2024蓝桥杯每日一题（区间合并）
一、第一题：挤牛奶
解题思路：区间合并
区间合并模板题
【Python程序代码】
n = int(input())
a = []
for i in range(n):l,r = map(int,input().split())a.append([l,r])
def cmp(x):return x[0],x[1]
a.sort(key=cmp)
res1,res2=0,0
st,ed = a[0][0],a[0][1]
for i in range(n):if a[i][0]>ed:res1 = max(res1,ed-st)if st:res2 = max(res2,a[i][0]-ed)st,ed = a[i][0],a[i][1]else:ed = max(ed,a[i][1])
res1 = max(res1,ed-st)
print(res1,res2)二、第二题：区间合并
解题思路：区间合并
区间合并模板题
【Python程序代码】
n = int(input())
a = []
for i in range(n):l,r = map(int,input().split())a.append([l,r])
def cmp(x):return x[0],x[1]
a.sort(key=cmp)
res = 0
ed = -1e9-1
for i in range(n):if a[i][0]>ed:res += 1ed = a[i][1]else:ed = max(ed,a[i][1])
print(res)三、第三题：校门外的树
解题思路：区间合并
区间合并模板题
【Python程序代码】
L,m = map(int,input().split())
a = []
for i in range(m):l,r = map(int,input().split())a.append([l,r])
def cmp(x):return x[0],x[1]
a.sort(key=cmp)
st,ed = 0,0
res = 0
for i in range(m):if a[i][0]>ed:if ed:res += ed - st + 1st = a[i][0]ed = a[i][1]else:ed = max(ed,a[i][1])
res += ed-st +1
print(L+1-res)四、第四题：管道
解题思路：区间合并+二分
用二分优化采用区间合并判断是否符合条件，这题在之前的二分习题里面写过了，直接见代码。
【Python程序代码】
n,L = map(int,input().split())
a = []
for i in range(n):l,r = map(int,input().split())a.append([l,r])
def cmp(x):return x[0],x[1]
a.sort(key=cmp)
def ck(mid):tp = []for i in range(n):if a[i][1]<=mid:tp.append([ a[i][0]-(mid-a[i][1]), a[i][0]+(mid-a[i][1]) ])tp.sort(key=cmp)ed = 0for i in range(len(tp)):if tp[i][0]>ed+1:return Falseelse:ed = max(ed,tp[i][1])if ed>=L:return Truereturn False
l,r = 1,2000000000
while l<r:mid = l+r>>1if ck(mid):r=midelse:l=mid+1
print(r)