How many nondecreasing subsequences can you find in the sequence S = {s1, s2, s3, ...., sn} ? For example, we assume that S = {1, 2, 3}, and you can find seven nondecreasing subsequences, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
The input consists of multiple test cases. Each case begins with a line containing a positive integer n that is the length of the sequence S, the next line contains n integers {s1, s2, s3, ...., sn}, 1 <= n <= 100000, 0 <= si <= 2^31.
For each test case, output one line containing the number of nondecreasing subsequences you can find from the sequence S, the answer should % 1000000007.
3
1 2 3
7
题目大意：给你一个串，求这个串中不递减的子串有多少个？初一看，完全想不到会是用树状数组，但是他就是这么神奇，不递减就想到逆序数，逆序数又想到了树状数组，居然是用他。他是求子串有多少个，又要用到DP，这里DP就是用树状数组慢慢推上去，最后是注意是求和会溢出，记得%1000000007。
1 #include<iostream> 2 #include<stdio.h> 3 #include<memory.h> 4 #include<algorithm> 5 6 using namespace std ; 7 8 struct node 9 { 10 int val, id ; 11 }a[100005]; 12 13 bool cmp(node a, node b) 14 { 15 return a.val < b.val ; 16 } 17 18 int b[100005] , c[100005] , s[100005] ,n ; 19 20 int lowbit( int i) 21 { 22 return i&(-i); 23 } 24 25 void update ( int i , int x ) 26 { 27 while(i<=n) 28 { 29 s[i]+=x; 30 if(s[i]>=1000000007) 31 s[i]%=1000000007; 32 i+=lowbit(i); 33 } 34 } 35 36 int sum( int i ) 37 { 38 int sum = 0 ; 39 while( i > 0 ) 40 { 41 sum += s[i] ; 42 if( sum >= 1000000007) 43 sum %= 1000000007; 44 i-=lowbit( i ) ; 45 } 46 return sum ; 47 } 48 49 50 51 int main() 52 { 53 int i , res ; 54 while(scanf("%d",&n)!=EOF) 55 { 56 memset( b , 0 , sizeof(b)) ; 57 memset( s , 0 , sizeof(s)) ; 58 for(i=1;i<=n;i++) 59 { 60 scanf("%d",&a[i].val); 61 a[i].id = i ; 62 } 63 sort(a+1,a+n+1,cmp); 64 b[a[1].id] = 1 ; 65 for(i=2;i<=n;i++) 66 { 67 if(a[i].val!=a[i-1].val) 68 b[a[i].id] = i ; 69 else b[a[i].id] = b[a[i-1].id] ; 70 } 71 res = 0 ; 72 for(i=1;i<=n;i++) 73 { 74 c[i] = sum( b[i] ) ; 75 update ( b[i] , c[i]+1 ) ; 76 } 77 printf("%d\n",sum(n)); 78 } 79 return 0 ; 80 }
HDU 2227 Find the nondecreasing subsequences (DP+树状数组+离散化),布布扣,bubuko.com
HDU 2227 Find the nondecreasing subsequences (DP+树状数组+离散化)
原文：http://www.cnblogs.com/ws5167/p/3915593.html
