problem 31 of project euler

Author: henryscala

rs/p031_coin_sum.rs

@@ -0,0 +1,72 @@
+//problem 31 of project euler 
+//coin sums 
+
+const LEN : usize = 8; 
+const COINS :[u8;LEN]=[200,100,50,20,10,5,2,1]; 
+const MAX :u8= 200; 
+
+
+fn sum(ary:&[u8])->bool{
+	let mut s:usize = 0; 
+	for i in 0..ary.len() {
+		s += ((ary[i] as usize) * (COINS[i] as usize)) as usize; 
+		if s > MAX as usize{
+			return false; 
+		}
+	}
+	if s == (MAX as usize ) {
+		true
+	} else {
+		false
+	}
+	
+}
+
+fn increase(ary:&mut [u8])->bool{
+	let mut index :usize = 0; 
+	
+	loop {
+		let max = MAX / COINS[index]; 
+		if ary[index] < max {
+			ary[index]+=1;
+			return true; //able to continue 
+		} else {
+			if index +1 >= ary.len(){
+				return false; 
+			}
+			ary[index]=0;
+			index += 1; 
+		}
+	}	
+}
+
+fn main (){
+	let mut num_coins:[u8;LEN]=[0;LEN]; 
+
+	
+	let mut total :usize = 0; 
+
+
+
+	loop {
+		let s = sum(&num_coins); 
+
+		if s  {
+			total += 1; 
+			if total % 500 == 0 {println!("total reaches={}", total)};
+		}
+		let go_on=increase(&mut num_coins);
+		if !go_on {break;}
+		
+		
+		
+	}
+	
+	println!("total={}",total);
+
+	
+
+}
+
+
+

rs/p031_coin_sum2.rs

@@ -0,0 +1,52 @@
+//problem 31 of project euler
+//coin sums
+
+const LEN : usize = 8;
+const COINS :[u8;LEN]=[200,100,50,20,10,5,2,1];
+const MAX :u8= 200;
+
+//this method return the number of ways to give the changes.
+//it is a recursive method.
+//the strategy shall be divide and counquer(divide the task of size n to sub tasks of size n-1 and 1).
+//it can be improved to use the dynamic programming strategy(store the intermediate result in a map and query it before calculation).
+//My first way of try solving this issue is a brute-force(or enumerate) way, it does not work because it takes so long time.
+fn f(index:usize,max:usize)->usize{
+ let coin_value = COINS[index] as usize;
+ if index == 0 {
+  if max / coin_value > 0 && max % coin_value == 0 {
+   return 1; //1 way
+  } else {
+   return 0; //no way
+  }
+ }
+
+ if max == 0 {
+  return 0;
+ }
+ //previous solutions + solutions only using the coins in index column
+ let mut sum:usize = f(index - 1, max);
+ if max / coin_value > 0 && max % coin_value == 0 {
+  sum += 1;
+ }
+ let mut i:usize = 1;
+ loop {
+  let scale = i*coin_value ;
+  if max > scale{
+   let next_max = max-scale ;
+   sum += f(index-1,next_max) ;
+  } else {
+   break;
+  }
+  i += 1;
+ }
+ sum
+
+}
+
+fn main (){
+ let total = f(LEN-1,MAX as usize);
+ println!("total={}",total);
+}
+
+
+