Problem: Given the nested list of integer, calculate the depth sum.
Sample Input: [[1,1], 2, [1,1]]
Output: 10
Explanation: 1* 2 + 1 * 2 + 2 * 1+ 1 * 2+ 1 * 2 = 10. ( Number in the red color are the level in the nested list. )
Sample Input: [1 [4 [6]]]
Output: 27
Explanation: 1 * 1 + 4 * 2 + 6 * 3 = 27( Number in the red color are the level in the nested list. )
Solution:
There are two ways to solve this problem. Either iterative or recursive.
- Iterative: You need a data structure to keep track of nested list. This can be Queue. At each level, if you see a list, add it in a queue and keep on traversing till queue is empty.
- Recursive: Easy way to solve it compared to iterative. At each level, you need to check if it is a list then increment the current level and make a recursive call. Return the sum once you hit the number.
Simplification of the depth tracking in Recursive approach:
So, in above approach, we are going to each list value and also keep track of depth and do a sum. Another way to approach is to, capture sums at each depth by maintaining an array. This array index represents the depth of nested list.
For example:
Input data : [ [ 1,5 ], 3, [ 8, [ 9 ] ] ]
Resulting array will be : [3, 14, 9] . At level one we have only one element, which is 3. At level 2 we have 1, 5, 8 = 14 and at level 3 we have 9.
Now, it easy to calculate the sum : 3 * 1 + 14 * 2 + 9 * 3 = 58
One tricky variation is to consider depth in decreasing order.
If you take above approach then its easy to solve. Once you have a result array you can calculate the sum in reverse order. i.e. 3 * 3 + 14 * 2 + 9 * 1 = 46
Refer to method caclulateDepthSumRecursiveV1 for updated version.
Code:
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package interviewque; import java.util.ArrayList; import java.util.LinkedList; import java.util.List; import java.util.Queue; public class DepthSum { public static int caclulateDepthSumIterative(NestedList nestedList) { Queue<NestedList> queue = new LinkedList<NestedList>(); queue.add(nestedList); Queue<Integer> depthQueue = new LinkedList<Integer>(); int depth = 0; int sum = 0; depthQueue.add(depth); while (!queue.isEmpty()) { nestedList = queue.poll(); depth = depthQueue.poll(); if (nestedList.isList) { ++depth; for (NestedList nL : nestedList.getNestedList()) { queue.add(nL); depthQueue.add(depth); } } else { sum += nestedList.getNumber() * depth; } } return sum; } public static int caclulateDepthSumRecursive(NestedList nestedList, int level) { int sum = 0; if (nestedList.isList) { for (NestedList nestedList2 : nestedList.getNestedList()) { sum += caclulateDepthSumRecursive(nestedList2, level + 1); } } else { sum = nestedList.number * level; } return sum; } public static void caclulateDepthSumRecursiveV1(NestedList nestedList, int level, List<Integer> results) { if (results.size() < level) { results.add(0); } if (nestedList.isList) { for (NestedList nestedList2 : nestedList.getNestedList()) { caclulateDepthSumRecursiveV1(nestedList2, level + 1, results); } } else { results.set(level - 1, results.get(level - 1) + nestedList.number); } } public static void main(String[] args) { NestedList n1Val = new NestedList(1); NestedList n2Val = new NestedList(1); NestedList n3Val = new NestedList(2); NestedList n4Val = new NestedList(1); NestedList n5Val = new NestedList(1); List<NestedList> nestedList1 = new ArrayList<NestedList>(); nestedList1.add(n1Val); nestedList1.add(n2Val); List<NestedList> nestedList2 = new ArrayList<NestedList>(); nestedList2.add(n4Val); nestedList2.add(n5Val); NestedList n1 = new NestedList(nestedList1); NestedList n2 = new NestedList(nestedList2); List<NestedList> nestedList3 = new ArrayList<NestedList>(); nestedList3.add(n1); nestedList3.add(n3Val); nestedList3.add(n2); NestedList n3 = new NestedList(nestedList3); System.out.println("[[1,1], 2, [1,1]] Iterative depth sum: " + caclulateDepthSumIterative(n3)); System.out.println("[[1,1], 2, [1,1]] Recursive depth sum: " + caclulateDepthSumRecursive(n3, 0)); List<Integer> results = new ArrayList<Integer>(); caclulateDepthSumRecursiveV1(n3, 0, results); System.out.println("\nVersion 1 : Depth is in increasing order"); int depth = 1; int sum = 0; for (Integer i : results) { sum += i * depth; depth++; } System.out.println("[[1,1], 2, [1,1]] Recursive depth sum: " + sum); System.out.println("\nVersion 1 : Depth is in decresing order"); depth = results.size(); sum = 0; for (Integer i : results) { sum += i * depth; depth--; } System.out.println("[[1,1], 2, [1,1]] Recursive depth sum: " + sum); NestedList n6Val = new NestedList(6); NestedList n7Val = new NestedList(4); NestedList n8Val = new NestedList(1); List<NestedList> nestedList6 = new ArrayList<NestedList>(); nestedList6.add(n6Val); NestedList n6 = new NestedList(nestedList6); List<NestedList> nestedList7 = new ArrayList<NestedList>(); nestedList7.add(n7Val); nestedList7.add(n6); NestedList n7 = new NestedList(nestedList7); List<NestedList> nestedList8 = new ArrayList<NestedList>(); nestedList8.add(n8Val); nestedList8.add(n7); NestedList n8 = new NestedList(nestedList8); System.out.println("\n[ 1 [ 4 [ 6 ] ] ] Iterative depth sum " + caclulateDepthSumIterative(n8)); System.out.println("[ 1 [ 4 [ 6 ] ] ] Recursive depth sum " + caclulateDepthSumRecursive(n8, 0)); results = new ArrayList<Integer>(); caclulateDepthSumRecursiveV1(n8, 0, results); System.out.println("\nVersion 1 : Depth is in increasing order"); depth = 1; sum = 0; for (Integer i : results) { sum += i * depth; depth++; } System.out.println("[ 1 [ 4 [ 6 ] ] ] Recursive depth sum: " + sum); System.out.println("\nVersion 1 : Depth is in decresing order"); depth = results.size(); sum = 0; for (Integer i : results) { sum += i * depth; depth--; } System.out.println("[ 1 [ 4 [ 6 ] ] ] Recursive depth sum: " + sum); } } class NestedList { int number; List<NestedList> nestedList; boolean isList = false; public NestedList(int number) { this.number = number; isList = false; } public NestedList(List<NestedList> nestedLists) { this.nestedList = nestedLists; isList = true; } public int getNumber() { return number; } public List<NestedList> getNestedList() { return nestedList; } } |
Complexity: O(n)
Github url: DepthSum.java