最大间隙问题

简介

采用鸽笼原理；可以达到O(1);

code

#include<stdio.h> 
#include <iostream>
#include <vector>
using namespace std;
typedef struct BLOCK {
	int blockNumber;
	double min;
	double max;
	BLOCK(int _blockNumber=0, double _min=1000, double _max=-1000) {
		min = _min;
		max = _max;
		blockNumber = _blockNumber;
	}
};
int main() {
	int n;
	cin >> n;
	vector<double> num(n);
	double min = 1000; double max = -1000;
	for (int i = 0; i < n; i++) {
		cin >> num[i];
		if (num[i] > max) {
			max = num[i];
		}
		if (num[i] < min) {
			min = num[i];
		}
	}
	vector<BLOCK> b(n - 1);
	double gap = (max - min) / (n - 1);
	//只选择去掉最大值进行  投球
	for (int i = 0; i < n; i++) {
		if (num[i] == max ) {
			continue;
		}
		int index = (n - 1)*(num[i] - min) / (max - min);
		b[index].blockNumber++;
		if (b[index].max < num[i]) {
			b[index].max = num[i];
		}
		if (b[index].min > num[i]) {
			b[index].min = num[i];
		}
	}
	// max分开处理
	b[n - 2].blockNumber++;
	if (b[n - 2].max < max) {
		b[n - 2].max = max;
	}
	if (b[n - 2].min > max) {
		b[n - 2].min = max;
	}
	double maxGap = 0;
	for (int i = 0; i < n - 2; i++) {
		if (b[i].max - b[i].min > maxGap) {
			maxGap = b[i].max - b[i].min;
		}
		double lastMax = b[i].max;
		while (b[i + 1].blockNumber == 0) {
			if (i + 1 == n - 1) {
				break;
			}
			i++;
		}
		if (b[i+1].min - lastMax > maxGap) {
			maxGap = b[i+1].min - lastMax;
		}
	}
	cout << maxGap << std::endl;
	system("pause");
	return 0;
}

测试样本

5 2.3 3.1 7.5 1.5 6.3

输出

3.2