区间重合判断
题目：给定一些无序区间，判断某个给定的特定区间是否在这些无序的区间内。
这个题目比较简单，首先将给定的区间排序，在对重合的区间进行排序，使得区间变成递增且不重叠的若干个区间，对于给定的区间在已经处理好的区间内进行二分查找，完成区间覆盖的判断。
程序如下：
[cpp] view plaincopy
- #include <stdio.h>
- #include <vector>
- #include <algorithm>
- class Interval {
- public:
- Interval(int start, int end) : start_(start), end_(end) {}
- Interval() :start_(0), end_(0) {}
- static bool OrderByStart(const Interval& left, const Interval& right) {
- return left.start_ < right.start_;
- 10. }
- 11. friend bool operator<(const Interval& left, const Interval& right) {
- 12. return left.start_ < right.start_;
- 13. }
- 14. int start_;
- 15. int end_;
16. };
17. void CombinInterval(std::vector<Interval>& orginal, std::vector<Interval>* combined) {
- 18. if (orginal.size() < 1) {
- 19. return;
- 20. }
- 21. sort(orginal.begin(), orginal.end(), Interval::OrderByStart);
- 22. Interval combined_interval = orginal[0];
- 23. int new_ending = orginal[0].end_;
- 24. for (int i = 1; i < orginal.size(); ++i) {
- 25. if (combined_interval.end_ >= orginal[i].start_) {
- 26. new_ending = combined_interval.end_ > orginal[i].end_ ? combined_interval.end_ : orginal[i].end_;
- 27. continue;
- 28. }
- 29. combined_interval.end_ = new_ending;
- 30. combined->push_back(combined_interval);
- 31. combined_interval = orginal[i];
- 32. new_ending = orginal[i].end_;
- 33. }
- 34. combined_interval.end_ = new_ending;
- 35. combined->push_back(combined_interval);
36. }
37. bool CoverTest(const Interval& interval, std::vector<Interval>& intervals, Interval* covered_interval) {
- 38. std::vector<Interval> combined_intervals;
- 39. CombinInterval(intervals, &combined_intervals);
- 40. for (int i = 0; i < combined_intervals.size(); ++i) {
- 41. printf("%d-%d\n", combined_intervals[i].start_, combined_intervals[i].end_);
- 42. }
- 43.
- 44. if (combined_intervals.size() < 1) {
- 45. return false;
- 46. }
- 47. int start = 0;
- 48. int end = combined_intervals.size() -1;
- 49. int middle = 0;
- 50. bool found = false;
- 51. while (end >= start) {
- 52. middle = (start + end) / 2;
- 53. if (interval < combined_intervals[middle]) {
- 54. end = middle - 1;
- 55. } else if (combined_intervals[middle] < interval) {
- 56. start = middle + 1;
- 57. } else {
- 58. found = true;
- 59. break;
- 60. }
- 61. }
- 62. int target_index = found ? middle : start - 1;
- 63. printf("target:%d\n", target_index);
- 64. if (target_index >= 0 &&
- 65. combined_intervals[target_index].start_ <= interval.start_ &&
- 66. combined_intervals[target_index].end_ >= interval.end_) {
- 67. *covered_interval = combined_intervals[target_index];
- 68. return true;
- 69. } else {
- 70. return false;
- 71. }
72. }
73. int main(int argc, char** argv) {
- 74. std::vector<Interval> intervals;
- 75. intervals.push_back(Interval(2,5));
- 76. intervals.push_back(Interval(3,4));
- 77. intervals.push_back(Interval(4,7));
- 78. intervals.push_back(Interval(9,13));
- 79. Interval target_interval(3, 4);
- 80. Interval covered_interval;
- 81. if (CoverTest(target_interval, intervals, &covered_interval)) {
- 82. printf("the covered interval is (%d, %d)\n", covered_interval.start_, covered_interval.end_);
- 83. } else {
- 84. printf("uncovered\n");
- 85. }
86. }
程序编写时开始犯了几个错误：
1、函数参数开始使用了const 修饰，导致sort时出错
2、区间合并时，没有将最后一个加入到向量中，new_ending设置的初值也要注意，开始就出错了
3、二分查找，找下界时，需要将查找过程走几遍就比较清楚了，下界是start-1，但如果start为0，下界可能是负数，要注意处理。另外循环条件是start <=end，等号也很重要，如果判断过程中只有一个元素时，就是等号覆盖的情况。
题目大意：
输入两个表示区间范围的整数[x,y]
然后输入N个无序区间[x1,y1], [x2, y2], [x3, y3]...
求解第一次输入的区间是否在N个无序区间组合成的大区间中。
法一：使用并查集，对每个区间合并到一个子树上，最后判断源区间的x和y的根是否相同。
View Code
#include<iostream>
using namespace std;
const int size = 100;
int father[size];
int rank[size];
void make_set(int n)
{
for(int i = 1; i <= n; i ++){
father[i] = i;
rank[i] = 1;
}
}
int find_set(int x)
{
if(x != father[x]){
father[x] = find_set(father[x]);
}
return father[x];
}
void Union(int x, int y)
{
x = find_set(x);
y = find_set(y);
if(x == y){
return ;
}
if(rank[x] < rank[y]){
father[x] = y;
}
else{
father[y] = x;
if(rank[x] == rank[y]){
rank[x] ++;
}
}
}
int main()
{
int x1, y1;
cin >> x1 >> y1;
int x, y;
int n;
cin >> n;
make_set(size);
while(n --){
cin >> x >> y;
if(x > y){
swap(x, y);
}
for(int i = x + 1; i <= y; i ++){
Union(x, i);
}
}
if(find_set(x1) == find_set(y1)){
cout << "yes" << endl;
}
else{
cout << "no" << endl;
}
system("pause");
}
法二：将无序的目标区间排序后，再合并成几个有序的区间，然后把源区间和有序的目标区间比较。
View Code
#include<iostream>
#include<vector>
using namespace std;
typedef pair<int, int> section;
bool cmp(section a, section b)
{
return a.first < b.first;
}
int main()
{
section src, tmp;
cin >> src.first >> src.second;
vector<section> v;
while(cin >> tmp.first >> tmp.second, tmp.first | tmp.second){
v.push_back(tmp);
}
sort(v.begin(), v.end(), cmp);
vector<section> res;
vector<section>::iterator it = v.begin();
int begin = it->first;
for(; (it + 1) != v.end(); it ++){
if(it->second < (it + 1)->first){
res.push_back(make_pair(begin, it->second));
begin = (it + 1)->first;
}
}
bool solve = false;
it = res.begin();
for(; it != res.end(); it ++){
if(src.first >= it->first && src.second <= it->second){
solve = true;
break;
}
}
if(solve){
cout << "in" << endl;
}
else{
cout << "out" << endl;
}
system("pause");
}