@@ -17,51 +17,35 @@ Write an algorithm to minimize the largest sum among these m subarrays.
1717
1818class Hard410 : ArraysTopic , BinarySearchTopic , DynamicProgrammingTopic , GreedyTopic {
1919
20- var memo = Array < Array < Int ?>>( 1001 ) { arrayOfNulls( 51 ) }
20+ lateinit var nums : IntArray
2121
22- private fun getMinimumLargestSplitSum (prefixSum : IntArray , currIndex : Int , subarrayCount : Int ): Int {
23- val n = prefixSum.size - 1
24- 25- // We have already calculated the answer so no need to go into recursion
26- if (memo[currIndex][subarrayCount] != null ) {
27- return memo[currIndex][subarrayCount]!!
28- }
29- 30- // Base Case: If there is only one subarray left, then all of the remaining numbers
31- // must go in the current subarray. So return the sum of the remaining numbers.
32- if (subarrayCount == 1 ) {
33- return prefixSum[n] - prefixSum[currIndex].also { memo[currIndex][subarrayCount] = it }
22+ fun splitArray (nums : IntArray , m : Int ): Int {
23+ this .nums = nums
24+ var low = 0
25+ var high = 0
26+ var min = Int .MAX_VALUE
27+ for (i in nums.indices) {
28+ low = Math .max(low, nums[i])
29+ high + = nums[i]
3430 }
35- 36- // Otherwise, use the recurrence relation to determine the minimum largest subarray
37- // sum between currIndex and the end of the array with subarrayCount subarrays remaining.
38- var minimumLargestSplitSum = Int .MAX_VALUE
39- for (i in currIndex.. n - subarrayCount) {
40- // Store the sum of the first subarray.
41- val firstSplitSum = prefixSum[i + 1 ] - prefixSum[currIndex]
42- 43- // Find the maximum subarray sum for the current first split.
44- val largestSplitSum = Math .max(
45- firstSplitSum,
46- getMinimumLargestSplitSum(prefixSum, i + 1 , subarrayCount - 1 )
47- )
48- 49- // Find the minimum among all possible combinations.
50- minimumLargestSplitSum = Math .min(minimumLargestSplitSum, largestSplitSum)
51- if (firstSplitSum >= minimumLargestSplitSum) {
52- break
53- }
31+ while (low <= high) {
32+ val mid = (low + high) / 2
33+ if (required_no_of_chunks(mid, m)) {
34+ min = Math .min(min, mid)
35+ high = mid - 1
36+ } else low = mid + 1
5437 }
55- return minimumLargestSplitSum. also { memo[currIndex][subarrayCount] = it }
38+ return min
5639 }
5740
58- fun splitArray (nums : IntArray , m : Int ): Int {
59- // Store the prefix sum of nums array.
60- val n = nums.size
61- val prefixSum = IntArray (n + 1 )
62- for (i in 0 until n) {
63- prefixSum[i + 1 ] = prefixSum[i] + nums[i]
41+ private fun required_no_of_chunks (mid : Int , m : Int ): Boolean {
42+ var chunks = 0
43+ var i = 0
44+ while (i < nums.size) {
45+ var `val ` = 0
46+ while (i < nums.size && nums[i] + `val ` <= mid) `val ` + = nums[i++ ]
47+ chunks++
6448 }
65- return getMinimumLargestSplitSum(prefixSum, 0 , m)
49+ return chunks <= m
6650 }
6751}
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