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 += 1
        ed = 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 + 1
        st = 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 = 0
    for i in range(len(tp)):
        if tp[i][0]>ed+1:return False
        else:ed = max(ed,tp[i][1])
    if ed>=L:return True
    return False
l,r = 1,2000000000
while l<r:
    mid = l+r>>1
    if ck(mid):r=mid
    else:l=mid+1
print(r)