回答此问题可获得 20 贡献值,回答如果被采纳可获得 50 分。
<blockquote>
<p>Alice has <strong>N</strong> coins of amount from 0 to <strong>(N-1)</strong>. Bob wants to take <strong>k</strong> coins out of them, but Alice will only give if the set of <strong>K</strong> coins is interesting.</p>
<p>A set of coins is interesting if the sum of them is divisible by a unique integer <strong>M</strong>. Now Bob wants to know in how many ways he can get <strong>K</strong> coins.</p>
<p>Print the result by answer%(10^9+7)</p>
<p>Input format:- Three space separated integers N,K,M</p>
<p>Constraints:-</p>
<ul>
<li>1 <= N, M <= 10 ^ 3</li>
<li>1 <= K <= 10 ^ 2</li>
</ul>
<p>Sample input:- 4 2 2</p>
<p>Sample output:- 2({1,3},{2,4})</p>
</blockquote>
<p>我尝试使用python库中的组合来解决这个问题,但结果超出了<strong>内存限制。</strong>
后来我使用递归方法对其进行测试,但它也导致超出了<strong>时间限制。</strong>,因为每个私有测试用例需要10秒的时间</p>
<p>有人能帮助有效地解决这个问题吗</p>
<p>递归方法的代码:</p>
<p><a href="https://i.stack.imgur.com/Ez60t.png" rel="noreferrer"><img src="https://i.stack.imgur.com/Ez60t.png" alt="enter image description here"/></a></p>
<pre><code>cou=0
n,k,m = input().split()
out_ = solve(k,m,n)
print(out_)
def getCombinations(data,n,k,m):
val=[0]*k
combiUtil(data,n,k,0,val,0,m)
def combiUtil(data,n,k,ind,val,i,m):
global cou
if(ind==k):
if(sum(val)%m==0):
cou+=1
return
if(i>=n):
return
val[ind]=data[i]
combiUtil(data,n,k,ind+1,val,i+1,m)
combiUtil(data,n,k,ind,val,i+1,m)
def solve(k,m,n):
global cou
k=int(k)
m=int(m)
n=int(n)
ans =0
data = [j for j in range(1,n+1)]
getCombinations(data,n,k,m)
return cou%(10**9+7)
</code></pre>