leetcode : 327. Count of Range Sum : 连续和在指定区间内
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Given an integer array nums
, return the number of range sums that lie in [lower, upper]
inclusive.
Range sum S(i, j)
is defined as the sum of the elements in nums
between indices i
and j
(i
≤ j
), inclusive.
Note:
A naive algorithm of O(n2) is trivial. You MUST do better than that.
Example:
Given nums = [-2, 5, -1]
, lower = -2
, upper = 2
,
Return 3
.
The three ranges are : [0, 0]
, [2, 2]
, [0, 2]
and their respective sums are: -2, -1, 2
.
这道题目肯定做过,在本科的时候,当时还认真思考过,现在做仍然没做出来,忘记了怎么做,看了题解才有种似曾相识的感觉。
这道题目确实需要技巧~
题意:一组数字,如果连续的数字之和在指定范围内,数量加1,计算总共在范围内的个数。
解法:
1)首先计算sums[],i表示从0到i的数字之和。问题就转化成寻找(i<j),sums[j]-sums[i]在指定范围内。目前仍然是O(N*N)
2)借助归并排序,合并的过程中,计算满足上面要求的个数。即:i在前一半,j在后一半,且sums[j]-sums[i]在指定范围内,然后在进行合并称有序的sums数组。
因为合并时,前一半和后一般的数量已计算出且数组有序,因此,计算个数和合并的时间复杂都均是O(N)
整体的时间复杂度是O(N*logN)
public class Solution { public int merge(long[] sums, int lower, int upper, int start, int end) {if (end - start <= 0)return 0;if (end - start == 1) {if (sums[start] >= lower && sums[start] <= upper)return 1;else {return 0;}}int mid = (start + end) / 2;int temp = merge(sums, lower, upper, start, mid)+ merge(sums, lower, upper, mid, end);long[] tttt = new long[(end - start) + 1];int t=mid;int l = mid;int r = mid;int index = 0;for (int i = start; i < mid; i++) {for (; l < end && lower + sums[i] > sums[l]; l++);for (; r < end && upper + sums[i] >= sums[r]; r++);for(;t<end&&sums[t]<sums[i];t++){tttt[index++]=sums[t];}tttt[index++]=sums[i];temp += (r - l);}while (t < end) {tttt[index++] = sums[t++];}System.arraycopy(tttt, 0, sums, start, end-start);return temp;}public int countRangeSum(int[] nums, int lower, int upper) {long[] sums = new long[nums.length];if (nums == null || nums.length == 0)return 0;sums[0] = nums[0];for (int i = 1; i < nums.length; i++)sums[i] = sums[i - 1] + nums[i];return merge(sums, lower, upper, 0, nums.length);}}
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