index <= i-1: n = length break # update result if less if result > curr + n: result = curr + n # update shortest length if less if curr < preMin[-1][-1]: preMin.append((j, curr)) # early stopping if found two single targets # if curr == 1: count += 1 # if count == 2: return 2 return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: min_range = None left = self.get_list(arr, target) right = list(reversed(self.get_list(list(reversed(arr)), target))) print(left) print(right) min_length = None for i in range(len(arr) - 1): if left[i] != -1 and right[i+1] != -1: if not min_length: min_length = left[i] + right[i+1] else: min_length = min(left[i] + right[i+1], min_length) return -1 if not min_length else min_length def get_list(self, arr, target): prefix_d = dict() prefix_d[0] = -1 min_range_list = [] current_min = -1 current = 0 for i in range(len(arr)): current += arr[i] if current - target in prefix_d: prev_idx = prefix_d[current - target] dis = i - prev_idx if current_min == -1: current_min = dis else: current_min = min(current_min, dis) min_range_list.append(current_min) prefix_d[current] = i return min_range_list
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: MAX = float('inf') n = len(arr)+1 best_till = [MAX for i in range(n+1)] # best subarray length until reach index i (exclusive) presum = 0 maps = {} # key: sum, val: index maps[0] = -1 ans = best = MAX for i, v in enumerate(arr): presum += v # check if we have a subarray key = presum - target if key in maps: left_idx = maps[key] # sums(arr[left_idx+1:i+1]) curr_len = i - left_idx best = min(best, curr_len) # check if this could be a second subarray if left_idx > -1: first_len = best_till[left_idx] ans = min(ans, first_len + curr_len) best_till[i] = best maps[presum] = i if ans == MAX: return -1 return ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # dp_leftは、右から見たときの最小長さarrayを保存 # dp_rightは、左から見たときの最小長さarrayを保存 def get_sub_arrays( arr ): lookup = collections.defaultdict(int) running_sum = 0 dp = [float('inf')] * len(arr) for i, num in enumerate(arr): running_sum += num if running_sum == target: dp[i] = i - 0 + 1 elif running_sum - target in lookup: dp[i] = i - lookup[running_sum - target] + 1 lookup[running_sum] = i+1 dp[i] = min( dp[i-1], dp[i] ) return dp dp_left = get_sub_arrays( arr ) # from front dp_right = get_sub_arrays( arr[::-1] )[::-1] # from backwards ans = float('inf') for i in range( 1, len(arr) ): ans = min( ans, dp_left[i-1] + dp_right[i] ) return ans if( ans != float('inf') ) else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
INF = int(1e9) class Solution: def shortest_subarrays(self, a, target): cum = [0] for x in a: cum.append(cum[-1] + x) hist = {0: 0} ret = [INF] for i in range(1, len(cum)): ci = cum[i] begin = hist.get(ci - target, -1) if begin >= 0: ret.append(min(i - begin, ret[-1])) else: ret.append(ret[-1]) hist[ci] = i return ret def minSumOfLengths(self, arr: List[int], target: int) -> int: forward = self.shortest_subarrays(arr, target) backward = self.shortest_subarrays(reversed(arr), target) ret = INF for i in range(1, len(arr) - 1 + 1): ret = min(ret, forward[i] + backward[len(arr) - i]) if ret >= INF: return -1 return ret
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: curr_sum = 0 h = {0 : 0} f = [100001] * (len(arr) + 1) ans = 100001 for index, a in enumerate(arr): curr_sum += a if curr_sum - target in h: ans = min(f[h[curr_sum - target]] + index + 1 - h[curr_sum - target], ans) f[index + 1] = min(f[index], index + 1 - h[curr_sum - target]) else: f[index + 1] = f[index] h[curr_sum] = index + 1 return -1 if ans >= 100001 else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i = window = count = 0 # preMin: store previous shortest length preMin = [(-1, inf)] # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: current length curr = j - i + 1 n = 0 # find first minimal length before window start i for index, length in preMin[::-1]: if index <= i-1: n = length break # update result if less if result > curr + n: result = curr + n # update shortest length if less if curr < preMin[-1][-1]: preMin.append((j, curr)) # early stopping if found two single targets if curr == 1: count += 1 if count == 2: return 2 return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from typing import List import math import sys class Solution: def __init__(self): self.preceeding_soln_lens = [] def minSumOfLengths(self, arr: List[int], target: int) -> int: # What's the best I can do ENDING at this index. self.preceeding_soln_lens = [sys.maxsize] * len(arr) min_len_sum = sys.maxsize buffer = [] buffer_sum = 0 buffer_len = 0 i = 0 # O(N) while i < len(arr): # update state buffer_sum += arr[i] buffer_len += 1 buffer.append(i) sub_array_end_idx = buffer[-1] # check constraint if buffer_sum < target: # copy over the previous one self.preceeding_soln_lens[sub_array_end_idx] = self.preceeding_soln_lens[sub_array_end_idx-1] while buffer_sum >= target: popped_idx = buffer.pop(0) if buffer_sum == target: # check for the min self.preceeding_soln_lens[sub_array_end_idx] = min(buffer_len, self.preceeding_soln_lens[sub_array_end_idx-1]) if popped_idx > 0: non_overlapping_previous_soln_idx = popped_idx - 1 min_len_sum = min(min_len_sum, self.preceeding_soln_lens[non_overlapping_previous_soln_idx] + buffer_len) else: self.preceeding_soln_lens[sub_array_end_idx] = self.preceeding_soln_lens[sub_array_end_idx-1] buffer_len -= 1 buffer_sum -= arr[popped_idx] i += 1 if min_len_sum == sys.maxsize: return -1 return min_len_sum
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from typing import List import heapq import math import sys class Solution: def __init__(self): self.preceeding_soln_lens = [] self.segment_tree = [] def has_overlap(self, rng, list_of_ranges): s, e = rng if len(list_of_ranges): os, oe = list_of_ranges[-1] if e < os or oe < s: pass else: return True return False def find_min(self, s, e): min_val = sys.maxsize for i in range(s, e): if self.preceeding_soln_lens[i]: min_val = min(min_val, self.preceeding_soln_lens[i]) if min_val == sys.maxsize: return None return min_val def n2_find(self, i, lengths): len_one = self.find_min(0,i) if len_one: len_two = self.find_min(i + len_one - 1, len(self.preceeding_soln_lens)) if len_two: heapq.heappush(lengths, len_one+len_two) def minSumOfLengths(self, arr: List[int], target: int) -> int: # What's the best I can do ENDING at this index. self.preceeding_soln_lens = [sys.maxsize] * len(arr) min_len_sum = sys.maxsize buffer = [] buffer_sum = 0 buffer_len = 0 i = 0 # O(N) while i < len(arr): # update state buffer_sum += arr[i] buffer_len += 1 buffer.append(i) sub_array_end_idx = buffer[-1] # check constraint if buffer_sum < target: # copy over the previous one self.preceeding_soln_lens[sub_array_end_idx] = self.preceeding_soln_lens[sub_array_end_idx-1] while buffer_sum >= target: popped_idx = buffer.pop(0) if buffer_sum == target: # check for the min self.preceeding_soln_lens[sub_array_end_idx] = min(buffer_len, self.preceeding_soln_lens[sub_array_end_idx-1]) if popped_idx > 0: non_overlapping_previous_soln_idx = popped_idx - 1 min_len_sum = min(min_len_sum, self.preceeding_soln_lens[non_overlapping_previous_soln_idx] + buffer_len) else: self.preceeding_soln_lens[sub_array_end_idx] = self.preceeding_soln_lens[sub_array_end_idx-1] buffer_len -= 1 buffer_sum -= arr[popped_idx] i += 1 if min_len_sum == sys.maxsize: return -1 return min_len_sum
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
# Reference : https://leetcode.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/discuss/685486/JAVA-O(N)-Time-Two-Pass-Solution-using-HashMap. class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # prefix sum # in dictionary, store {sum_until_idx: idx} # iterate through the array and keep current sum # 1. have a left_min_len to track the min length until current idx # if current sum + target is in the dictionary, # then it means there is a target in the right side of the array prefix_sum = {0:-1} cur_sum = 0 for i, val in enumerate(arr): cur_sum += val prefix_sum[cur_sum] = i left_min_len = float('inf') ans = float('inf') cur_sum = 0 for i, val in enumerate(arr): cur_sum += val if (cur_sum - target) in prefix_sum: left_min_len = min(left_min_len, i-prefix_sum[cur_sum-target]) if (cur_sum + target) in prefix_sum: ans = min(ans, left_min_len + prefix_sum[cur_sum+target]-i) return ans if ans < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: left_min = self.getMinArr(arr, target, True) right_min = self.getMinArr(arr, target, False) result = sys.maxsize for i in range(0, len(arr)-1): if max(left_min[i], right_min[i+1]) != sys.maxsize: result = min(left_min[i] + right_min[i+1], result) return result if result < sys.maxsize else -1 def getMinArr(self, arr, target, right): result = [sys.maxsize] * len(arr) current_sum = 0 num_map = {0: 0} nums = arr if right else arr[::-1] for i, num in enumerate(nums): if i > 0: result[i] = result[i-1] current_sum += num if current_sum - target in num_map: current_len = i - num_map[current_sum-target] + 1 result[i] = min(result[i], current_len) num_map[current_sum] = i+1 if not right: result.reverse() return result
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) def aux(arr): h = {0:0} preSum = 0 left = [n+1 for i in range(n)] for i in range(1, n+1): preSum = preSum + arr[i-1] h[preSum] = i if preSum-target in h: left[i-1] = i-h[preSum-target] if i > 1: left[i-1] = min(left[i-2], left[i-1]) return left left = aux(arr) arr.reverse() right = aux(arr) # print(left) # print(right) ans = n+1 for i in range(n-1): ans = min(ans, left[i] + right[n-1-(i+1)]) return ans if ans < n+1 else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: def get_shortest(array): shortest = [float('infinity') for _ in range(len(arr))] prefix_pos = {} prefix_sum = 0 for i in range(len(array)): prefix_sum += array[i] if prefix_sum == target: if i == 0: shortest[i] = i+1 else: shortest[i] = min(shortest[i-1], i+1) elif prefix_sum - target in prefix_pos: shortest[i] = i - prefix_pos[prefix_sum-target] +1 shortest[i] = min(shortest[i-1], shortest[i]) prefix_pos[prefix_sum] = i+1 return shortest left = get_shortest(arr) right = get_shortest(arr[::-1])[::-1] res = float('infinity') for i in range(len(left)-1): res = min(res, left[i]+right[i+1]) if res == float('infinity'): return -1 return res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: left_sub_array = [len(arr)]*len(arr) sub_sum, next_index = 0, 0 for index in range(len(arr)): while sub_sum < target and next_index < len(arr): sub_sum += arr[next_index] if sub_sum > target: sub_sum -= arr[next_index] break else: if sub_sum == target : left_sub_array[next_index] = (next_index - index) + 1 next_index += 1 sub_sum -= arr[index] left_sub_array[index] = min(left_sub_array[index], left_sub_array[index - 1]) r_arr = arr[::-1] right_sub_array = [len(r_arr)]*len(r_arr) sub_sum, next_index = 0, 0 for index in range(len(r_arr)): while sub_sum < target and next_index < len(r_arr): sub_sum += r_arr[next_index] if sub_sum > target: sub_sum -= r_arr[next_index] break else: if sub_sum == target : right_sub_array[next_index] = (next_index - index) + 1 next_index += 1 sub_sum -= r_arr[index] right_sub_array[index] = min(right_sub_array[index], right_sub_array[index - 1]) right_sub_array = right_sub_array[::-1] min_length = 2*len(arr) # print(left_sub_array, right_sub_array) for index, val in enumerate(left_sub_array[:-1]): min_length = min(min_length, val + right_sub_array[index + 1]) if min_length > len(arr): return -1 else: return min_length
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def getArraysx (self, arr,target): leftSizes = {} rightSizes = {} #include start-range posleft = 0 posright = 0 currSum = 0 while posright < len(arr): currSum += arr[posright] if currSum == target: #update rifht of i, including i rightList = rightSizes.get(posleft,[]) rightList.append(posright-posleft + 1) rightSizes[posleft] = rightList #update left of i, not including i if (posright +1 < len(arr)): leftList = leftSizes.get(posright+1,[]) leftList.append(posright-posleft + 1) leftSizes[posright+1]=leftList #move pointers to the right posright +=1 currSum -= arr[posleft] posleft +=1 elif currSum > target: #remove leftmost element currSum = currSum - arr[posright] - arr[posleft] posleft +=1 else: #currSum < target #include current element move right pointer posright +=1 #print ('left', leftSizes) #print('right', rightSizes) leftArray = [0]*len(arr) fullList = [] for i in range(len(arr)): additional = leftSizes.get(i,[]) fullList.extend(additional) if len(fullList) > 0: leftArray[i] = min(fullList) else: leftArray[i] = -1 rightArray = [0]*len(arr) fullList = [] for j in range(len(arr)-1, -1,-1): additional = rightSizes.get(j,[]) fullList.extend(additional) if len(fullList) > 0: rightArray[j] = min (fullList) else: rightArray[j] = -1 return leftArray, rightArray def updateArrays (self, leftSizes, rightSizes, posleft, posright,maxvalue): # 3 4 5 # 1 3 2. target = 6 # update i =3 for right or equal of 3 # update i = 6 for left of 6 #update rifht of i, including i value = rightSizes.get(posleft,maxvalue) rightSizes[posleft] = min (value,posright-posleft + 1 ) #update left of i, not including i if posright +1 < maxvalue: value = leftSizes.get(posright+1,maxvalue) leftSizes[posright+1]=min (value,posright-posleft + 1 ) def getArrays (self, arr,target): leftArray = [0]*len(arr) rightArray = [0]*len(arr) leftSizes = {} rightSizes = {} #include start-range posleft = 0 posright = 0 currSum = 0 while posright < len(arr): currSum += arr[posright] if currSum == target: self.updateArrays(leftSizes,rightSizes, posleft, posright, len(arr)) #move pointers to the right posright +=1 currSum -= arr[posleft] posleft +=1 elif currSum > target: #remove leftmost element currSum = currSum - arr[posright] - arr[posleft] posleft +=1 else: #currSum < target #include current element move right pointer posright +=1 #print ('left', leftSizes) #print('right', rightSizes) leftArray = [len(arr)]*len(arr) for i in range(1,len(arr)): minValue = leftSizes.get(i,len(arr)) leftArray[i] = min(minValue, leftArray[i-1]) rightArray = [len(arr)]*len(arr) for j in range(len(arr)-1, -1,-1): minValue = rightSizes.get(j,len(arr)) if j == len(arr)-1: rightArray[j] = minValue else: rightArray[j] = min (minValue, rightArray[j+1]) return leftArray, rightArray def minSumOfLengths(self, arr: List[int], target: int) -> int: leftArray, rightArray = self.getArrays ( arr,target) #print ('left', leftArray) #print ('right', rightArray) #process hashmaps by i position minSum = 2*len(arr) for i in range (1,len(arr)): if leftArray[i] < len(arr): leftSize = leftArray[i] else: continue if rightArray[i] < len(arr): rightSize = rightArray[i] else: continue #print (i, leftSize, rigthSize) minSum = min(minSum, leftSize + rightSize) if minSum == 2*len(arr): minSum = -1 return minSum def minSumOfLengthsx(self, arr: List[int], target: int) -> int: #two pointers #loop until sum = target or > target #if greather than target, move posleft one to the right #keep array of lenghts and get the samllet two (this can be optimized) #or get subarrays, even if they overlap, and then choose the smalles when overalp posleft = 0 posright = 0 lengths = [] # keeping two smallest? currSum = 0 while posright < len(arr): currSum += arr[posright] #`print (posleft, posright, currSum) if currSum == target: lengths.append(posright-posleft + 1) posright +=1 posleft = posright currSum = 0 #if posright < len(arr): # currSum = arr[posright] elif currSum > target: #remove leftmost element currSum = currSum - arr[posright] - arr[posleft] posleft +=1 else: #include current element move right pointer posright +=1 #if posright < len(arr): # currSum += arr[posright] print(lengths) if len(lengths) < 2: return -1 lengths.sort() return sum(lengths[0:2])
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = {0: -1} best_till = [math.inf] * len(arr) ans = best = math.inf for i, curr in enumerate(itertools.accumulate(arr)): if curr - target in prefix: # j is on the left # i is on the right j = prefix[curr - target] if j > -1: # Update the ans, the current one and the non-overlapping best one ans = min(ans, i - j + best_till[j]) # update the shortest length until i best = min(best, i - j) best_till[i] = best prefix[curr] = i return -1 if ans == math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: record = collections.defaultdict() record[0] = 0 l1 = l2 = float('Inf') tmp_sum = 0 res = float('Inf') dp = [float('Inf') for _ in range(len(arr))] for i in range(len(arr)): tmp_sum += arr[i] if tmp_sum - target in record: dp[i] = i - record[tmp_sum - target] + 1 record[tmp_sum] = i + 1 if i>0: dp[i] = min(dp[i], dp[i-1]) record.clear() tmp_sum = 0 record[0] = len(arr) for i in range(len(arr)-1, 0, -1): tmp_sum += arr[i] if tmp_sum - target in record: res = min(res, dp[i-1] + record[tmp_sum - target] - i) record[tmp_sum] = i return res if res<float('Inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: def prefix_sum(arr): lookup = {} dp = [float('inf')] * len(arr) cumsum = 0 for i, num in enumerate(arr): cumsum += num if cumsum == target: dp[i] = i - 0 + 1 elif cumsum - target in lookup: dp[i] = i - lookup[cumsum - target] lookup[cumsum] = i dp[i] = min(dp[i-1], dp[i] ) return dp prefix = prefix_sum(arr) suffix = prefix_sum(arr[::-1])[::-1] ans = float('inf') for i in range(1, len(arr)): ans = min(ans, prefix[i-1] + suffix[i]) return ans if ans != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: if len(arr) < 2: return -1 n = len(arr) curSum = 0 prefixSum = {0:-1} dp = [float('inf')]*n ans = float('inf') for i in range(n): curSum += arr[i] if curSum - target in prefixSum: j = prefixSum[curSum - target] + 1 ans = min(ans, i - j + 1 + dp[j-1]) dp[i] = min(dp[i-1], i - j + 1) else: dp[i] = dp[i-1] prefixSum[curSum] = i return ans if ans < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def getMinArr(self, arr, target, right=False): pre_sum = 0 res = [float('inf') for i in range(len(arr))] sum_dict = {0:0} if right: arr = arr[::-1] for i, num in enumerate(arr): pre_sum += num if i > 0: res[i] = res[i-1] if pre_sum - target in sum_dict: cur_len = i - sum_dict[pre_sum - target] + 1 res[i] = min(res[i], cur_len) sum_dict[pre_sum] = i + 1 if right: res.reverse() return res def minSumOfLengths(self, arr: List[int], target: int) -> int: left_min = self.getMinArr(arr, target) right_min = self.getMinArr(arr, target, True) min_len = float('inf') for i in range(len(arr) - 1): min_len = min(min_len, left_min[i] + right_min[i+1]) if min_len == float('inf'): return -1 return min_len # prefix_sum = [0 for i in range(len(arr) + 1)] # for i in range(len(arr)): # prefix_sum[i+1] = prefix_sum[i] + arr[i] # prefix = [float('inf') for i in range(len(arr))] # suffix = [float('inf') for i in range(len(arr))] # for i in range(1, len(arr)): # # found = False # for j in range(i-1, -1, -1): # if prefix_sum[i] - prefix_sum[j] == target: # # found = True # prefix[i] = i - j # break # for i in range(len(arr) - 1, -1, -1): # # found = False # for j in range(i+1, len(arr) + 1): # if prefix_sum[j] - prefix_sum[i] == target: # # found = True # suffix[i] = j - i # break # for i in range(1, len(prefix)): # prefix[i] = min(prefix[i], prefix[i-1]) # for i in range(len(suffix) - 2, -1, -1): # suffix[i] = min(suffix[i], suffix[i+1]) # min_len = float('inf') # for i in range(len(arr)): # min_len = min(min_len, prefix[i] + suffix[i]) # if min_len == float('inf'): # return -1 # return min_len
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
import sys class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: table={0:-1} cursum=0 dp1 = [sys.maxsize for i in range(len(arr))] for i in range(len(arr)): if i>0: dp1[i] = dp1[i-1] cursum += arr[i] if cursum - target in list(table.keys()): dp1[i] = min(dp1[i],i-table[cursum-target]) table[cursum]=i #print(table) #print(dp1) table={0:len(arr)} cursum=0 dp2 = [sys.maxsize for i in range(len(arr))] for i in range(len(arr)-1,-1,-1): if i< len(arr)-1: dp2[i] = dp2[i+1] cursum += arr[i] if cursum - target in list(table.keys()): dp2[i] = min(dp2[i],table[cursum-target]-i) table[cursum]=i #print(table) #print(dp2) res = sys.maxsize for i in range(len(dp1)-1): if dp1[i] != sys.maxsize and dp2[i+1] != sys.maxsize: res = min(res,dp1[i]+dp2[i+1]) if res == sys.maxsize: return -1 else: return res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) def get_dp(arr): dp = [] ptr = 0 total = 0 min_val = float('inf') for i in range(n): total += arr[i] while ptr < i and total > target: total -= arr[ptr] ptr += 1 if total == target: min_val = min(min_val, i - ptr + 1) dp.append(min_val) return dp dp_left = get_dp(arr) dp_right = get_dp(arr[::-1])[::-1] min_val = float('inf') for i in range(n-1): min_val = min(min_val, dp_left[i] + dp_right[i+1]) return min_val if min_val != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = [0] d = {0: -1} for i in range(len(arr)): prefix.append(arr[i] + prefix[-1]) d[prefix[-1]] = i ans = first = second = float('inf') for i in range(len(arr)): if (prefix[i + 1] - target) in d: first = min(first, i - d[(prefix[i + 1] - target)]) if first < float('inf') and (prefix[i + 1] + target) in d: second = d[(prefix[i + 1] + target)] - i ans = min(ans, first + second) return -1 if ans == float('inf') else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: preSum = [0] for val in arr: preSum.append(preSum[-1] + val) sumMap = {} preCands = [sys.maxsize] * len(arr) sufCands = [sys.maxsize] * len(arr) for i, val in enumerate(preSum): if val - target in sumMap: sufCands[sumMap[val - target]] = i - sumMap[val - target] preCands[i - 1] = i - sumMap[val - target] sumMap[val] = i # print(preCands) # print(sufCands) prefixSum = [sys.maxsize] * len(arr) suffixSum = [sys.maxsize] * len(arr) for i, val in enumerate(preCands): if i + 1 < len(prefixSum): prefixSum[i + 1] = min(preCands[i], prefixSum[i]) for i, val in reversed(list(enumerate(sufCands))): if i + 1 < len(suffixSum): suffixSum[i] = min(sufCands[i], suffixSum[i + 1]) else: suffixSum[i] = sufCands[i] # print(prefixSum) # print(suffixSum) res = sys.maxsize for i in range(len(arr)): res = min(res, prefixSum[i] + suffixSum[i]) return res if res != sys.maxsize else -1 # t = 6 # idx 0 1 2 3 4 5 6 7 8 # arr 1 2 3 3 2 1 1 1 1 # 3 3 # 1 2 3 # 3 2 1 # 2 1 1 1 1 # preSum 0 1 3 6 9 11 12 13 14 15 # preCands M M 3 2 M 3 M M 5 # sufCands 3 M 2 3 5 M M M M # prefix M M M 3 2 2 2 2 2 # suffix 2 2 2 3 5 M M M M
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: length=len(arr) cumulative=[0]*length reverse_cumulative=[0]*length s=0 sr=0 for i in range(length): s=s+arr[i] cumulative[i]=s sr+=arr[(length-1)-i] reverse_cumulative[i]=sr d={0:-1} dr={0:-1} forward_vals=[math.inf]*length backward_vals=[math.inf]*length best1=math.inf best2=math.inf i=0 while i<length: d[cumulative[i]]=i dr[reverse_cumulative[i]]=i if (cumulative[i]-target) in d: # print(\"found\",cumulative[i]-target,\"!\") l=i-d[cumulative[i]-target] best1=min(best1,l) forward_vals[i]=best1 # print(\"the subarray with sum=target is\",(start+1,i)) if (reverse_cumulative[i]-target) in dr: l=i-dr[reverse_cumulative[i]-target] best2=min(best2,l) backward_vals[i]=best2 i+=1 # print(cumulative,reverse_cumulative) #print(d,dr) #print(forward_vals,backward_vals) best1=math.inf for i in range(len(forward_vals)-1): best1=min(best1,forward_vals[i]+backward_vals[(length-2)-i]) if best1==math.inf: return -1 return best1 #print(d)
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: # 872 ms def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i = window = 0 premin = [inf] * len(arr) # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: length curr = j - i + 1 if result > curr + premin[i - 1]: result = curr + premin[i - 1] premin[j] = curr if curr < premin[j - 1] else premin[j - 1] else: premin[j] = premin[j - 1] return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: ''' 1 1 1 2 2 3 1 1 1 1 1 target : 5 ''' sP = 0 fP = 0 intervalHeap = [] sumSoFar = 0 while fP < len(arr): sumSoFar += arr[fP] if sumSoFar >= target: if sumSoFar == target: heapq.heappush(intervalHeap, (fP - sP + 1, sP, fP)) while sumSoFar >= target: sumSoFar -= arr[sP] sP += 1 if sumSoFar == target: heapq.heappush(intervalHeap, (fP - sP + 1, sP, fP)) fP += 1 if len(intervalHeap) > 1: first = heapq.heappop(intervalHeap) second = heapq.heappop(intervalHeap) if first[2] < second[1] or second[2] < first[1]: return first[0] + second[0] else: while intervalHeap: third = heapq.heappop(intervalHeap) if third and first[2] < third[1] or third[2] < first[1]: return first[0] + third[0] elif third and second[2] < third[1] or third[2] < second[1]: return second[0] + third[0] return -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
import numpy as np class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: cumsum = np.cumsum(arr) h2idx = {} print(cumsum) minSum = [] for idx,c in enumerate(cumsum): # print(c, target, target-c, h2idx) if c == target: minSum.append(idx+1) if (c - target) in h2idx: minSum.append(idx - h2idx[c - target]) h2idx[c] = idx if len(minSum) < 2: return -1 return sum(list(sorted(minSum))[:2]) # t = 7 # [ 2, 2, 3, 4, 3, 4] def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = {0: -1} best_till = [math.inf] * len(arr) ans = best = math.inf for i, curr in enumerate(itertools.accumulate(arr)): if curr - target in prefix: end = prefix[curr - target] if end > -1: ans = min(ans, i - end + best_till[end]) best = min(best, i - end) best_till[i] = best prefix[curr] = i return -1 if ans == math.inf else ans def minSumOfLengths(self, arr: List[int], target: int) -> int: cumsum = np.cumsum(arr) h2idx = {} INF = math.inf print(cumsum) best_at_i = [INF] * len(arr) best = INF for idx,c in enumerate(cumsum): # print(c, target, target-c, h2idx) if c == target: # print('sdfjsldfjksdl') # best = min(best, best_at_i[left-1] + idx+1) best_at_i[idx] = min(best_at_i[idx-1], idx+1) if (c-target) in h2idx: # print('fhgjdkg') left = h2idx[c-target] best = min(best, best_at_i[left] + idx - left) best_at_i[idx] = min(best_at_i[left], idx - left) # print(idx, left, best_at_i[left], best) h2idx[c] = idx best_at_i[idx] = min(best_at_i[idx-1], best_at_i[idx]) print(best_at_i, h2idx) return best if best != INF else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: lim = len(arr) pref = [arr[0]] d = dict() e = dict() d[arr[0]]=[0] e[arr[0]]=1 for i in range(1,lim): pref.append(pref[-1]+arr[i]) try: d[pref[-1]].append(i) e[pref[i]]+=1 except: d[pref[-1]]=[i] e[pref[i]]=1 A = [lim]*lim for i in range(0,lim): val = target+pref[i]-arr[i] if val in d: l = 0 h = e[val]-1 mn = lim+1 while l<=h: m = (l+h)//2 if d[val][m]>=i: if d[val][m]<mn: mn = d[val][m] h = m-1 else: l = m+1 if mn!=lim+1: A[i]=mn-i+1 if arr[i]==target: A[i]=1 pmn = lim p = [lim]*lim s = [lim]*lim for i in range(0,lim): if i+A[i]<lim and p[i+A[i]]>A[i]:p[i+A[i]]=A[i] smn = lim if A[-1]<lim: smn=A[-1] for i in range(lim-1,-1,-1): if A[i]<smn: smn = A[i] s[i]=smn mn = lim+1 for i in range(0,lim): if p[i]+s[i]<mn: mn = p[i]+s[i] if mn>=lim+1:return -1 return mn
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr, target): inf = 2**31-1 i, window, result = 0, 0, inf premin = [inf] * len(arr) # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: length # print(premin, i, j) curr = j - i + 1 if result > curr + premin[i - 1]: result = curr + premin[i - 1] premin[j] = curr if curr < premin[j - 1] else premin[j - 1] else: premin[j] = premin[j - 1] return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) prefix_sum = list(accumulate(arr)) suffix_sum = list(accumulate(arr[::-1])) def helper(prefix_sum, n, target): dict_x = {0:-1} l_1 = [n+1 for _ in range(n)] for i in range(n): t1 = prefix_sum[i]-target x = n+1 if dict_x.get(t1, 'x') != 'x': x = i-dict_x[t1] l_1[i] = min(x, l_1[i-1] if i > 0 else n+1) dict_x[prefix_sum[i]] = i return l_1 l = helper(prefix_sum, n, target) r = helper(suffix_sum, n, target)[::-1] ans = sys.maxsize for i in range(n-1): ans = min(ans, l[i]+r[i+1]) print(ans) return ans if ans <= n else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: smallest = [math.inf] * len(arr) q = deque() curr_sum = 0 result = math.inf for i, n in enumerate(arr): curr_sum += n q.append(i) while curr_sum > target: curr_sum -= arr[q.popleft()] if curr_sum == target: if i == 0: smallest[i] = len(q) else: smallest[i] = min(len(q), smallest[i-1]) # if q[0] > 0: result = min(result, smallest[q[0]-1] + len(q)) else: # if i > 0: smallest[i] = smallest[i-1] return -1 if result == math.inf else result
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n_arr = len(arr) if n_arr == 0: return -1 def get_minlen_ending_before(array: List[int]) -> List[int]: n_array = len(array) minlen_array = [float('inf')] * n_array curr_sum = array[0] i = 0 j = 0 min_len = float('inf') while i < n_array and j < n_array: increment_i = False increment_j = False if curr_sum == target: min_len = min(min_len, j - i + 1) curr_sum -= array[i] increment_i = True elif curr_sum < target: increment_j = True if j < n_array - 1: curr_sum += array[j+1] elif curr_sum > target: curr_sum -= array[i] increment_i = True if j < n_array - 1: minlen_array[j+1] = min_len if increment_i: i += 1 if increment_j: j += 1 if j < i and i < n_array: j = i curr_sum = array[i] return minlen_array prefix = get_minlen_ending_before(arr) postfix = (get_minlen_ending_before(arr[::-1] + [0])[1:])[::-1] min_sum = float('inf') for i in range(n_arr): min_sum = min(min_sum, prefix[i] + postfix[i]) return min_sum if min_sum < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) su = 0 s = 0 min_len = float('inf') min_lens = [float('inf') for _ in range(n)] ans = float('inf') for e in range(n): su += arr[e] while su > target: su -= arr[s] s += 1 if su == target: cur_len = e - s + 1 if s > 0 and min_lens[s - 1] != float('inf'): ans = min(ans, cur_len + min_lens[s - 1]) min_len = min(min_len, cur_len) min_lens[e] = min_len return -1 if ans >= float('inf') else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: left = list(itertools.accumulate(arr)) right = list(itertools.accumulate(arr[::-1])) right = right[::-1] rans = [500000] * len(arr) lans = [500000] * len(arr) i, j, n = 0, 0, len(arr) while i < n and j < n: sm = left[j] - (left[i-1] if i else 0) while sm > target and i <= j: i += 1 sm = left[j] - (left[i-1] if i else 0) if sm == target: lans[j] = min(lans[j], j - i + 1) # i += 1 j += 1 i, j = n-1, n-1 while i > -1: sm = right[i] - (right[j+1] if (j+1 < n) else 0) # print(i, j, sm) while sm > target and j >= i: j -= 1 sm = right[i] - (right[j+1] if (j+1 < n) else 0) if sm == target: rans[i] = min(rans[i], j - i + 1) # j -= 1 i -= 1 ans = math.inf # print(lans) # print(rans) mv = 999999999 for i in range(n): mv= min(mv, lans[i]) lans[i] = mv mv = 212498174 for i in range(n-1,-1,-1): mv = min(mv, rans[i]) rans[i] = mv for i in range(n-1): ans = min(ans, lans[i] + rans[i+1]) return ans if ans < 500000 else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from collections import deque import heapq class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # record the best at outcome at each index shortest = sys.maxsize record = {} left = 0 curr_sum = 0 for right in range(len(arr)): curr_sum += arr[right] while curr_sum > target and left <= right: # shrink the window curr_sum -= arr[left] left += 1 if curr_sum == target: # found subarray curr_len = right - left + 1 prev_len = record.get(left - 1, sys.maxsize) record[right] = min(record.get(right - 1, sys.maxsize), curr_len) # update the result shortest = min(shortest, curr_len + prev_len) else: # keep looking record[right] = record.get(right - 1, sys.maxsize) if shortest == sys.maxsize: return -1 return shortest
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: res = [float('inf')] * len(arr) ans = float('inf') currMin = float('inf') i = 0 s = 0 for j in range(len(arr)): s += arr[j] while s > target: s -= arr[i] i += 1 if s == target: currMin = min(currMin, j - i + 1) ans = min(ans, j - i + 1 + res[i-1]) res[j] = currMin return ans if ans < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) dp = [10000000] * n presum = {} presum[0] = -1 s = 0 bestsofar = 10000000 ans = 10000000 for i in range(n): s += arr[i] if s - target in presum: j = presum[s - target] bestsofar = min(bestsofar, i - j) if j >= 0: ans = min(ans, dp[j] + i - j) presum[s] = i dp[i] = bestsofar return ans if ans < 10000000 else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr, target): result = inf = 2**31-1 i, window = 0, 0 premin = [inf] * len(arr) # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: length # print(premin, i, j) curr = j - i + 1 if result > curr + premin[i - 1]: result = curr + premin[i - 1] premin[j] = curr if curr < premin[j - 1] else premin[j - 1] else: premin[j] = premin[j - 1] return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: if not arr: return -1 def getdp(arr): dp = [float('inf')]*(len(arr)) summ = 0 lookup = defaultdict(int) for index, num in enumerate(arr): summ += num if summ == target: dp[index] = index - 0 + 1 elif summ - target in lookup: dp[index] = min(index - lookup[summ-target] + 1, dp[index-1]) else: dp[index] = dp[index-1] lookup[summ] = index + 1 return dp dp_left = getdp(arr) dp_right = getdp(arr[::-1])[::-1] ans = float('inf') for i in range(1, len(arr)): ans = min(ans, dp_left[i-1] + dp_right[i]) return ans if (ans!=float('inf')) else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution(object): def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = {0: -1} best_till = [math.inf] * len(arr) ans = best = math.inf for i, curr in enumerate(itertools.accumulate(arr)): if curr - target in prefix: end = prefix[curr - target] if end > -1: ans = min(ans, i - end + best_till[end]) best = min(best, i - end) best_till[i] = best prefix[curr] = i return -1 if ans == math.inf else ans def OldminSumOfLengths(self, arr, target): ans, l = math.inf, len(arr) la = [math.inf] * l p1, p2, s, ml = 0, 0, arr[0], math.inf while p1 < l and p2 < l: action = None la[p2] = ml curl = p2 - p1 + 1 if s == target: ml = min(ml, curl) la[p2] = ml if p1 - 1 >= 0: ans = min(ans, la[p1 - 1] + curl) p2 += 1 action = 1 elif s < target: p2 += 1 action = 1 elif s > target: p1 += 1 action = -1 if p1 >= l or p2 >= l: break elif p1 > p2: p2 = p1 s = arr[p1] else: if action == 1: s += arr[p2] elif action == -1: s -= arr[p1 - 1] return -1 if ans == math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: pref = { 0: -1 } result = best = math.inf best_till = [math.inf] * len(arr) for i, curr in enumerate(itertools.accumulate(arr)): diff = curr - target if diff in pref: left = pref[diff] length = i - left result = min(result, best_till[left] + length) best = min(best, length) pref[curr] = i best_till[i] = best return result if result < math.inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # premin[i] is the min len of subarr with sum in arr[:i+1] premin = [float('inf')] * len(arr) l, cur, res = 0, 0, float('inf') for r, num in enumerate(arr): if r > 0: premin[r] = premin[r - 1] cur += num while cur > target: cur -= arr[l] l += 1 if cur == target: size = r - l + 1 if l > 0: res = min(res, size + premin[l - 1]) premin[r] = min(premin[r], size) return res if res < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: psum={0:-1} csum=0 re=100001 dp=[100001]*(len(arr)) best=100001 for i,csum in enumerate(itertools.accumulate(arr)): psum[csum]=i if csum-target in psum: best=(min(best,i-psum[csum-target])) re=min(re,dp[psum[csum-target]]+i-psum[csum-target]) dp[i]=best if re<100001: return re return -1 # def minSumOfLengths(self, arr: List[int], target: int) -> int: # prefix = {0: -1} # best_till = [math.inf] * len(arr) # ans = best = math.inf # for i, curr in enumerate(itertools.accumulate(arr)): # if curr - target in prefix: # end = prefix[curr - target] # if end > -1: # ans = min(ans, i - end + best_till[end]) # best = min(best, i - end) # best_till[i] = best # prefix[curr] = i # return -1 if ans == math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: # 872 ms def minSumOfLengths(self, arr, target): if len(arr) < 2: return -1 if arr.count(target) >= 2: return 2 result = inf = 2**31-1 i = window = 0 premin = [inf] * len(arr) # i: window start, j: window end for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: # curr: length curr = j - i + 1 if result > curr + premin[i - 1]: result = curr + premin[i - 1] premin[j] = curr if curr < premin[j - 1] else premin[j - 1] else: premin[j] = premin[j - 1] return result if result < inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix={0:-1} best_till=[math.inf]*len(arr) ans=best=math.inf for i in range(1,len(arr)): arr[i]+=arr[i-1] for i,cur in enumerate(arr): if cur-target in prefix: end=prefix[cur-target] if end>-1: ans=min(ans,i-end+best_till[end]) best=min(best,i-end) best_till[i]=best prefix[cur]=i return -1 if ans==math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: psum={0:-1} csum=0 re=100001 dp=[100001]*(len(arr)) best=100001 for i,csum in enumerate(itertools.accumulate(arr)): psum[csum]=i if csum-target in psum: end=psum[csum-target] best=(min(best,i-end)) if end>-1: re=min(re,dp[end]+i-end) dp[i]=best if re<100001: return re return -1 # def minSumOfLengths(self, arr: List[int], target: int) -> int: # prefix = {0: -1} # best_till = [math.inf] * len(arr) # ans = best = math.inf # for i, curr in enumerate(itertools.accumulate(arr)): # if curr - target in prefix: # end = prefix[curr - target] # if end > -1: # ans = min(ans, i - end + best_till[end]) # best = min(best, i - end) # best_till[i] = best # prefix[curr] = i # return -1 if ans == math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr, target): i, window, result = 0, 0, float('inf') premin = [float('inf')] * len(arr) for j, num in enumerate(arr): window += num while window > target: window -= arr[i] i += 1 if window == target: curr = j - i + 1 result = min(result, curr + premin[i - 1]) premin[j] = min(curr, premin[j - 1]) else: premin[j] = premin[j - 1] return result if result < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengthsOld(self, arr: List[int], target: int) -> int: n = len(arr) if n == 1: return -1 i = 0 j = 0 sum_=arr[i] interval = [] while i < n and j < n: #print(i,j, sum_) if sum_ == target: interval.append([i,j, (j-i+1)]) sum_-=arr[i] i+=1 j+=1 if j <n: sum_+=arr[j] elif sum_<target: if j < n-1: sum_+= arr[j+1] j+=1 else: sum_-=arr[i] i+=1 if len(interval) == 0: return -1 interval.sort(key = lambda x: x[2] ) interval_val_sorted = [x for x in interval] interval.sort(key = lambda x: x[0] ) ''' for i in range(len(interval)): s, e, val = interval_val_sorted[i][0], interval_val_sorted[i][1], interval_val_sorted[i][2] ind = findCeil(e, interval) if ind == -1: continue val1 = ind[2] return val + val1 ''' print(interval_val_sorted ) print(interval) i_ , j_, l_ = interval[0][0], interval[0][1], interval[0][2] #l_1 = 0 found = False for i in range(1, len(interval), 1): i_1, j_1, l_1 = interval[i][0], interval[i][1], interval[i][2] #print(i_1, j_1) if i_1 >= i_ and i_1 <= j_: continue if i_ >=i_1 and i_ <=j_1: continue found = True break if found == False: return -1 return l_ + l_1 def findCeil(self, x, starts): s = 0 e = len(starts) -1 res = -1 while s<=e: mid = s+(e-s) // 2 if starts[mid] > x: res = mid e = mid -1 else: s = mid +1 return res def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) i = 0 j = 0 overlaps = list() #sum_ = arr[i] sum_= 0 j = 0 while i < n and j < n: sum_+=arr[j] while j<n-1 and sum_ < target: j+=1 #print(j) sum_+= arr[j] #print(\"B:\", i,j, sum_) if sum_ == target: overlaps.append([i, j]) sum_-=arr[i] sum_-=arr[j] i+=1 #j+=1 #print(\"A:\", i,j, sum_) if sum_== target: if i <=n-1: overlaps.append([i,j-1]) starting = [x for [x,y] in overlaps] length = [y-x+1 for [x,y] in overlaps] l_o = len(length) if l_o == 0: return -1 min_arr = [length[-1]] s = 1 min_ = length[-1] for i in range(l_o-2, -1, -1): min_ = min(length[i], min_) min_arr.append(min_) min_length = sys.maxsize #print(overlaps) #print(starting) #print(length) #print(min_arr) min_arr = list(reversed(min_arr)) for overlap in overlaps: s, e = overlap[0], overlap[1] indi = self.findCeil(e, starting) #print(\"s,e, indi\", s, e, indi) if indi == -1: continue min_length = min(min_length, e-s+1 + min_arr[indi]) #print(min_length) if min_length == sys.maxsize: return -1 return min_length
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: left = self.shortestTails(arr, target, False) right = self.shortestTails(arr, target, True) mn = float('inf') for i in range(len(arr)-1): if left[i][0] < float('inf') and right[i+1][0] < float('inf'): mn = min(mn, left[i][0]+right[i+1][0]) return mn if mn < float('inf') else -1 def shortestTails(self, arr, target, reverse): end = len(arr)-1 if reverse else 0 prefixSumMap = { 0: len(arr) if reverse else -1 } s = 0 shortestAt = [None]*len(arr) shortest = (float('inf'), -1, -1) for _ in range(len(arr)): s+=arr[end] diff = s-target if diff in prefixSumMap: start = prefixSumMap[diff] if abs(end-start) < shortest[0]: shortest = (abs(end-start), start, end) shortestAt[end] = shortest prefixSumMap[s] = end end = end-1 if reverse else end+1 #print(shortestAt) return shortestAt
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: mp = {} sum_list = 0 mp[0] = -1; for i, val in enumerate(arr): sum_list += val mp[sum_list] = i res = float('inf') lvalue = float('inf') sum_list = 0 # print(mp) for i, val in enumerate(arr): sum_list += val if sum_list - target in mp: lvalue = min(lvalue, i - mp[sum_list - target]) if sum_list + target in mp and lvalue != float('inf'): res = min(res, lvalue + mp[sum_list + target] - i) return -1 if res == float('inf') else res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: if not arr: return 0 min_at_curr = [float('inf')]*len(arr) start = end = 0 currSum = 0 minSum = float('inf') while end < len(arr): currSum += arr[end] while start <= end and currSum > target: currSum -= arr[start] start += 1 if currSum == target: minSum = min(minSum, min_at_curr[start-1] + (end-start) + 1) min_at_curr[end] = min(min_at_curr[end-1], end-start+1) else: min_at_curr[end] = min_at_curr[end-1] end += 1 return minSum if minSum != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) # dp[i] means the minimum length of the sub-array with sum equal to target from 0 to i dp = [100001] * (n) presum = {0: -1} s = 0 ans = 100001 best_so_far = sys.maxsize for i in range(n): s += arr[i] presum[s] = i if s - target in presum: j = presum[s - target] best_so_far = min(best_so_far, i - j) if j >= 0: ans = min(ans, dp[j] + i - j) dp[i] = best_so_far return ans if ans < 100001 else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) dp = [float('inf')] * n sums, res = 0, float('inf') sum_record = {0: -1} for i, num in enumerate(arr): sums += num dp[i] = dp[i - 1] if sums - target in sum_record: cur_len = i - sum_record[sums - target] if i - cur_len >= 0: res = min(res, cur_len + dp[i - cur_len]) dp[i] = min(dp[i - 1], cur_len) sum_record[sums] = i return res if res != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: H = {0: -1} total = 0 M = len(arr) + 1 for i, a in enumerate(arr): total += a H[total] = i result = M minL = M total = 0 for i, a in enumerate(arr): total += a if total - target in H: minL = min(minL, i - H[total - target]) if total + target in H and minL < M: result = min(result, minL + H[total + target] - i) return result if result < M else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = {0: -1} best_till = [math.inf] * len(arr) ans = best = math.inf for i, curr in enumerate(itertools.accumulate(arr)): if curr - target in prefix: end = prefix[curr - target] if end > -1: ans = min(ans, i - end + best_till[end]) best = min(best, i - end) best_till[i] = best prefix[curr] = i return -1 if ans == math.inf else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) dp = [float('inf')]*(n+1) s, e = 0, 0 total = 0 while e < n: total += arr[e] e += 1 while total > target: total -= arr[s] s += 1 if total == target: dp[e] = e-s ans = float('inf') for i in range(1, n+1): if dp[i]<= i: ans = min(ans, dp[i-dp[i]]+dp[i]) dp[i] = min(dp[i], dp[i-1]) return ans if ans<float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: minlen = [float('inf')] * len(arr) res = float('inf') l, r, windsum = 0, 0, 0 for r in range(len(arr)): windsum += arr[r] while windsum > target: windsum -= arr[l] l += 1 if windsum == target: if minlen[l-1] != float('inf'): temp = minlen[l-1] + r - l + 1 res = min(res, temp) minlen[r] = min(minlen[r-1], r - l + 1) else: minlen[r] = minlen[r-1] return res if res < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: accuArr = [] y = 0 for x in arr: y += x accuArr.append(y) bestTill = [float('inf')] * len(arr) bestTillNow = float('inf') sum2Pos = dict() sum2Pos[0] = -1 res = float('inf') for i in range(len(accuArr)): currAccu = accuArr[i] preSum = currAccu - target if preSum in sum2Pos: preEnd = sum2Pos[preSum] currLength = i - preEnd if preEnd != -1: res = min(res, currLength + bestTill[preEnd]) bestTillNow = min(bestTillNow, currLength) sum2Pos[currAccu] = i bestTill[i] = bestTillNow return res if res != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: minLen = float('inf') lsize = float('inf') preSum = {0: -1} curSum = 0 for i, val in enumerate(arr): curSum += val preSum[curSum] = i curSum = 0 for i, val in enumerate(arr): curSum += val if curSum-target in preSum: lsize = min(lsize, i-preSum[curSum-target]) if curSum+target in preSum and lsize != float('inf'): minLen = min(minLen, preSum[curSum+target]-i+lsize) return minLen if minLen != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # PreSum. for every i, find the minimum value of length of sub-array on the left or starting with i whose value is equal to target. Find another sub-array starting with i+1, whose sum is target. Update the result with the minimum value of the sum of both the sub-array. This is possible because all values are positive and the value of sum is strictly increasing, meaning arr[i]+target will always be on the right of i, and, if arr[i]+target exists, there will only be one answer (this condition also applies to arr[i]-target, there will only be one answer for each i if the answer exists, as the array is strictly increasing and there's no zeros) preSum = {0: -1} n = len(arr) curSum = 0 minLen = float('inf') lsize = float('inf') for i in range(n): curSum += arr[i] preSum[curSum] = i curSum = 0 for i in range(n): curSum += arr[i] if curSum-target in preSum: lsize = min(lsize, i-preSum[curSum-target]) if curSum+target in preSum and lsize != float('inf'): minLen = min(minLen, preSum[curSum+target]-i+lsize) return minLen if minLen != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: start, ans, sum = 0, float('inf'), 0 best = [float('inf')]*(len(arr)) best_so_far = float('inf') for i in range(len(arr)): sum += arr[i] while sum > target: sum -= arr[start] start += 1 if sum == target: if start > 0 and best[start-1] != float('inf'): ans = min(ans, best[start-1] + i-start +1) best_so_far = min(best_so_far, i-start+1) best[i] = best_so_far return -1 if ans == float('inf') else ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # PreSum. for every i, find the minimum value of length of sub-array on the left or starting with i whose value is equal to target. Find another sub-array starting with i+1, whose sum is target. Update the result with the minimum value of the sum of both the sub-array. This is possible because all values are positive and the value of sum is strictly increasing, meaning arr[i]+target will always be on the right of i, and, if arr[i]+target exists, there will only be one answer (this condition also applies to arr[i]-target, there will only be one answer for each i if the answer exists, as the array is strictly increasing and there's no zeros) # Again the array is strictly increasing, so at each i, there may exist one left solution including i and one right solution including i, compare those against all prior left solutions and all prior right solutions. Now, no need to compare right solution if there has never been a left solution. preSum = {0: -1} n = len(arr) curSum = 0 minLen = float('inf') lsize = float('inf') for i in range(n): curSum += arr[i] preSum[curSum] = i curSum = 0 for i in range(n): curSum += arr[i] # compare current solution to hit curSum-target including i with all prior left solutions if curSum-target in preSum: lsize = min(lsize, i-preSum[curSum-target]) # If left solution exists, compare current solution to hit curSum+target including i with all prior right solutions if curSum+target in preSum and lsize != float('inf'): minLen = min(minLen, preSum[curSum+target]-i+lsize) return minLen if minLen != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) res = n + 1 pre = {} pre[0] = -1 dp = [float('inf')] * n p = 0 for i, a in enumerate(arr): p += a dp[i] = dp[i - 1] if (p - target) in pre: cur = i - pre[p - target] if pre[p - target] >= 0 and dp[pre[p - target]] != float('inf'): res = min(res, cur + dp[pre[p - target]]) dp[i] = min(i - pre[p - target], dp[i - 1]) pre[p] = i return -1 if res == n + 1 else res #https://leetcode-cn.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/solution/biao-zhun-de-dong-tai-gui-hua-zhu-xing-jiang-jie-b/
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: l = 0 currentSum = 0 res = -1 record = [-1] * len(arr) for r in range(len(arr)): currentSum += arr[r] while currentSum > target and l < r: currentSum -= arr[l] l += 1 if currentSum == target: curr = r - l + 1 print(curr) if record[l-1] != -1: res = curr + record[l-1] if res == -1 else min(res, curr + record[l-1]) record[r] = curr if record[r-1]==-1 else min(record[r-1], curr) else: record[r] = record[r-1] return res
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix_sum2_idx = defaultdict(int) prefix_sum2_idx[0] = -1 prefix_sum = 0 n = len(arr) for i in range(n): prefix_sum += arr[i] prefix_sum2_idx[prefix_sum] = i prefix_sum = 0 l_min_len = float('inf') min_len = float('inf') for i in range(n): prefix_sum += arr[i] # find min length whose right end point is i if prefix_sum - target in prefix_sum2_idx: l_min_len = min(l_min_len, i - prefix_sum2_idx[prefix_sum - target]) # find min length whose left start point is i + 1 if prefix_sum + target in prefix_sum2_idx: min_len = min(min_len, prefix_sum2_idx[prefix_sum + target] - i + l_min_len) return -1 if min_len == float('inf') else min_len
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: for i in range(1, len(arr)): arr[i] += arr[i-1] # arr is now prefix_sum index = {0: -1} # map prefix_sum -> index of that sum best_till = [float('inf')] * len(arr) # best_till[i] is best answer up till that res = float('inf') best = float('inf') for i,val in enumerate(arr): if val-target in index: start_of_window = index[val-target] length = i - start_of_window res = min(res, best_till[start_of_window+1] + length) best = min(best, length) if i+1 < len(best_till): best_till[i+1] = best index[val] = i return -1 if res == float('inf') else res ''' target=7 [1,6,1] arr=[1,7,8] index { 0->-1, 1->0, } best_till= [inf, 2, 2] res = inf i=2, val=8 start_of_window = 0 length = 2 '''
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: sums_list = [0] sums_dict ={0:0} s=0 for i in range(len(arr)): s += arr[i] sums_dict[s] = i + 1 sums_list.append(s) lengths = [0]*len(sums_list) min_length = float('+inf') for start in range(len(sums_list) - 1, -1, -1): #s[end] - s[start] = target val = sums_list[start] + target if val in sums_dict: end = sums_dict[val] min_length = min(min_length, end - start) lengths[start] = min_length min_length = float('+inf') for start in range(len(sums_list)): val = sums_list[start] + target if val in sums_dict: end = sums_dict[val] l = end - start + lengths[end] min_length = min(min_length, l) if min_length != float('+inf'): return min_length else: return -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) # def aux(arr): # h = {0:0} # preSum = 0 # left = [n+1 for i in range(n)] # for i in range(1, n+1): # preSum = preSum + arr[i-1] # h[preSum] = i # if preSum-target in h: # left[i-1] = i-h[preSum-target] # if i > 1: # left[i-1] = min(left[i-2], left[i-1]) # return left # left = aux(arr) # arr.reverse() # right = aux(arr) # ans = n+1 # for i in range(n): # ans = min(ans, left[i] + right[n-1-(i+1)]) # return ans if ans < n+1 else -1 # h = {0:-1} # preSum = [0 for i in range(n)] # for i in range(n): # preSum[i] = preSum[i-1] + arr[i] if i > 0 else arr[0] # h[preSum[i]] = i # left = [n+1 for i in range(n)] # ans = n+1 # for i in range(n): # if preSum[i]-target in h: # left[i] = i-h[preSum[i]-target] # if i > 0: # left[i] = min(left[i-1], left[i]) # if left[i] < n+1 and preSum[i]+target in h: # right = h[preSum[i]+target]-i # ans = min(ans, left[i]+right) # return ans if ans < n+1 else -1 h = {0:-1} preSum = 0 for i in range(n): preSum = preSum + arr[i] if i > 0 else arr[0] h[preSum] = i ans = n+1 left = n+1 preSum = 0 for i in range(n): preSum += arr[i] if preSum-target in h: left = min(left, i-h[preSum-target]) if left < n+1 and preSum+target in h: right = h[preSum+target]-i ans = min(ans, left+right) return ans if ans < n+1 else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: mapsum = {} mapsum[0] = -1 totsum = 0 best_till = [math.inf] * len(arr) best = math.inf end = -1 res = float('inf') for i in range(len(arr)): totsum += arr[i] if (totsum - target) in mapsum : end = mapsum[totsum-target] if end > -1: res = min(res, i-end+best_till[end]) best = min(best,i-end) best_till[i] = best mapsum[totsum] = i if res < math.inf: return res return res if res < math.inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # They are all positive n = len(arr) # DP is shortest array up to i dp = [float('inf') for _ in range(n+1)] ans = float('inf') start = 0 curr_sum = 0 for end in range(n): curr_sum += arr[end] while start < end and curr_sum > target: curr_sum -= arr[start] start += 1 if curr_sum == target: ans = min(ans, end - start + 1 + dp[start-1]) # or start - 1 dp[end] = min(dp[end-1], end - start + 1) else: dp[end] = dp[end-1] return ans if ans != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix = [] for n in arr: if len(prefix) == 0: prefix.append(n) else: prefix.append(prefix[-1] + n) indexMap = {} indexMap[0] = -1 best = output = float('inf') best_till = [float('inf')] * len(arr) for i, p in enumerate(prefix): if p - target in indexMap: output = min(output, i - indexMap[p - target] + best_till[indexMap[p - target]]) best = min(best, i - indexMap[p - target]) best_till[i] = best indexMap[p] = i return -1 if output == float('inf') else output
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: dp = [float('inf') for i in range(len(arr))] curr_sum = 0 hist = {0:-1} res = float('inf') shortest_length = float('inf') for i, num in enumerate(arr): curr_sum += num diff = curr_sum - target if diff in hist: index = hist[diff] length = i - index # print(i, index) if index > 0 and dp[index] != float('inf'): res = min(res, dp[index] + length) shortest_length = min(shortest_length, length) hist[curr_sum] = i dp[i] = shortest_length # print(dp) return res if res != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: p = [0] m = {0: -1} minLen = [float('inf')] cur = 0 ans = best = float('inf') for i, a in enumerate(arr): cur += a p.append(cur) if cur-target in m: ans = min(ans, i-m[cur-target]+minLen[m[cur-target]+1]) best = min(i-m[cur-target], best) minLen.append(best) m[cur] = i return ans if ans != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: start, window_sum, result = 0, 0, float('inf') pre_min = len(arr) * [float('inf')] for i, num in enumerate(arr): window_sum += num while window_sum > target: window_sum -= arr[start] start += 1 if window_sum == target: curr_len = i - start + 1 result = min(result, curr_len + pre_min[start-1]) pre_min[i] = min(curr_len, pre_min[i-1]) else: pre_min[i] = pre_min[i-1] return result if result < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: sums = {0:-1} prefix = 0 dp = [math.inf for _ in range(len(arr)+1)] ans = math.inf for idx, num in enumerate(arr): prefix += num dp[idx+1] = min(dp[idx+1], dp[idx]) if prefix-target in sums: ans = min(ans, idx-sums[prefix-target] + dp[sums[prefix-target]+1]) dp[idx+1] = min(dp[idx+1], idx-sums[prefix-target]) sums[prefix] = idx return ans if ans != math.inf else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefxSum, prefx=0, [] suffxSum, suffx=sum(arr), [] dct={0:-1} dp = [float('inf')] * len(arr) for i in range(0, len(arr)): x=arr[i] prefxSum+=x prefx.append(prefxSum) suffx.append(suffxSum) suffxSum-=x dct[prefxSum]=i prefxSum=0 mn=float('inf') for i in range(0, len(arr)): prefxSum+=arr[i] #if prefxSum==target: # dp[i]=1 ''' if prefxSum-arr[i] in dct: start=dct[prefxSum-arr[i]] if dp[start]!=float('inf'): mn=min(mn, dp[start]+dp[i]) ''' if prefxSum-target in dct: start=dct[prefxSum-target] #print(\"i: \",i,\", j: \",dct[prefxSum-target]) if start>-1: if dp[start]!=float('inf'): mn=min(mn, dp[start]+i-start) dp[i]=min(dp[i-1], i-start) else: dp[i]=i+1 elif i>0: dp[i]=dp[i-1] #print(dp) return mn if mn!=float('inf') else -1 ''' below brute force DOES NOT WORK idx=[] for i in range(0, len(arr)): for j in range(i, len(arr)): if sum(arr[i:(j+1)])==target: idx.append([j-i+1,i, j]) #print(idx) if len(idx)<2: return -1 idx=sorted(idx) #print(idx) a1=idx[0][0] L0, i,j=idx[0] for k in range(1, len(idx)): L, start, end=idx[k] #if not (start<=i<=end or start<=j<=end): if not (i<=start<=j or i<=end<=j): #idx.append([j-i+1,i, j]) a2=end-start+1 return a1+a2 #return idx[0][0] + idx[1][0] return -1 '''
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: if not arr: return 0 n = len(arr) dp = [float('inf')] * n presum = 0 indexes = {0: -1} res = float('inf') for i, a in enumerate(arr): presum += a if i > 0: dp[i] = dp[i - 1] if presum - target in indexes: idx = indexes[presum - target] l = i - idx if dp[idx] != float('inf'): res = min(res, l + dp[idx]) dp[i] = min(dp[i], l) indexes[presum] = i # print(indexes) # print(dp) return res if res < float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: prefix_sum = [float('inf')] * len(arr) suffix_sum = [float('inf')] * len(arr) prefix_map = {0: -1} suffix_map = {0: len(arr)} cur_sum = 0 _min_till_now = float('inf') for i in range(len(arr) - 1): cur_sum += arr[i] if cur_sum - target in prefix_map: _min_till_now = min(_min_till_now, i - prefix_map[cur_sum - target]) prefix_sum[i + 1] = _min_till_now prefix_map[cur_sum] = i cur_sum = 0 _min_till_now = float('inf') for i in range(len(arr) - 1, -1, -1): cur_sum += arr[i] if cur_sum - target in suffix_map: _min_till_now = min(_min_till_now, suffix_map[cur_sum - target] - i) suffix_sum[i] = _min_till_now suffix_map[cur_sum] = i ans = min([x+y for x, y in zip(prefix_sum, suffix_sum)]) return ans if ans != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: if not arr: return -1 prefixes = [0] * len(arr) suffixes = [0] * len(arr) left = right = 0 curr = 0 min_len = float('inf') while right < len(arr): curr += arr[right] while curr >= target and left <= right: if curr == target: l = right - left + 1 if l < min_len: min_len = l curr -= arr[left] left += 1 prefixes[right] = min_len right += 1 left = right = len(arr)-1 curr = 0 min_len = float('inf') while left >= 0: curr += arr[left] while curr >= target and left <= right: if curr == target: l = right - left + 1 if l < min_len: min_len = l curr -= arr[right] right -= 1 suffixes[left] = min_len left -= 1 #print(prefixes) #print(suffixes) min_len = float('inf') for i in range(len(arr)-1): s = prefixes[i] + suffixes[i+1] if s < min_len: min_len = s return min_len if min_len != float('inf') else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: arr_len = len(arr) dp = [sys.maxsize] * arr_len left = right = 0 sum_tmp = 0 length, ans_len = sys.maxsize, sys.maxsize while right < arr_len: sum_tmp += arr[right] while sum_tmp > target: sum_tmp -= arr[left] left += 1 if sum_tmp == target: if left > 0 and dp[left-1] != sys.maxsize: length = min(length, dp[left-1] + right - left + 1) ans_len = min(ans_len, right - left + 1) dp[right] = ans_len right += 1 return length if length != sys.maxsize else -1
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: n = len(arr) best_to = [n + 1 for _ in range(n)] best_from = dict() min_total = n + 1 # Naturally impossible length. Will be updated if any possible case exist. Will tell when no possible case min_left = n + 1 sum_left = 0 s_left = 0 for i in range(n): sum_left += arr[i] if sum_left == target: best_to[i] = i - s_left + 1 best_from[s_left] = i - s_left + 1 elif sum_left > target: while s_left < i and sum_left > target: sum_left -= arr[s_left] s_left += 1 if sum_left == target: best_to[i] = i - s_left + 1 best_from[s_left] = i - s_left + 1 for i in range(1, n): best_to[i] = min(best_to[i], best_to[i-1]) for i in range(n - 1): if best_to[i] > n: continue if i + 1 in best_from: min_total = min(min_total, best_to[i] + best_from[i + 1]) if min_total > n: return -1 return min_total
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
from collections import * class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: mapper = defaultdict(int) prefix = [0] * len(arr) prefix[0] = arr[0] mapper[0] = -1 mapper[arr[0]] = 0 for i in range(1, len(arr)): prefix[i] = prefix[i-1] + arr[i] mapper[prefix[i]] = i cumu = count = 0 l = r = None ans = float('inf') vis = [] # print(mapper) for i, a in enumerate(arr): cumu += a # print(cumu, cumu - target in mapper) if cumu - target in mapper: if l == None: count += 1 l = i - mapper[cumu - target] # print(i, mapper[cumu - target]) vis.append((mapper[cumu - target] + 1, i)) else: l = min(l, i - mapper[cumu - target]) if l != None and cumu + target in mapper: ans = min(ans, mapper[cumu+target]-i+l) if ans == float('inf'): return -1 return ans
Given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.   Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Example 4: Input: arr = [5,5,4,4,5], target = 3 Output: -1 Explanation: We cannot find a sub-array of sum = 3. Example 5: Input: arr = [3,1,1,1,5,1,2,1], target = 3 Output: 3 Explanation: Note that sub-arrays [1,2] and [2,1] cannot be an answer because they overlap.   Constraints: 1 <= arr.length <= 10^5 1 <= arr[i] <= 1000 1 <= target <= 10^8
class Solution: def minSumOfLengths(self, arr: List[int], target: int) -> int: # left to right, compute min length of subarray using elems from 0 up to and including i # right to left, compute min length of subarray using elems from i+1 to n-1 # go thru array, pick i s.t. leftmin[i] + rightmin[i] is smallest n = len(arr) # compute left to right curr_sum = 0 curr_best = -1 lo = hi = 0 lmin = [] while lo <= hi < n: curr_sum += arr[hi] while curr_sum > target and lo <= hi: curr_sum -= arr[lo] lo += 1 if curr_sum == target: tmp = (hi-lo+1) if tmp < curr_best or curr_best == -1: curr_best = tmp lmin.append(curr_best) hi += 1 # compute right to left curr_sum = 0 curr_best = -1 lo = hi = n-1 rmin = [-1] # since lo is exclusive, rmin[n-1] should be -1 while 0 < lo <= hi: curr_sum += arr[lo] while curr_sum > target and lo <= hi: curr_sum -= arr[hi] hi -= 1 if curr_sum == target: tmp = (hi-lo+1) if tmp < curr_best or curr_best == -1: curr_best = tmp rmin.append(curr_best) lo -= 1 rmin = rmin[::-1] # print(lmin) # print(rmin) # compute best res = -1 for i in range(n): if lmin[i] != -1 and rmin[i] != -1: if res == -1 or lmin[i]+rmin[i] < res: res = lmin[i] + rmin[i] return res