[HDOJ5542]The Battle of Chibi(DP,树状数组)
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题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5542
题意:n个数中找m个数,使得从左到右读是上升的子序列。问一共有多少种。
dp(i,j)表示取到第i个位置,长为j并且最后一个数为a(i)的方案总数。
更新就比较容易了,dp(i,j)=∑(k=1->j-1)dp(i-1,k),初始化dp(i,1)=1。
1 #include <bits/stdc++.h> 2 using namespace std; 3 #define lowbit(x) x & (-x) 4 5 const int mod = int(1e9+7); 6 const int maxn = 1010; 7 int dp[maxn][maxn]; 8 int a[maxn], h[maxn]; 9 int n, m, hcnt; 10 11 int sum(int i, int x) { 12 int ret = 0; 13 while(x) { 14 ret = (ret + dp[i][x]) % mod; 15 x -= lowbit(x); 16 } 17 return ret; 18 } 19 20 void update(int i, int x, int k) { 21 while(x <= n) { 22 dp[i][x] = (dp[i][x] + k) % mod; 23 x += lowbit(x); 24 } 25 } 26 27 int getid(int x) { 28 return lower_bound(h, h+hcnt, x) - h; 29 } 30 31 int main() { 32 // freopen("in", "r", stdin); 33 int T, _ = 1; 34 scanf("%d", &T); 35 while(T--) { 36 printf("Case #%d: ", _++); 37 scanf("%d %d", &n, &m); 38 for(int i = 1; i <= n; i++) { 39 scanf("%d", &a[i]); 40 h[i-1] = a[i]; 41 } 42 sort(h, h+n); hcnt = unique(h, h+n) - h; 43 for(int i = 1; i <= n; i++) a[i] = getid(a[i]) + 1; 44 memset(dp, 0, sizeof(dp)); 45 for(int i = 1; i <= n; i++) { 46 int lo = min(i, m); 47 for(int j = 1; j <= lo; j++) { 48 if(j == 1) { 49 update(j, a[i], 1); 50 continue; 51 } 52 int tmp = sum(j-1, a[i]-1); 53 update(j, a[i], tmp); 54 } 55 } 56 printf("%d\n", sum(m, n)); 57 } 58 return 0; 59 }
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