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287. Find the Duplicate Number
Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.
Note:
- You must not modify the array (assume the array is read only).
- You must use only constant, O(1) extra space.
- Your runtime complexity should be less than
O(n2)
.- There is only one duplicate number in the array, but it could be repeated more than once.
题目要求空间复杂度为O(1),也就是说不能使用Hash表算法。不能更改原序列,因此,原来交换位置的做法就行不通了。
进一步优化:面对如此有归可寻的序列,我们应当尽可能地想办法优化时间复杂度至O(nlogn)或O(n),蛮力算法的时间复杂度是O(n2)。
我们在区间[1, n]中搜索,首先求出中点mid,然后遍历整个数组,统计所有小于等于mid的数的个数,如果个数大于mid,则说明重复值在[mid+1, n]之间,反之,重复值应在[1, mid]之间,然后依次类推,直到区间长度变为1,此时的low就是我们要求的重复值。
class Solution { public: int findDuplicate(vector<int>& nums) { int n = nums.size(); if (n < 2) return 0; int low = 1; int high = n - 1; while (low < high) { int mid = (low + high) / 2; int count = 0; for (int i = 0; i < n; ++i) { if (nums[i] <= mid) count++; } if (count <= mid) low = mid + 1; else high = mid; } return low; } };
287. Find the Duplicate Number
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