用 Python 写了个代码，对 DP 有少量修改： 初值：  dp[m][m] = 1 for m in 1,10,20,30,50,100 状态：  dp[m][k] = \sum_{i <= m} dp[i][k-m] for k in 1:n if k > m 结果：  N = sum_m dp[m][n] 代码： from sys import stdin N = int(stdin.readline()) C = [1, 10, 20, 30, 50, 100] C.sort() dp = dict([(c,[0]*(N+1)) for c in C]) for k in xrange(1,N+1): for c in C: if k == c: dp[c][c] = 1 elif k > c: dp[c][k] = sum([dp[i][k-c] for i in C if i <= c]) CS = sum([dp[c][N] for c in C]) print CS