Friday, December 4, 2015

Coin change DP solution to keep track of coins


http://www.1point3acres.com/bbs/forum.php?mod=viewthread&tid=148775&extra=page%3D1%26filter%3Dsortid%26sortid%3D311%26sortid%3D311
题目是这样的,输入是一个int amount 和 vector<int> coins,分别表示总货币量、各个coin的价值量,要求以最少的coin个数凑齐总货币量。 (大家应该都熟悉吧?入门级的DP题目。。)
然后输出的是每种货币的数目,vector<int> nums。. 鍥磋鎴戜滑@1point 3 acres
举例:  amount  = 40, coins = [1,5,15,25],输出[0,1,1,1]. 鍥磋鎴戜滑@1point 3 acres
再举例: amount  = 40, coins = [1,5,20,25],输出[0,0,2,0]

关键是刚开始没怎么听清楚,问了好几遍才确认,自己也是太紧张了。然后先确认了几个细节要求:
都是整数?是的
最后是要凑齐exact的目标数值amount?是的
会有无解的情况吗?默认总会有价值为“1”的coin. Waral 鍗氬鏈夋洿澶氭枃绔�,

我刚开始想着用backtracking+贪心来做,先sort,再用最贵的coin开始凑,后来一想不对,应该bottom up用dp,转移方程就是dp = min(dp[i-1]+1, dp[i-coins[j]]+j) for all j from 1~coins.size()-1;

然后写着写着就迷糊了,忘记目标不是coin的总数而是每个coin的个数。。。事实上,我写完之后(当时是只记录dp,即总数),他说yes I think this works. 然后follow up问如果amount很大怎么办。
我想着想着发现只要keep tracking dp 里后面 coins.size() 数量的dp即可,only store the dp, dp[i-coins[1]]....., dp[i-coins[coins.size()-1]]. more info on 1point3acres.com
他说好的,很好,又问了总体的时间空间复杂度。(好了到目前为止我们两个估计都忘记了刚开始要的是各个coin的个数。。。)

然后闲聊了几句,他突然问我,噢等一下,我们要求的不是总数。。。我就突然紧张了,想了一会后,在每个dp的循环里加了个stack用来记录插入过的coin index,如果dp更新的话就把前面
的那个pop出来回滚回去,再把新的弄进来,感觉好像可以。。。

http://stackoverflow.com/questions/20185590/coin-change-dp-solution-to-keep-track-of-coins
public static int minimumNumberOfWays(int []deno, int amount){
    int dp[] = new int[amount+1];
    dp[0]=0;
    int []prevCoin = new int[amount+1];  
    for(int j=1;j<=amount;j++){
        dp[j]=Integer.MAX_VALUE;
        for(int i=0;i<deno.length;i++){
            if(deno[i]<=j && (1+dp[j-deno[i]] < dp[j]) ){               
                dp[j]=1+dp[j-deno[i]];
                prevCoin[j]=deno[i];
            }                   
        }
    }

    int result = dp[amount];
    List<Integer> coinsAdded = new ArrayList<Integer>();
    for(int i=amount;i>=1;){
        coinsAdded.add(prevCoin[i]);
        int j=i;
        i=amount-prevCoin[i];
        amount = amount - prevCoin[j];
    }
    Integer [] coins = coinsAdded.toArray(new Integer[coinsAdded.size()]);
    System.out.println( Arrays.toString(coins)); 
You don't need the first dimension of your dp. You can use an array with only one dimension - the sum of all used coins. Then you can simply store the index of your last used coin for each state of your dp. What I mean is something like:
int[] dp = new int[n];
int[] usedCoin = new int[n];

for (int i=0; i < n; ++i) {
    dp[i] = -1; // state not reached
    usedCoin[i] = -1;
}

dp[0] = 0; // initial state -- we can have sum 0 without any coins
for (int coinId = 0; coinId < m; coinId++)
    for (int sum = 0; sum + denom[coinId] < n; sum++) {
        int newSum = sum + denom[coinId];
        if (dp[newSum] == -1 || dp[newSum] > 1 + dp[sum]) {
            dp[newSum] = 1 + dp[sum];
            usedCoin[newSum] = coinId;
        }
    }
If you want to find a concrete decomposition with minimum amount of coins, you can do something like:
int sum = changeAmount;
System.out.println("The used coins are:");
while (usedCoin[sum] != -1) {
    System.out.print(denom[ usedCoin[sum] ].toString() + " ");
    sum -= denom[ usedCoin[sum] ];
}
Related: Coin change problem with limit on number of coins of each denomination

No comments:

Post a Comment

Labels

GeeksforGeeks (1105) LeetCode (878) Algorithm (811) Review (618) to-do (615) LeetCode - Review (380) Classic Algorithm (334) Classic Interview (298) Dynamic Programming (285) Google Interview (240) Tree (146) POJ (140) Difficult Algorithm (136) EPI (127) Different Solutions (119) Bit Algorithms (114) Lintcode (111) Cracking Coding Interview (110) Smart Algorithm (109) Math (103) HackerRank (88) Binary Search (77) Graph Algorithm (75) Greedy Algorithm (65) Binary Tree (63) Interview Corner (61) DFS (60) List (58) Codility (54) Algorithm Interview (53) Advanced Data Structure (52) BFS (52) ComProGuide (52) Geometry Algorithm (48) LeetCode - Extended (47) USACO (46) Data Structure (42) Mathematical Algorithm (42) ACM-ICPC (41) Stack (41) Binary Search Tree (40) Interval (39) Jobdu (39) Knapsack (39) Recursive Algorithm (38) String Algorithm (38) Trie (38) Matrix (37) Codeforces (36) Introduction to Algorithms (36) Must Known (36) Space Optimization (36) Backtracking (35) Beauty of Programming (35) Sort (35) Union-Find (34) Array (33) prismoskills (33) Segment Tree (32) Sliding Window (32) HDU (31) Google Code Jam (30) Permutation (30) Puzzles (30) Array O(N) (29) Data Structure Design (29) Company-Zenefits (28) Microsoft 100 - July (28) to-do-must (28) Random (27) GeeksQuiz (25) Logic Thinking (25) Palindrome (25) hihocoder (25) Graph (24) Company-Facebook (23) High Frequency (23) TopCoder (23) Algorithm Game (22) Company - LinkedIn (22) Hash (22) Queue (22) Binary Indexed Trees (21) DFS + Review (21) Pre-Sort (21) Brain Teaser (20) CareerCup (20) Company - Twitter (20) Merge Sort (20) Lintcode - Review (19) Post-Order Traverse (19) UVA (19) Bisection Method (18) Follow Up (18) Probabilities (18) Company-Uber (17) Priority Quieue (17) Codercareer (16) Game Theory (16) Heap (16) Shortest Path (16) String Search (16) Topological Sort (16) Tree Traversal (16) itint5 (16) Difficult (15) Iterator (15) O(N) (15) Ordered Stack (15) Number (14) Number Theory (14) Amazon Interview (13) BST (13) Basic Algorithm (13) Binary Search - Bisection (13) Codechef (13) Euclidean GCD (13) KMP (13) Long Increasing Sequence(LIS) (13) Majority (13) mitbbs (13) Combination (12) Computational Geometry (12) Modify Tree (12) Reconstruct Tree (12) Reservoir Sampling (12) 尺取法 (12) AOJ (11) DFS+Backtracking (11) Fast Power Algorithm (11) Graph DFS (11) LCA (11) LeetCode - DFS (11) Miscs (11) Princeton (11) Time Complexity (11) Tree DP (11) 挑战程序设计竞赛 (11) Coin Change (10) Company - Microsoft (10) Company-Airbnb (10) Facebook Hacker Cup (10) HackerRank Easy (10) Reverse Thinking (10) Rolling Hash (10) SPOJ (10) Theory (10) Tutorialhorizon (10) Two Pointers (10) X Sum (10) Divide and Conquer (9) Mathblog (9) Max-Min Flow (9) Prefix Sum (9) Quick Sort (9) Stack Overflow (9) Stock (9) System Design (9) Use XOR (9) Book Notes (8) Bottom-Up (8) Bucket Sort (8) DP-Space Optimization (8) Graph BFS (8) LeetCode - DP (8) LeetCode Hard (8) Longest Common Subsequence(LCS) (8) O(1) Space (8) Prime (8) Suffix Tree (8) Tech-Queries (8) 穷竭搜索 (8) Algorithm Problem List (7) Company-Amazon (7) DFS+BFS (7) Facebook Interview (7) Fibonacci Numbers (7) Game Nim (7) HackerRank Difficult (7) Hackerearth (7) Interval Tree (7) Inversion (7) Level Order Traversal (7) Linked List (7) Math-Divisible (7) Minimum Spanning Tree (7) Probability DP (7) Radix Sort (7) Simulation (7) Xpost (7) n00tc0d3r (7) 蓝桥杯 (7) Catalan Number (6) Classic Data Structure Impl (6) DFS+Cache (6) DFS+DP (6) DP - Tree (6) DP-Multiple Relation (6) Dutch Flag (6) How To (6) Interviewstreet (6) Kadane - Extended (6) Kadane’s Algorithm (6) Knapsack - MultiplePack (6) Manacher (6) One Pass (6) Programming Pearls (6) Quick Select (6) Rabin-Karp (6) Randomized Algorithms (6) Sampling (6) Schedule (6) Suffix Array (6) Threaded (6) reddit (6) AI (5) Algorithm - Brain Teaser (5) Art Of Programming-July (5) Big Data (5) Brute Force (5) Code Kata (5) Codility-lessons (5) Coding (5) Company - WMware (5) Convex Hull (5) Crazyforcode (5) DP-Include vs Exclude (5) DP-Print Solution (5) Fast Slow Pointers (5) Graph Cycle (5) Hash Strategy (5) Immutability (5) Java (5) Matrix Chain Multiplication (5) Maze (5) Microsoft Interview (5) Morris Traversal (5) Pruning (5) Quadtrees (5) Quick Partition (5) Quora (5) SPFA(Shortest Path Faster Algorithm) (5) Subarray Sum (5) Sweep Line (5) Traversal Once (5) TreeMap (5) jiuzhang (5) 单调栈 (5) 树形DP (5) 1point3acres (4) Abbreviation (4) Anagram (4) Approximate Algorithm (4) Backtracking-Include vs Exclude (4) Brute Force - Enumeration (4) Chess Game (4) Consistent Hash (4) Cycle (4) Dijkstra (4) Distributed (4) Eulerian Cycle (4) Flood fill (4) Graph-Classic (4) HackerRank AI (4) Histogram (4) Kadane Max Sum (4) Knapsack - Mixed (4) Knapsack - Unbounded (4) LeetCode - TODO (4) Left and Right Array (4) MinMax (4) Multiple Data Structures (4) N Queens (4) Nerd Paradise (4) Parallel Algorithm (4) Practical Algorithm (4) Pre-Sum (4) Probability (4) Programcreek (4) Spell Checker (4) Stock Maximize (4) Subset Sum (4) Subsets (4) Sudoku (4) Symbol Table (4) TreeSet (4) Triangle (4) Water Jug (4) Word Ladder (4) algnotes (4) fgdsb (4) to-do-2 (4) 最大化最小值 (4) A Star (3) Algorithm - How To (3) Algorithm Design (3) Anagrams (3) B Tree (3) Big Data Algorithm (3) Binary Search - Smart (3) Caterpillar Method (3) Coins (3) Company - Groupon (3) Company - Indeed (3) Cumulative Sum (3) DP-Fill by Length (3) DP-Two Variables (3) Dedup (3) Dequeue (3) Dropbox (3) Easy (3) Edit Distance (3) Expression (3) Finite Automata (3) Forward && Backward Scan (3) Github (3) GoLang (3) Graph - Bipartite (3) Include vs Exclude (3) Joseph (3) Jump Game (3) Knapsack-多重背包 (3) LeetCode - Bit (3) Linked List Merge Sort (3) LogN (3) Master Theorem (3) Min Cost Flow (3) Minesweeper (3) Missing Numbers (3) NP Hard (3) Online Algorithm (3) Pascal's Triangle (3) Pattern Match (3) Project Euler (3) Rectangle (3) Scala (3) SegmentFault (3) Sieve of Eratosthenes (3) Stack - Smart (3) State Machine (3) Stream (3) Streaming Algorithm (3) Subtree (3) Transform Tree (3) Two Pointers Window (3) Warshall Floyd (3) With Random Pointer (3) Word Search (3) bookkeeping (3) codebytes (3) Activity Selection Problem (2) Advanced Algorithm (2) AnAlgorithmADay (2) Application of Algorithm (2) Array Merge (2) BOJ (2) BT - Path Sum (2) Balanced Binary Search Tree (2) Bellman Ford (2) Binomial Coefficient (2) Bit Mask (2) Bit-Difficult (2) Bloom Filter (2) Book Coding Interview (2) Branch and Bound Method (2) Clock (2) Codesays (2) Company - Baidu (2) Complete Binary Tree (2) DFS+BFS, Flood Fill (2) DP - DFS (2) DP-3D Table (2) DP-Classical (2) DP-Output Solution (2) DP-Slide Window Gap (2) DP-i-k-j (2) DP-树形 (2) Distributed Algorithms (2) Divide and Conqure (2) Doubly Linked List (2) GoHired (2) Graham Scan (2) Graph BFS+DFS (2) Graph Coloring (2) Graph-Cut Vertices (2) Hamiltonian Cycle (2) Huffman Tree (2) In-order Traverse (2) Include or Exclude Last Element (2) Information Retrieval (2) Interview - Linkedin (2) Invariant (2) Islands (2) Knuth Shuffle (2) LeetCode - Recursive (2) Linked Interview (2) Linked List Sort (2) Longest SubArray (2) Lucene-Solr (2) MST (2) MST-Kruskal (2) Math-Remainder Queue (2) Matrix Power (2) Minimum Vertex Cover (2) Negative All Values (2) Number Each Digit (2) Numerical Method (2) Object Design (2) Order Statistic Tree (2) Palindromic (2) Parentheses (2) Parser (2) Peak (2) Programming (2) Range Minimum Query (2) Reuse Forward Backward (2) Robot (2) Rosettacode (2) Scan from right (2) Search (2) Shuffle (2) SimHash (2) Simple Algorithm (2) Skyline (2) Spatial Index (2) Strongly Connected Components (2) Summary (2) TV (2) Tile (2) Traversal From End (2) Tree Sum (2) Tree Traversal Return Multiple Values (2) Word Break (2) Word Graph (2) Word Trie (2) Yahoo Interview (2) Young Tableau (2) 剑指Offer (2) 数位DP (2) 1-X (1) 51Nod (1) Akka (1) Algorithm - New (1) Algorithm Series (1) Algorithms Part I (1) Analysis of Algorithm (1) Array-Element Index Negative (1) Array-Rearrange (1) Auxiliary Array (1) Auxiliary Array: Inc&Dec (1) BACK (1) BK-Tree (1) BZOJ (1) Basic (1) Bayes (1) Beauty of Math (1) Big Integer (1) Big Number (1) Binary (1) Binary String (1) Binary Tree Variant (1) Bipartite (1) Bit-Missing Number (1) BitMap (1) BitMap index (1) BitSet (1) Bug Free Code (1) BuildIt (1) C/C++ (1) CC Interview (1) Cache (1) Calculate Height at Same Recusrion (1) Cartesian tree (1) Check Tree Property (1) Chinese (1) Circular Buffer (1) Code Quality (1) Codesolutiony (1) Company - Alibaba (1) Company - Palantir (1) Company - WalmartLabs (1) Company-Apple (1) Company-Epic (1) Company-Salesforce (1) Company-Snapchat (1) Company-Yelp (1) Compression Algorithm (1) Concurrency (1) Convert BST to DLL (1) Convert DLL to BST (1) Custom Sort (1) Cyclic Replacement (1) DFS-Matrix (1) DP - Probability (1) DP Fill Diagonal First (1) DP-Difficult (1) DP-End with 0 or 1 (1) DP-Fill Diagonal First (1) DP-Graph (1) DP-Left and Right Array (1) DP-MaxMin (1) DP-Memoization (1) DP-Node All Possibilities (1) DP-Optimization (1) DP-Preserve Previous Value (1) DP-Print All Solution (1) Database (1) Detect Negative Cycle (1) Diagonal (1) Directed Graph (1) Do Two Things at Same Recusrion (1) Domino (1) Dr Dobb's (1) Duplicate (1) Equal probability (1) External Sort (1) FST (1) Failure Function (1) Fraction (1) Front End Pointers (1) Funny (1) Fuzzy String Search (1) Game (1) Generating Function (1) Generation (1) Genetic algorithm (1) GeoHash (1) Geometry - Orientation (1) Google APAC (1) Graph But No Graph (1) Graph Transpose (1) Graph Traversal (1) Graph-Coloring (1) Graph-Longest Path (1) Gray Code (1) HOJ (1) Hanoi (1) Hard Algorithm (1) How Hash (1) How to Test (1) Improve It (1) In Place (1) Inorder-Reverse Inorder Traverse Simultaneously (1) Interpolation search (1) Interview (1) Interview - Easy (1) Interview - Facebook (1) Isomorphic (1) JDK8 (1) K Dimensional Tree (1) Knapsack - Fractional (1) Knapsack - ZeroOnePack (1) Knight (1) Kosaraju’s algorithm (1) Kruskal (1) Kruskal MST (1) Kth Element (1) Least Common Ancestor (1) LeetCode - Binary Tree (1) LeetCode - Coding (1) LeetCode - Detail (1) LeetCode - Related (1) LeetCode Diffcult (1) Linked List Reverse (1) Linkedin (1) Linkedin Interview (1) Local MinMax (1) Logic Pattern (1) Longest Common Subsequence (1) Longest Common Substring (1) Longest Prefix Suffix(LPS) (1) Machine Learning (1) Manhattan Distance (1) Map && Reverse Map (1) Math - Induction (1) Math-Multiply (1) Math-Sum Of Digits (1) Matrix - O(N+M) (1) Matrix BFS (1) Matrix Graph (1) Matrix Search (1) Matrix+DP (1) Matrix-Rotate (1) Max Min So Far (1) Median (1) Memory-Efficient (1) MinHash (1) MinMax Heap (1) Monotone Queue (1) Monto Carlo (1) Multi-Reverse (1) Multiple DFS (1) Multiple Tasks (1) Next Successor (1) Offline Algorithm (1) PAT (1) Parent-Only Tree (1) Parenthesis (1) Partition (1) Path Finding (1) Patience Sort (1) Persistent (1) Pigeon Hole Principle (1) Power Set (1) Pratical Algorithm (1) PreProcess (1) Probabilistic Data Structure (1) Proof (1) Python (1) Queue & Stack (1) RSA (1) Ranking (1) Rddles (1) ReHash (1) Realtime (1) Recurrence Relation (1) Recursive DFS (1) Recursive to Iterative (1) Red-Black Tree (1) Region (1) Regular Expression (1) Resources (1) Reverse Inorder Traversal (1) Robin (1) Selection (1) Self Balancing BST (1) Similarity (1) Sort && Binary Search (1) String Algorithm. Symbol Table (1) String DP (1) String Distance (1) SubMatrix (1) Subsequence (1) System of Difference Constraints(差分约束系统) (1) TSP (1) Ternary Search Tree (1) Test (1) Thread (1) TimSort (1) Top-Down (1) Tournament (1) Tournament Tree (1) Transform Tree in Place (1) Tree Diameter (1) Tree Rotate (1) Trie + DFS (1) Trie and Heap (1) Trie vs Hash (1) Trie vs HashMap (1) Triplet (1) Two Data Structures (1) Two Stacks (1) USACO - Classical (1) USACO - Problems (1) UyHiP (1) Valid Tree (1) Vector (1) Wiggle Sort (1) Wikipedia (1) ZOJ (1) ZigZag (1) baozitraining (1) codevs (1) cos126 (1) javabeat (1) jum (1) namic Programming (1) sqrt(N) (1) 两次dijkstra (1) 九度 (1) 二进制枚举 (1) 夹逼法 (1) 归一化 (1) 折半枚举 (1) 枚举 (1) 状态压缩DP (1) 男人八题 (1) 英雄会 (1) 逆向思维 (1)

Popular Posts