题意：给你一个序列，找两个长度为 k 且没有重合区间的数使得其和最大
解题思路：
1）线段树
想了半天想不出只能先用线段树撸了一发，这题dp 第一名只要了 9分钟。
就是把起点为 i 长度为 k 的和预处理出来，再用线段树枚举去找。
解题代码：
1 // File Name: 332b.cpp
2 // Author: darkdream
3 // Created Time: 2014年07月30日 星期三 08时10分45秒
4
5 #include<vector>
6 #include<list>
7 #include<map>
8 #include<set>
9 #include<deque>
10 #include<stack>
11 #include<bitset>
12 #include<algorithm>
13 #include<functional>
14 #include<numeric>
15 #include<utility>
16 #include<sstream>
17 #include<iostream>
18 #include<iomanip>
19 #include<cstdio>
20 #include<cmath>
21 #include<cstdlib>
22 #include<cstring>
23 #include<ctime>
24 #define LL long long
25 using namespace std;
26 #define M 200004
27 struct node{
28 int l , r ,m;
29 LL maxn,s;
30 }tree[M <<2];
31 LL a[200004];
32 LL sum[200004];
33 int L(int x)
34 {
35 return 2 * x;
36 }
37 int R(int x)
38 {
39 return 2 * x + 1;
40 }
41 void pushup(int c)
42 {
43 if(tree[L(c)].maxn >=tree[R(c)].maxn)
44 {
45 tree[c].maxn = tree[L(c)].maxn;
46 tree[c].s = tree[L(c)].s;
47 }else{
48 tree[c].maxn = tree[R(c)].maxn;
49 tree[c].s = tree[R(c)].s;
50 }
51 }
52 void build(int c ,int l, int r)
53 {
54 tree[c].l = l ;
55 tree[c].r = r ;
56 tree[c].m = (l+r)/2;
57 if(l == r)
58 {
59 tree[c].maxn = sum[l];
60 tree[c].s = l ;
61 return ;
62 }
63 build(L(c),l,tree[c].m);
64 build(R(c),tree[c].m+1,r);
65 pushup(c);
66 }
67 LL maxa;
68 int site;
69 void find(int c, int l , int r)
70 {
71 //printf("%d %d %d %d %d\n",c,tree[c].l,tree[c].r,l,r);
72 if(r < l )
73 return ;
74 if(l <= tree[c].l && r >= tree[c].r)
75 {
76 if(tree[c].maxn > maxa)
77 {
78 maxa = tree[c].maxn;
79 site = tree[c].s;
80 }
81 return ;
82 }
83 if(l <= tree[c].m)
84 find(L(c),l,r);
85 if(r > tree[c].m)
86 find(R(c),l,r);
87 }
88 int main(){
89 int n , k;
90 scanf("%d %d",&n,&k);
91 int temp ;
92 a[0] = 0 ;
93 for(int i = 1; i <= n;i ++)
94 {
95 scanf("%d",&temp);
96 a[i] = a[i-1] + temp;
97 }
98 for(int i = 1 ;i <= n-k+1; i ++)
99 {
100 sum[i] = a[i+k-1] - a[i-1];
101 }
102 build(1,1,n-k+1);
103 LL ans = -1e9;
104 int a, b ;
105 for(int i =1 ;i <= n-k+1;i ++)
106 {
107 maxa = -1e9 ;
108 site = 0 ;
109 find(1,i+k,n-k+1);
110 if(sum[i] + maxa > ans)
111 {
112 ans = sum[i] + maxa;
113 a= i ;
114 b = site;
115 }
116 }
117 printf("%d %d\n",a,b);
118 return 0;
119 }
2）由第一种思路突然想到还可以预处理出来 i 以后 的最大值是多少，位置是多少，这样就可以直接dp了
1 // File Name: 332b.1.cpp
2 // Author: darkdream
3 // Created Time: 2014年07月30日 星期三 10时13分41秒
4
5 #include<vector>
6 #include<list>
7 #include<map>
8 #include<set>
9 #include<deque>
10 #include<stack>
11 #include<bitset>
12 #include<algorithm>
13 #include<functional>
14 #include<numeric>
15 #include<utility>
16 #include<sstream>
17 #include<iostream>
18 #include<iomanip>
19 #include<cstdio>
20 #include<cmath>
21 #include<cstdlib>
22 #include<cstring>
23 #include<ctime>
24 #define LL long long
25 #define maxn 200050
26 using namespace std;
27 LL a[maxn];
28 LL sum[maxn];
29 LL m[maxn];
30 int s[maxn];
31 int n , k ;
32 int main(){
33 scanf("%d %d",&n,&k);
34 a[0] = 0 ;
35 int temp ;
36 for(int i = 1;i <= n;i ++)
37 {
38 scanf("%d",&temp);
39 a[i] =a[i-1]+ temp;
40 }
41 int p = n - k + 1;
42 for(int i = 1;i <= p ; i ++)
43 {
44 sum[i] = a[i+k-1] - a[i-1];
45 }
46 m[p] = sum[p];
47 s[p] = p ;
48
49 for(int i = p -1;i >= 1 ;i --)
50 {
51 if(sum[i] >= m[i+1])
52 {
53 m[i] = sum[i];
54 s[i] = i ;
55 }else{
56 m[i] = m[i+1];
57 s[i] = s[i+1];
58 }
59 }
60 int a, b ;
61 LL maxa = -1e9 ;
62 for(int i =1 ;i <= p;i ++)
63 {
64 if(sum[i] + m[i+k] > maxa)
65 {
66 a = i ;
67 b = s[i+k];
68 maxa = sum[i] + m[i+k];
69 }
70 }
71 printf("%d %d\n",a,b);
72 return 0;
73 }
codeforces332B - Maximum Absurdity 线段数 or dp
时间： 2024-10-01 22:37:09